Applied Ontology Terminology

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Sandra Lovrenčić

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Jul 28, 2016, 11:56:16 AM7/28/16
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Dear all,

the International Association for Ontology and It's Applications Education Committee previously sent you invitation to help us create a list of applied ontology courses around the world.

We would also like to create a list of terms and their definitions in this field by continuing work of former IAOA Ontology Terminology Sub-committee.
(http://ontolog.cim3.net/wiki/IaoaOntologyTerminology.html)

Their list of terms serves as initial list and is placed on the IAOA Education Wiki. (http://iaoaedu.cs.uct.ac.za/pmwiki.php?n=IAOAEdu.TermList)

If you would like to contribute with new terms and/or their definitions, please send me your proposals (if possible with references) or links to information sources that you find relevant.


Best,
Sandra

Faculty of organization and informaticsAssoc. Prof. Sandra Lovrenčić, Ph.D.
University of Zagreb, Faculty of organization and informatics
Pavlinska 2, HR-42000 Varaždin, Croatia
tel: +385 42 390 851; fax: +385 42 213 413; mob: +385 98 243 341
e-mail: sandra.l...@foi.hr
http://www.foi.unizg.hr/eng/staff/sandra.lovrencic


Patrick Cassidy

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Jul 28, 2016, 12:22:28 PM7/28/16
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Sandra,

    The foundation ontology I have been working on (“COSMO”) is on the web at http://micra.com/COSMO/COSMO.owl. 

    It is best retrieved by going to the parent folder http://micra.com/COSMO/  and downloading the OWL file.

  It has about 9000 classes and 900 relations.  This is  general ontology (“upper ontology”) intended for use as an interlingua for translating other domain ontologies.  But it has not yet been tested in a practical application.

    If there is some format other than just the ontology itself that is required, could you send me a direct pointer to the specifics?  This ontology is still in development, so I have not been trying to push it onto others at this point.

 

Pat

Patrick Cassidy

MICRA Inc.

cas...@micra.com

1-908-561-3416

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John F Sowa

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Jul 28, 2016, 2:32:28 PM7/28/16
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Sandra and Pat,

This is an important project. I also believe that that the subscribers
to Ontolog Forum are a good group of ontology experts to collaborate
on the project and evaluate the proposed definitions.

PC
> Is there is some format other than just the ontology itself that is
> required, could you send me a direct pointer to the specifics?

As the subject line of Sandra's note says, this is not a project
to develop an ontology, but a project to develop and define the
metalevel terminology used to describe ontologies.

Following is the set of terms that the IOAO subcommittee has selected:
http://ontolog.cim3.net/wiki/IaoaOntologyTerminology.html

That page has a list of 30 terms. If you click on any one of them,
you get an empty place holder. That's a good beginning, but much
more is needed.

The Ontolog Wiki has more information at the following location:
http://ontolog.cim3.net/wiki/IaoaOntologyTerminology.html

On that page, I noticed the following comment:
> Given the limited resources available to develop this list of
> terminology we will not follow John Sowa's commendable suggestion
> (below), but proceed from the 'core' terms identified during the
> 2012 IAOA Summer School.

Since my name was mentioned several times on that page, I don't know
exactly what suggestion will not be followed. In any case, I would
like to recommend the following suggestion by Christiane Fellbaum:

> "I suppose one needs as many definitions as necessary to accommodate
> everyone's concept (!) behind the terms. Giving real (not made-up)
> example sentences is always a good idea. One can sort these contexts
> into groups where each group of examples uses the word with the same
> meaning and differently from the usages in other groups."

This is a summary of the methodology used by lexicographers who define
the entries in commercial dictionaries. Lexicographers also use many
other practices that should be considered:

1. Appoint a general editor who is in charge of keeping the entire
project on schedule.

2. Have some number of associate editors, each in charge of some
subset of the terms, gathering citations and related information
for each term, and organizing the information in the wiki entry
for that term.

3. Take advantage of definitions that have been published in earlier
editions of the dictionary they're updating and related information
from various sources.

4. Solicit an open-ended number of contributors, who may send citations
and related information on any term to the associate editor in
charge of that term.

5. Also make provision for enabling contributors to suggest more terms
that should be added to the starting set.

There is much more to say, but this is a good starting point for
further discussion.

John

Peter Yim

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Jul 29, 2016, 4:02:51 AM7/29/16
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John, Sandra, et al.


1.
[JohnSows] Following is the set of terms that the IOAO subcommittee has selected:
http://ontolog.cim3.net/wiki/IaoaOntologyTerminology.html

That page has a list of 30 terms.  If you click on any one of them,
you get an empty place holder.  That's a good beginning, but much
more is needed.

  [ppy]  you probably meant to say: 
//
Following is the set of terms that the IAOA subcommittee has selected:

That page has a list of 30 terms.  If you click on any one of them,
you get an empty place holder.  That's a good beginning, but much
more is needed.
//


[JohnSowa] The Ontolog Wiki has more information at the following location:
http://ontolog.cim3.net/wiki/IaoaOntologyTerminology.html

  [ppy] some of the pages aren't resolving properly, due mainly to links being broken when migrating data from the earlier wiki (dynamic) to the archive-pages (static). ... If you come across a link that does not resolve properly, try to tweak the links which are patterned like:


to:


You should be able to find the few pages on this set (that were previously populated) under: 
(just scroll down till you see "IaoaOntologyTerminology"
 

2. Additionally, I have recently reviewed and updated the following pages:


... so the links on them should resolve properly. Please use them to augment your navigation through the historic archives of the original OntologWiki content (from 2002 through end 2014) at: http://ontolog.cim3.net/wiki/ 


Best regards. =ppy
--

 

On Thu, Jul 28, 2016 at 11:32 AM, John F Sowa <so...@bestweb.net> wrote:
Sandra and Pat,

This is an important project.  I also believe that that the subscribers
to Ontolog Forum are a good group of ontology experts to collaborate
on the project and evaluate the proposed definitions.

PC
Is there is some format other than just the ontology itself that is
required, could you send me a direct pointer to the specifics?

As the subject line of Sandra's note says, this is not a project
to develop an ontology, but a project to develop and define the
metalevel terminology used to describe ontologies.

Following is the set of terms that the IOAO subcommittee has selected:
http://ontolog.cim3.net/wiki/IaoaOntologyTerminology.html

That page has a list of 30 terms.  If you click on any one of them,
you get an empty place holder.  That's a good beginning, but much
more is needed.

The Ontolog Wiki has more information at the following location:
http://ontolog.cim3.net/wiki/IaoaOntologyTerminology.html

On that page, I noticed the following comment:
Given the limited resources available to develop this list of
terminology we will not follow John Sowa's commendable suggestion
(below), but proceed from the 'core' terms identified during the
2012 IAOA Summer School.

Since ...[snip]...


John F Sowa

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Jul 29, 2016, 9:29:22 AM7/29/16
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Peter,

Thanks for the update:

> [John Sowa] Following is the set of terms that the IOAO subcommittee has
> selected: http://ontolog.cim3.net/wiki/IaoaOntologyTerminology.html
> ...
>[ppy] you probably meant to say:
>
> Following is the set of terms that the IAOA subcommittee has selected:
> http://iaoaedu.cs.uct.ac.za/pmwiki.php?n=IAOAEdu.TermList "

Some of the entries on this list have more info, but it's still
"a good beginning, but more is needed."

In any case, that page is located on the IAOA Education web site.
That would be a good place to post the results of an Ontolog project,
but the project itself should use the Ontolog wiki:

1. The IAOA web site may be read by anyone, but updates are limited
to IAOA members, who would have to pay a membership fee.

2. The Ontolog wiki does not require subscribers to pay any fees.

3. We have talked about collaborations that would use Ontolog wiki,
but very little has happened. A project for developing the
terminology would be good exercise for getting started.

4. If the terminology project gets people to collaborate on something
useful, it may be a good basis for further developments.

John

Sandra Lovrenčić

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Jul 30, 2016, 1:55:37 PM7/30/16
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John, Todd et al.,

thank you for interest, clarifications and suggestions. We will discuss everything at next meetings in August and September and we are hopeful that this work will be successful.

If someone wants to join us, please contact Maria Keet at mk...@cs.uct.ac.za.

I am looking forward to further discussions on this topic.

Best,

Sandra


Faculty of organization and informaticsAssoc. Prof. Sandra Lovrenčić, Ph.D.
University of Zagreb, Faculty of organization and informatics
Pavlinska 2, HR-42000 Varaždin, Croatia
tel: +385 42 390 851; fax: +385 42 213 413; mob: +385 98 243 341
e-mail: sandra.l...@foi.hr
http://www.foi.unizg.hr/eng/staff/sandra.lovrencic


Gary Berg-Cross

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Jul 31, 2016, 12:34:55 PM7/31/16
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It is nice to know about this effort and I look forward to some work on this.

I took a quick look at the  diagram (created to provide a simple view of the areas addressed (during the lectures) and their (perceived) relations).  I wondered about the very liberal employment of the "use" relation between many of the items and whether some distinctions might be made here such as UsedforX. So the use of a r\Representation language for a formal ontology is very different  that the use of reasoning by an application.

Also it seems to me that the upper box labeled Conceptual models/metamodels/upper ontology would also have a "use" relation (usedForRepresentation) to representation language.

Gary Berg-Cross, Ph.D.  
Member, Ontolog Board of Trustees
Independent Consultant
Potomac, MD

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Todd Schneider

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Jul 31, 2016, 2:31:30 PM7/31/16
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Gary,

I put that diagram together rather quickly during the 2014 IAOA
Summer School with input from some other participants. And yes,
the term 'use' was used in a (some what intentionally) vague fashion
due to the multiplicity of possible interpretations of 'use' (i.e., the
context dependence).

The overall intent was to highlight the interdisciplinary nature of
(the current notion of) applied ontology.

Todd

Alan Rector

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Aug 4, 2016, 6:39:53 AM8/4/16
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Gary, All

(I'm having trouble posting to the group from my usual email address since it changed.  I'm trying this while it is sorted out.)

Gary


Alan,

Thanks for kicking off some discussion of ontology "definition" with some apt issues.

One thing that I wonder about in your discussion is that you seem to talk about ontologies as a special kind of knowledge representation.  I tend to think of universals and generalizations, (empirically arrived at?) as you call them, as forms of knowledge (something understood epistemologically) which can be expressed as a knowledge representation (using a KR language).

Is that a useful distinction?


What I was trying to point out was that there are two portions of any knowledge representation

1) "universals" - roughly things that are true by definition or in all possible "worlds"/models and which are therefore do not admit of exceptions.  In my field, "pneumonia" is a disease of the lung.  It makes no sense to talk of "pneumonia of the foot".  It is "contradiction in terms".  I take these entities and the necessary relations between them (or more accurately between all individuals of the classes represented) as being the "Ontology proper" or "Ontology (narrow sense)" and close to what I think the Smith-Ceusters definition on the web is intended to convey.

*   



Alan Rector

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Aug 4, 2016, 7:54:44 AM8/4/16
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Gary, All

(I'm having trouble posting to the group from my usual email address since it changed.  I'm trying this while it is sorted out.)

Gary


Alan,

Thanks for kicking off some discussion of ontology "definition" with some apt issues.

One thing that I wonder about in your discussion is that you seem to talk about ontologies as a special kind of knowledge representation.  I tend to think of universals and generalizations, (empirically arrived at?) as you call them, as forms of knowledge (something understood epistemologically) which can be expressed as a knowledge representation (using a KR language).

Is that a useful distinction?

That's close to what I'm trying to say.  My main point is that if we are to have a terminology for talking about ontologies, we need a broader terminology for knowledge representation sufficient to allow us to say what part of knowleldge representation should be included in ontologies and what should be excluded. (unless, of course,  we intend "ontology" to include all of "knowledge representation",).  Correspondingly, we need an agreed terminology for discussing the different families of formalisms available and their relation to different aspects of knowledge representation.

 My understanding is that there are (at least) two kinds of knowledge and correspondingly two parts to most knowledge representations, and that much confusion in the field stems from confusion about the distinctions and the relationships between them.

1)    Universal knowledge - those entities and the relations between them - roughly those things that are true by definition or at least necessarily true in all possible models/"worlds" that fit with our the representation of our fundamental understanding.  (There are a variety of more technical philosophical terms and controversies, but leave that for now.).  From my own field, "Pneumonia"'s definition makes it a disease of the lung.  It makes no sense to speak of a "pneumonia of the foot".  Such an expression is a "contradiction in terms".   Likewise, "Dogs are mammals".  If we found a species of supposed dog that was not a mammal, we would say it was not a dog, however "dog-like".     I take to be the representation of this knowledge that we mean by an "ontology proper", or as I sometimes put it to avoid arguments over "proper", "ontology (narrow sense)".  I think this fits closely with the intent of the SmithCeusters definition currently on the web site.

2)    Generalisations - (aka "contingent knowledge", aka...) Knowledge that is generally true in one world but to which there may be exceptions even in that one world - i.e. is defeasible.  The classic example is "typical birds fly".  We have no problem with the notion of "flightless bird", but flightless birds are something of an anomaly.  A large proportion of the knowledge in textbooks and that we need to function in the world is of this form.  (We can break it down further, into various means of dealing with uncertainty and defeasibility, but leave that for now.).  They draw on the universal knowledge, but are not universal themselves.  I take "generalisations" in this sense to be explicitly excluded from an "ontology (narrow sense)" because they are not "universal".

One important way in which this distinctions are significant for our representations and applications is that we have two general families of computational formalisms. 

1)  Open-world, axiom/logic/theorem proving based formalisms such as FoL, DLs, OWL-DL, CGs etc. which fit very well with the ontology, as described above (although not all such formalisms are powerful enough to express everything we might want to say in any given ontology).  Most of these methods depend on proofs that involve demonstrating that it is impossible to build a consistent model (world) in which a proposed statement is false.  To prove a statement false, it is necessary to prove that it would cause a contradiction if added to the knowledge base.  In these representations are sufficient to allow us to deduce information about individuals - e.g. John has a mother - even if there is no representation of John's mother.  Since there can be no exceptions, it is safe to make the inference.  (Put another way, these formalisms support existential quantifiers)

2) Closed world  logic-programming and database languages which are much easier to use for generalisations.  Proof is that a given proposition is true in the specific (closed) model represented (or that its contrary is false) under the assumption that any entity or proposition not represented is false - negation is equivalent to failure to prove truth (rather than to proof of falsehood).  If it can't be proved true of the model at hand, then it is false (negation as failure) .  In these representations, the only way to say that "John has a mother" is to exhibit at least a dummy representation (Skolem constant) for John's mother .  (These formalisms do not support existential quantifiers) These representations include most frame representations, database representations, etc.  These are easier to use for representing generalisations, but less powerful when trying to represent universals but often more powerful, and arguably more faithful, when trying to represent generalisatons.  (In practice, in most there representations, there is no way of distinguishing generalisatons from universals.) 

The correspondence above is not perfect.  There are ways of using each type of representation to represent each kinds of knowledge, at least up to a point. What I am arguing is that we need  an agreed terminology for talking about both the knowledge represented and the formalisms used to represent it which makes at least these distinctions.

At one level, the above is elementary.  I apologise if any of my colleagues are insulted by the discussion - or wish to correct it.  However, my experience is that these issues are not well understood in the broader community, indeed that there is not even a widely agreed terminology to allow them to be discussed.   If we are trying to build an outward looking resource, such a terminology is needed.

Regards

Alan

------------------
Alan Rector
Professor of Medical Informatics (emeritus)
School of Computer Science
University of Manchester
Manchester M13 9PL, UK
www.cs.man.ac.uk/~rector

Please note new email address:
alan....@manchester.ac.uk


 



Gary Berg-Cross, Ph.D. 
gberg...@gmail.com    
​​​http://ontolog.cim3.net/cgi-bin/wiki.pl?GaryBergCross
Member, Ontolog Board of Trustees
Independent Consultant
Potomac, MD
240-426-0770

On Tue, Aug 2, 2016 at 9:43 AM, Alan Rector <Alan....@manchester.ac.uk> wrote:
All

I’ve been quiet and disengaged for some time for various reasons. 

I think this is an important effort, and important way to present ontology to the outside world and establish its appropriate role with respect to other formalisms and approaches in applications.  For that we need to be clear about what an “ontology” is and is not.

A few quick thoughts...

There is widespread confusion amongst the various sorts of artefacts that are sometimes called “ontologies” by various authors - which range from formal logical representations to data base models to frame systems to general logical theories.  I presume that the intention is that ontologies be confined to representations of universal entities and their necessary characteristics , what I sometimes term “ontology (narrow sense)” in the spirit of the definition given.   I am not convinced that the combination of the definitions for “ontology” and “universal” as given will be sufficient for those not already familiar with the terms.

More importantly and in a bit more detail,,,

It seems to me we need to clarify and distinguish:

1)    Ontologies and more general forms of knowledge representation.  All too frequently “ontology” is used almost as a synonym for knowledge representation, in which case the usefulness of the label for the part and/or kind of knowledge representation concerning universals is lost.  This is the heart of my concern about improving  I think the definition of "Ontology” needs clarifying.

2)     An agreed pair of terms for representations that are intended to be a) universal - either by definition or otherwise - and therefore indefeasible vs b) statements of what is generally true but defeasible - for which I would propose the label “Generalizations”.

3)      We need to be a able to say clearly what is, and is not, included in an “ontology” in our intended sense.  I would expect an “ontology”, in our sense, to include only universal statements and to exclude defeasible “Generalisations”. (Otherwise, how do we distinguish “ontology” from “knowledge representation” more generally?  For a given knowledge base, how do we say what is “ontology” and what is not?)

3)     Between the abstract “ontology” and its representation/implementation in any particular formalism.  Without that, how can we discuss questions such as the appropriate formalism for representing a particular ontology?  Or alternatively, a statement of what it means for two artefacts to be equivalent even though they may be represented in different formalisms.

4)     Between the different families of computational logic formalisms / inference mechanisms.  In particular we need to differentiate - and we need a better terminology for - a)  theorem proving axiom-based formalisms such as FoL, OWL-DL, DLs, CGs, etc. based on model theoretic semantics and the open-world assumption and b) database and logic programming formalisms using closed world reasoning mechanisms amongst a given set of symbols in a given model. 

Closely related,  would also be useful to have a better general term for the class of semantics of logic-programming and other closed world systems that provide proofs in a specific model/world to contrast them with model-theoretic semantics which provide proofs as to what is possible, or more precisely impossible, in any model/world.   (I know of names for specific methods - e.g. linear resolution - but can find no term for the general class of methods.  Perhaps it’s just my ignorance)

These may not be “core terms”, but they are central to many of the misunderstandings around “ontologies”.

5)  Query languages against a representation vs the representation itself - e.g. SPARQL queries vs OWL class definitions.  To be able to explain why “not classified under MyClass in this ontology” - something that can only be determined by a query against this representation - and the class of all things in the class "NOT MyClass".

Regards

Alan
------------------
Alan Rector
Professor of Medical Informatics (emeritus)
School of Computer Science
University of Manchester
Manchester M13 9PL, UK
www.cs.man.ac.uk/~rector

Please note new email address:
alan....@manchester.ac.uk





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Alan Rector

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Aug 7, 2016, 10:45:11 AM8/7/16
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Leo, All

My main point was about the terminology to have a discussion rather than the discussion itself.  My goal is to contribute towards a terminology relevant to discussing the applications we envisage for Applied Ontology. 

On the substance…

I never suggested that Skolemization was relevant _only_ to closed world formalisms, but rather that in most closed world formalisms the only way of representing existential quantification is Skolemization.   In most open world representations, existential quantification without Skolemization is supported, at least in some contexts - for example in DLs within the context of a restriction - Skolemization may still have a role in others.

I certainly also accept that Answer Set Programming provides some measure of both open and closed world programming, and that indeed there is a whole research field working on various combinations including also DL-safe rules, etc.  However, the issues are still far from clear to many people and far from being accepted in standards.

On  developing a terminology for discussing these issues…

I take it we are trying to provide an outward facing terminology to discuss these, and many other issues with those who are not already familiar with ontologies - and also to improve our own discussions.  For that purpose I would argue that it is important to identify the two poles of open and closed world programming so that we can discuss mechanisms for combining them and the most appropriate mechanisms for particular applications.

I Ontologies and Knowledge

I think it important to be clear about what we mean by an “ontology” and what sort of knowledge it is meant to include - and therefore what ontological representations should represent.  The Smith-Ceusters definition on the Wiki confines ontologies to “Universals” - although the definition of “universals” isn’t necessarily helpful without more background on their specific usage. Other writers use “ontology” more broadly, sometimes so broadly as to to seem a synonym for “knowledge representation” - at which point the term becomes little more than an advertising slogan - a more modern word for what we used to call “knowledge representation”. Other authors fall between those two extremes.  (The early Gruber definition of “a conceptualisation of a domain” is still widely quoted, but unhelpful in this regard.  At the time it really meant the “static knowledge base” as opposed to the “rule base” and “dynamic knowledge base” as seen in the architectures of the time. Likewise, getting into arguments about “analytic”, “synthetic” and (possibly) synthetic-analytic truths seems likely to take us off track.) 

To say what an “ontology” is and what knowledge it represents, we need to clarify the terminology to describe the kinds  knowledge and, separately, the kinds of knowledge representation plus a terminology to discuss the relationships between the two. 

For kinds of knowledge, I am suggesting as a staring point for one distinction “Universal truths” and “Generalisations”.  (Understanding of course that “universal” is within a given domain of discourse or set of model.).   These terms have seemed to be easier to explain then the alternatives I’ve tried and carry less baggage, but I would invite other candidate terms for the group to consider as long as one of the goals is being to be able to discuss clearly what knowledge should, and should not be, represented in an “ontology” and how then the “ontology” fits into a broader scheme of knowledge and “knowledge representation”.  (I would prefer not to get into philosophical arguments about “analytic”, “synthetic” and (possibly) “synthetic-analytic” truths which would seem likely to take us off track)

II Representations

I’d also be pleased to see concise terms to describe the difference between formalisms based on model-theoretic and similar proof methods (e.g tableau calculus) - mostly open world - and those based on symbolic proof methods such a linear resolution - mostly closed world.  And a terminology to discuss their appropriateness for different kinds of knowledge.  (Plus a terminology to discuss the relation to database queries and database schema with which many more people are familiar.)  If there are other distinctions and dimensions for which we need terminology, please suggest them.

Regards

Alan

Topic for another post…  there is also the whole question of meta- and higher-order- knowledge and its representation, but I take that to be an orthogonal dimension to the above.




-------------------

Alan Rector
Professor of Medical Informatics (emeritus)
School of Computer Science
University of Manchester
Manchester M13 9PL, UK
www.cs.man.ac.uk/~rector

Please note new email address:
alan....@manchester.ac.uk

(sent via gmail)

On 5 August 2016 at 19:28, Obrst, Leo J. <lob...@mitre.org> wrote:

Alan,

 

Skolemization can occur under both Open World Assumption (consider blank nodes in OWL/RDF; also first-order theorem provers) or Closed World Assumption. And there are some logic programming languages (e.g., Answer Set Programming) which have both finite-failure negation and strong (logical) negation (under stable model semantics, e.g.) and increased support for existentials in the rule body.

 

In the past, when we tried to use both OWL/RDF (+ SWRL) and Prolog more directly, we translated the former into the latter by providing an interpreter/compiler that supported at least a reasonable fragment of OWL ([4-5]; back in 2004+ when we did this work, there were few such efforts; now there are many more) in the research area often called “description logic programming”. The  latter now comes in various flavors, often a hybrid DL+LP form, but sometimes more directly (example: [1-3])).

 

In our mentioned work, we used a kind of “constructive negation”, since we worked in Prolog then, not ASP.

 

Thanks,

Leo

 

[1] Knorr, Matthias, José Júlio Alferes, and Pascal Hitzler. "Local closed world reasoning with description logics under the well-founded semantics." Artificial Intelligence 175.9 (2011): 1528-1554.

[2] Lutz, Carsten, Inanç Seylan, and Frank Wolter. (2012). "Mixing open and closed world assumption in ontology-based data access: Non-uniform data complexity." Description Logics 846 (2012): 268-278.

[3] Motik, B., & Rosati, R. (2010). Reconciling description logics and rules. Journal of the ACM (JACM), 57(5), 30. http://dl.acm.org/ft_gateway.cfm?id=1754403&ftid=812997&dwn=1&CFID=810831107&CFTOKEN=18986656.

[4] Samuel, Ken; Leo Obrst. 2007. Answer Set Programming: Final Report on a Comparison Between ASP and Prolog for Semantic Web Ontology and Rule Reasoning. October, 2007. MITRE Technical Report MTR090069.

[5] Samuel, Ken; Leo Obrst; Suzette Stoutenberg; Karen Fox; Paul Franklin; Adrian Johnson; Ken Laskey; Deborah Nichols; Steve Lopez; and Jason Peterson. 2008. Applying Prolog to Semantic Web Ontologies & Rules: Moving Toward Description Logic Programs. The Journal of the Theory and Practice of Logic Programming (TPLP), Massimo Marchiori, ed., Cambridge University Press, Volume 8, Issue 03, May 2008, pp. 301-322.

 

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Barry Smith

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Aug 7, 2016, 11:25:03 AM8/7/16
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 Alan

​Re:
I Ontologies and Knowledge

I think it important to be clear about what we mean by an “ontology” and what sort of knowledge it is meant to include - and therefore what ontological representations should represent.  The Smith-Ceusters definition on the Wiki confines ontologies to “Universals” - although the definition of “universals” isn’t necessarily helpful without more background on their specific usage. Other writers use “ontology” more broadly, sometimes so broadly as to to seem a synonym for “knowledge representation” - at which point the term becomes little more than an advertising slogan - a more modern word for what we used to call “knowledge representation”. 

​The Smith-Ceusters definition distinguishes ontology-in-the-narrow sense -- which is a representation of universals and of the relations between them, where universals are the sorts of things represented by the proper nouns used to formulate scientific theories (nouns like 'cell', 'patient', 'oophorectomy'
)
In the wide sense ontologies can include also representations of what we called defined classes (for instance ​
 
​'patient in clinical trial #12345', 'human being who has bathed in the river Ganges'). 
Details are provided in the Building Ontologies with BFO book:
http://mitpress.mit.edu/building-ontologies​
BS

Matthew West

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Aug 7, 2016, 5:13:22 PM8/7/16
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Dear Barry,
I would also expect Ontologies in the wide sense to include distinguished particulars. For example, you might wish to capture the NHS NICE rules for funding treatments, or in another context be able to distinguish between US law and UK law.
No problem with narrower kinds of ontology though such as you define.
It would be good to have agreed qualifiers for these different types to avoid pointless arguments.
Regards
Matthew West


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Ronald Fuller

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Aug 8, 2016, 12:52:30 AM8/8/16
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Dear All,

I introduced the following term at an ASL session in January, which I think has relevance to applied ontology:

Sophotaxis (Greek wisdom + order) combines the notion of entailment with that of intent.  If a logical vocabulary can be used to express an intended set of statements and their antecedents then it is sophotaxically complete.  If it cannot, then it is sophotaxically deranged or incomplete.

I discuss it in more detail at http://oninfo.info.  I'd appreciate any comments or critique, especially any reference to an existing term or concept that would show this to be redundant or unnecessary.

Regards,
Ron
From: alan....@gmail.com
Date: Sun, 7 Aug 2016 15:45:06 +0100

Subject: Re: [ontolog-forum] Applied Ontology Terminology
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joseph simpson

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Aug 8, 2016, 1:09:59 AM8/8/16
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Ron:

The ASL session link appears to be broken..

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--
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“Reasonable people adapt themselves to the world. 

Unreasonable people attempt to adapt the world to themselves. 

All progress, therefore, depends on unreasonable people.”

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Ronald Fuller

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Aug 8, 2016, 1:23:28 AM8/8/16
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Here's a good link to the session abstract:  http://bit.ly/2aEn54y
my apologies.
Ron
From: rgfu...@hotmail.com
To: ontolo...@googlegroups.com; lob...@mitre.org
Subject: RE: [ontolog-forum] Applied Ontology Terminology
Date: Sun, 7 Aug 2016 21:52:26 -0700

John F Sowa

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Aug 9, 2016, 10:41:33 AM8/9/16
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Alan, Barry, Matthew, and Ron,

Alan
> I think it important to be clear about what we mean by an “ontology”
> and what sort of knowledge it is meant to include - and therefore
> what ontological representations should represent.

That issue is critical for Ontolog Forum, but I doubt that any two
subscribers have identical opinions about it.

Barry
> ​The Smith-Ceusters definition distinguishes ontology-in-the-narrow
> sense -- which is a representation of universals and of the relations
> between them...
> In the wide sense ontologies can include also representations of what
> we called defined classes (for instance ​'patient in clinical trial
> #12345', 'human being who has bathed in the river Ganges').
> Details are provided in the Building Ontologies with BFO book.

Yes. But even the wide sense is insufficient for interpreting the
already overwhelming and rapidly growing amount of natural language data
on the WWW. For an overview of the issues, see
http://www.jfsowa.com/talks/nlu.pdf

Matthew
> I would also expect Ontologies in the wide sense to include
> distinguished particulars.

Certainly. The earth, sun, and moon are particulars that occur
in the definitions of day, night, year, geography, geology, etc.
Once you admit them, it's hard to find any natural stopping point.

Matthew
> It would be good to have agreed qualifiers for these different
> types to avoid pointless arguments.

This raises questions about who should make decisions about such
issues: (a) Professionals in the subject matter, who have standard
terminology and conventions for their field, or (b) ontologists who
are professionals in the form, but amateurs in the content.

Ron F.
> I introduced the following term...
> Sophotaxis (Greek wisdom + order) combines the notion of
> entailment with that of intent...

I sympathize with the goal, but I doubt that many people will adopt
the term 'sophotaxis'. The words 'intent' and 'intentionality' are
critical. If you include intentionality in the ontology, logic will
give you entailment.

Ron (from the abstract cited)
> This concept has important application in the field of enterprise
> information management. Organizations are frequently unable to
> produce desired outputs even when their systems are known to
> contain all necessary inputs...

I agree. But I suggest the word 'intentionality' as a term that
is already recognized as essential to ontology. Husserl treated it
at length in his book _Logical Investigations_, which is considered
a classic in formal ontology. But analytic philosophers usually
ignored intentionality. One stumbling block is Brentano's Thesis:
"all and only mental phenomena are _intrinsically_ intentional."

The following article by R. Macintyre & D. W. Smith discusses
the controversies: http://consc.net/neh/papers/smith2.pdf

C. S. Peirce clarified these issues with his theory of semiotic.
Instead of 'mental', he used the phrase "mind or quasi-mind".
His definition of quasi-mind is so broad that it includes all
living things from bacteria to humans and perhaps beyond. For
a brief overview of Peirce's semiotic and its importance for
formal ontology, see http://www.jfsowa.com/pubs/signs.pdf

For a longer discussion of related issues, see
http://www.jfsowa.com/pubs/worlds.pdf

John

Barry Smith

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Aug 9, 2016, 10:58:33 AM8/9/16
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Matthew
I think the idea of creating an ontology for US Law and another ontology for UK Law is fully compatible with my proposed delineation of the use of the term 'ontology'. (I would assume that both of these ontologies would be improved by being founded on the reuse of terms representing legal universals such as promise and contract.)
BS


On Sun, Aug 7, 2016 at 5:13 PM, Matthew West <dr.matt...@gmail.com> wrote:

Dear Barry,
I would also expect Ontologies in the wide sense to include distinguished particulars. For example, you might wish to capture the NHS NICE rules for funding treatments, or in another context be able to distinguish between US law and UK law.
No problem with narrower kinds of ontology though such as you define.

It would be good to have agreed qualifiers for these different types to avoid pointless arguments.

Regards
Matthew West


On Sun, 7 Aug 2016, 16:25 Barry Smith, <phis...@buffalo.edu> wrote:
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Chris Partridge

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Aug 9, 2016, 11:18:58 AM8/9/16
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Barry,

I think the issue would be that without having UK or US in the ontology, one could not say that these were UK (or US) laws. With attendant problems when trying to merge the ontologies.

I had a very similar practical problem with bank reporting; where Bank of England and Federal Reserve reporting needed to be distinguished.

More generally, the universal-particular divide does not seem to track the division one wants (it also does not track well the similar difference between data application model and operational data needed in systems development).

Chris

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Alan Rector

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Aug 9, 2016, 11:48:04 AM8/9/16
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Matthew, All

I agree that we need a notion such as  "distinguished particular" if by that you mean a particular that participates in some necessary/universal truth for purposes of the field of discourse, e.g. political entities for an ontology about the law.   However, we need an agreed name and definition.

I would argue that the principled distinction is between the "truths"/"axioms"/"statements" rather than the entities, although most entities in most ontologies will be universals, but then so will many entities that are the subject of generalisations.

Therefore, I would argue we also need is a clearer distinction between "Universals" and "Universal truths" - i.e. statements meant to be true in all possible worlds without our field of discourse.  I actually prefer "necessary truths", which fits with the modal logic usage, or perhaps the older philosophical term "essential truths", although that has lots of baggage.

I think the distinction we need to be making is between universal/necessary/esssential truths and generalisations. 

That distinction can be mapped roughly, but not dogmatically, onto the distinction between open and closed world reasoning, and is a useful guide to a number of questions about architecture

Regards

Alan


Ronald Fuller

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Aug 9, 2016, 12:54:51 PM8/9/16
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Thanks John,  I don't think anyone would use the term unless they thought it would help them communicate more easily.  I don't want to use it either if I can find an alternative, and I'll look through your references to see.   'Intentionality' alone leaves a lot more to be explained.  I use 'sophotaxis' sometimes to explain to business practitioners that (and why) some information management tasks require more subject matter expertise than others to perform effectively (this is by no means self evident),  and also to support my recommendation that business schools should include an introductory course in logic (see here and here).  The coauthor of the sophotaxis abstract is the past president of the Association for Business Communication, and I think he may be close to endorsing that recommendation.  Neither of us are determined that others should adopt the term, we offer it only for the sake of convenience and clarity.

Regards,
Ron

ps- the Smith2.pdf link is broken.  Your Worlds paper is excellent, thank you for sharing it.


> From: so...@bestweb.net
> Subject: Re: [ontolog-forum] Applied Ontology Terminology
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Barry Smith

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Aug 9, 2016, 1:06:59 PM8/9/16
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So in order to have the Gene Ontology (which represents attributes of gene products on planet earth), we would need to have the term 'Planet Earth' included in the Gene Ontology? 
Even if we discovered gene products on another planet, so that we had sub-ontologies GO-Earth and GO-Mars, we could for example add corresponding subclasses of each attribute, thus for example:

GO: 0007617 mating behavior
GO:0060180 female mating behavior
GO:01777777 Martian female mating bevahior
GO:01777778 Earthly female mating behavior

and so on.
​ ​

BS

On Tue, Aug 9, 2016 at 11:18 AM, Chris Partridge <partri...@gmail.com> wrote:
Barry,

I think the issue would be that without having UK or US in the ontology, one could not say that these were UK (or US) laws. With attendant problems when trying to merge the ontologies.

I had a very similar practical problem with bank reporting; where Bank of England and Federal Reserve reporting needed to be distinguished.

More generally, the universal-particular divide does not seem to track the division one wants (it also does not track well the similar difference between data application model and operational data needed in systems development).

Chris
On 9 August 2016 at 15:57, Barry Smith <phis...@buffalo.edu> wrote:

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Matthew West

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Aug 9, 2016, 1:59:39 PM8/9/16
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Dear Barry,
Even if you kept the ontogeny for US law and UK law separate. I would still expect the Supreme Court to be mentioned in the US one.
Regards
Matthew West


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Matthew West

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Aug 9, 2016, 2:02:34 PM8/9/16
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That you might need particulars in some Ontologies does not imply that you must have particulars in all Ontologies.
Regards
Matthew West

Barry Smith

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Aug 9, 2016, 4:05:02 PM8/9/16
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Perhaps it would be mentioned in a definition, for instance.
BS

On Tue, Aug 9, 2016 at 1:59 PM, Matthew West <dr.matt...@gmail.com> wrote:

Dear Barry,


Even if you kept the ontogeny for US law and UK law separate. I would still expect the Supreme Court to be mentioned in the US one.
Regards
Matthew West

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John F Sowa

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Aug 9, 2016, 4:43:58 PM8/9/16
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On 8/7/2016 11:24 AM, Barry Smith wrote:
> The Smith-Ceusters definition on the Wiki confines ontologies to
> “Universals”

Such a restriction is anathema in science. It's important to define
individual terms precisely. But no definition of an entire field should
be so narrow that it rules out current practices and future innovations.

As a clear, general, and flexible definition, I suggest:

"A knowledge base has three components: a logic for specifying the
form of what can be expressed, an ontology for specifying the subject
domain, and a database for collecting information about individuals
that exist or may exist within the specified domain."

This definition covers most, if not all current ontologies, DBs, and
KBs. It imposes no restrictions on the choice of logic, the choice
of definitions and axioms in the ontology, the contents of the DB,
or the choice of philosophical jargon for talking about ontology.

John

Matthew West

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Aug 9, 2016, 4:53:56 PM8/9/16
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Each decision of a lower court may be appealed to a higher court.
There is no court higher than the Supreme Court.
Regards
Matthew West


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Barry Smith

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Aug 9, 2016, 5:20:58 PM8/9/16
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John
We are not defining 'knowledge base'
The definition of 'ontology' that is at issue is the one expounded upon in the https://mitpress.mit.edu/building-ontologies book. I will of course be happy to amend it to accommodate future innovations, in true scientific spirit, when you tell me what they are. 
BS

On Tue, Aug 9, 2016 at 4:43 PM, John F Sowa <so...@bestweb.net> wrote:
On 8/7/2016 11:24 AM, Barry Smith wrote:
> The Smith-Ceusters definition on the Wiki confines ontologies to
> “Universals”

Such a restriction is anathema in science.  It's important to define
individual terms precisely.  But no definition of an entire field should
be so narrow that it rules out current practices and future innovations.

As a clear, general, and flexible definition, I suggest:

"A knowledge base has three components:  a logic for specifying the
form of what can be expressed, an ontology for specifying the subject
domain, and a database for collecting information about individuals
that exist or may exist within the specified domain."

This definition covers most, if not all current ontologies, DBs, and
KBs.  It imposes no restrictions on the choice of logic, the choice
of definitions and axioms in the ontology, the contents of the DB,
or the choice of philosophical jargon for talking about ontology.

John

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rrov...@buffalo.edu

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Aug 9, 2016, 9:31:47 PM8/9/16
to ontolog-forum
Dr.Sowa can correct me if I'm mistaken, but I believe the suggestion might be to define 'ontology' in a similar manner as that of 'knowledge base', where the definition does not impose restrictions. He is also correct that the definition should not be narrow and rule out such things. The fact that universals (the problem of universals) are one of the foundational and unsolved problems/questions/topics in philosophy makes a definition of 'ontology' confined to or in terms of universals problematic. Not least because when asked what universals actually are, developers cannot answer that question, and neither can many philosophers...and the fact is, it probably does not need to be answered, and a definition of 'ontology' without appeal to them is at least conceivable. And as Dr. Rector mentioned: 'the definition of “universals” isn’t necessarily helpful without more background'.

I do not believe Dr.Sowa or anyone can say precisely what the future innovations are, and I think such sarcastic comments might not be helpful.

Finally, Looking at the thread, I do not believe the issue was or has been with the definition of 'ontology' in that book. Dr.Rector simply mentioned it as one definition among others. There are other ontologies, are other viewpoints. That particular definition should not be the focus. The point is to form a definition.

John F Sowa

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Aug 10, 2016, 10:38:47 AM8/10/16
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On 8/9/2016 5:17 PM, Barry Smith wrote:
> We are not defining 'knowledge base'

I agree. Pure ontology is the study of existence without regard
to any applications. But applied ontologies are used in large
computational systems. In addition to a formal ontology, they
require at least two other components: (1) a reasoning engine that
processes the logic, and (2) a system that manages data about the
individuals in the domain of interest.

> I will of course be happy to amend it to accommodate future
> innovations, in true scientific spirit, when you tell me what
> they are.

I can't predict future innovations, but I can generalize my previous
definition (copy below) and restate it in genus-differentiae format:

Definition: A _formal ontology_ is a theory T stated in a logic L
that is designed to specify the functions and predicates that
describe the kinds of individuals in some domain D and their
possible relationships and interactions with each other.

Comments:

1. The theory T is a collection of statements in L. They may be
called axioms and definitions.

2. The domain D is a Tarski-style model for which all statements in T
are true. (If T is inconsistent, there is no model or domain.)

Definition: An _applied ontology_ is a formal ontology T with logic L
that is used in a computational system that has at least two additional
components: (1) a reasoning engine that can process statements in L
by methods of deduction, induction, abduction, and/or analogy; and
(2) a system for storing and retrieving statements in L.

To make these definitions as general as possible, I avoided any
philosophical terminology about the theory T, the logic L, the
domain D, or the intended use of the functions and relations.

I certainly believe that philosophy is important. But as history
shows, there has been endless debate about these issues for the past
few millennia. A consensus seems unlikely, and a requirement for
a fixed terminology could (a) make many current systems nonconforming
and (b) stifle future innovation.

Suggestion:

1. Adopt the above two definitions (or some reasonable rewording)
as the minimum requirements for formal ontologies and any
applications of them.

2. Encourage the development of methods of analysis and design that
are based on or inspired by philosophy, linguistics, lexicography,
knowledge engineering, systems analysis, and/or other branches
of cognitive science and computer science.

3. Allow different methodologies to use terminology appropriate for
their users, subject matter, and applications.

4. But compatibility among systems should be determined only by
the statements in whatever logic is used, not by the methodology
or terminology used to derive the statements in that logic.

5. For ontologies that are stated in different logics, compatibility
among them may be determined by formal mappings between the logics.

I have no complaints about any methodology or terminology that anybody
has found useful. As you have shown, many people have found BFO quite
useful. But I have also found Peirce's semiotic fruitful for many
applications. See http://www.jfsowa.com/pubs/signs.pdf

The five points of my suggestion are intended make compatibility
among ontologies independent of their method of development, the
terminology for describing them, or the notation in which they
are stated. I would be happy to work with anyone who may have
further suggestions for clarifying and generalizing them.

John
___________________________________________________________________

From my previous note to Ontolog Forum:

Chris Partridge

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Aug 10, 2016, 11:16:42 AM8/10/16
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John,

These are a couple of old topics, but none the less worth repeating.

"specify the functions and predicates that describe the kinds of individuals"
If one has types of types (e.g. describing at the genus and species level) then one is describing the kinds of types as well as the kinds of individual (of course, one can interpret 'universals' as individuals - The Physical Basis of Predication, Andrew Newman, but then what are kinds, and so on ....). Note: these types of types typically form a large part of the reference data in most business computer systems - and for this reason they are useful.

"But applied ontologies are used in large computational systems. In addition to a formal ontology, they require at least two other components:(1) a reasoning engine that processes the logic, and (2) a system that manages data about the individuals in the domain of interest."
In most business systems, there is epistemic/doxastic and deontic processes. One needs to have a mechanism for these types of processes to use the ontology. I guess this happens under "(2) a system that manages data ..." - or maybe it another item on the list. Given the importance of these processes, it is probably worth mentioning them. Or one could exclude the official use of ontology from most business systems.

Chris


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Barry Smith

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Aug 10, 2016, 11:42:54 AM8/10/16
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On Wed, Aug 10, 2016 at 10:38 AM, John F Sowa <so...@bestweb.net> wrote:
On 8/9/2016 5:17 PM, Barry Smith wrote:
> We are not defining 'knowledge base'

I agree.  Pure ontology is the study of existence without regard
to any applications.  But applied ontologies are used in large
computational systems.  In addition to a formal ontology, they
require at least two other components: (1) a reasoning engine that
processes the logic, and (2) a system that manages data about the
individuals in the domain of interest.
> I will of course be happy to amend it to accommodate future
> innovations, in true scientific spirit, when you tell me what
> they are.

I can't predict future innovations, but I can generalize my previous
definition (copy below) and restate it in genus-differentiae format:

Definition:  A _formal ontology_ is a theory T stated in a logic L
that is designed to specify the
​​
functions and predicates that
describe the kinds of individuals in some domain D and their
possible relationships and interactions with each other.

Comments:

  1. The theory T is a collection of statements in L.  They may be
     called axioms and definitions.

  2. The domain D is a Tarski-style model for which all statements in T
     are true.  (If T is inconsistent, there is no model or domain.)

Definition:  An _applied ontology_ is a formal ontology T with logic L
that is used in a computational system that has at least two additional
components: (1) a reasoning engine that can process statements in L
by methods of deduction, induction, abduction, and/or analogy; and
(2) a system for storing and retrieving statements in L.

To make these definitions as general as possible, I avoided any
philosophical terminology about the theory T, the logic L, the
domain D, or the intended use of the functions and relations.

​Unfortunately you did not quite succeed. You used at least the following:

function 
predicate
describe
kind
individual
domain
relationship
interaction

​​of these only 'domain' is defined: you identity it as a Tarski-style model for which all statements in T​ a​re true. But is it right to identify 'domain' with 'model'? (surely a model has adomain). And if we had all of the conditions you specify for being an applied ontology satisfied for a domain consisting of just one object, say: the number 2, would we thereby have an applied ontology? If not, then there is something missing from your definition.

BS



"A knowledge base has three components:  a logic for specifying the
form of what can be expressed, an ontology for specifying the subject
domain, and a database for collecting information about individuals
that exist or may exist within the specified domain."

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John F Sowa

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Aug 10, 2016, 3:52:03 PM8/10/16
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Chris P. and Barry,

Thank you the comments. They are good examples of the points
I was trying to make.

Chris
> If one has types of types (e.g. describing at the genus and species
> level) then one is describing the kinds of types as well as the kinds
> of individual (of course, one can interpret 'universals' as individuals
> - The Physical Basis of Predication, Andrew Newman, but then what are
> kinds, and so on ....).

These are some of the many points on which philosophers have not
reached a consensus. For example, see David Armstrong's book on
Universals, which I quoted on p. 1 of http://jfsowa.com/pubs/signs.pdf :
> Metaphysicians should not expect any certainties in their inquiries...
> Of all the results that have been argued for here, the most secure, I
> believe, is the real existence of properties and relations. Whether
> they be universals or particulars is a more delicate matter, and just
> what properties and relations are required is obscure, and in any case
> not for the philosopher to determine.

Philosophy is important for guidance, but all those terms are in flux,
and we "should not expect any certainties". That is not a promising
basis for an ISO standard.

Chris
> Note: these types of types typically form a large part of the
> reference data in most business computer systems - and for this
> reason they are useful.

This is another of the many reasons why philosophers cannot reach
a consensus about universals and particulars. First-order logic
cannot represent types of types. Common Logic (CL) is one of the few
logics with a first-order proof theory *and* the ability to represent
relations of relations. It can indeed express the features you
request. In fact, CL is an excellent foundation for stating and
clarifying these issues.

Chris
> In most business systems, there are epistemic/doxastic and deontic
> processes. One needs to have a mechanism for these types of processes
> to use the ontology... Or one could exclude the official use of
> ontology from most business systems.

Business applications are major drivers of computer technology.
If we can't use ontology for business, then we should abandon hope
of promoting applied ontologies. Fortunately, There is a way of
supporting those modalities, but that requires a new and lengthy
thread. See http://www.jfsowa.com/pubs/worlds.pdf

Barry
> You used at least the following [terms]: function, predicate, describe,
> kind, individual, domain, relationship, interaction. Of these only
> 'domain' is defined...

Yes, indeed. Precise definitions can only be stated within a formally
defined framework. As I said to Chris, I recommend Common Logic, which
is sufficiently expressive to define all the logics of the Semantic Web
and many other logics used in computer science. In my previous note,
I assumed that most readers could use their informal knowledge of those
terms to get the point I was trying to make.

Barry
> But is it right to identify 'domain' with 'model'?
> (surely a model has a domain).

In model-theoretic semantics for a logic L (Tarski style), a model M
includes a domain D plus an evaluation function Phi. The domain D
is a set-theoretic construction, which consists of a set of entities
(often called individuals) and a set of functions and relations over D.
For any sentence s in L, Phi(s) is called the denotation of s in M.
The value Phi(s)=T, if s is true of D. Otherwise, Phi(s)=F.

I apologize for not spelling out all these details in my previous note,
but I assumed that the phrase "Tarski style" would be sufficient for
most readers.

Barry
> And if we had all of the conditions you specify for being an applied
> ontology satisfied for a domain consisting of just one object, say:
> the number 2, would we thereby have an applied ontology?

That is certainly a trivial case, which is unlikely to be used in any
practical application. But there is no reason to exclude it from the
definition.

In fact, somebody might indeed use that example. They might want to
test their software by starting with a trivial case and building up
a more complex version by adding new items one at a time.

If either of you have more questions and concerns, I'd be happy
to show how they would be handled according to the definitions
below and the five suggestions in my previous note.

John
__________________________________________________________________

Definition: A _formal ontology_ is a theory T stated in a logic L
that is designed to specify the functions and predicates that
describe the kinds of individuals in some domain D and their
possible relationships and interactions with each other.

Alan Rector

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Aug 12, 2016, 5:27:38 AM8/12/16
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John, Barry, All


I think it important to be clear about what we mean by an “ontology”
and what sort of knowledge it is meant to include - and therefore
what ontological representations should represent.

That issue is critical for Ontolog Forum, but I doubt that any two
subscribers have identical opinions about it.


Precisely why I am arguing for a better vocabulary to at least discuss the issue.  The term “ontology” has become so blurred as to be often meaningless and/or subject to irreconcilable controversies because different authors are talking about different things.

I am actually not terribly interested in what “ontology’ is or isn’t.  I am interested in having a clear vocabulary to discuss different aspects of knowledge and its representation. I suspect the best we can hope for is that “ontology” becomes and “umbrella term”, covering a range of different sorts of knowledge and knowledge representations.  But for that to work, we need a more specific terminology for discussing the specifics of what falls under the umbrella.


To carry on in that vein…

Barry

The Smith-Ceusters definition distinguishes ontology-in-the-narrow
sense -- which is a representation of universals and of the relations
between them...

In the wide sense ontologies can include also representations of what
we called defined classes (for instance 'patient in clinical trial
#12345', 'human being who has bathed in the river Ganges').
Details are provided in the Building Ontologies with BFO book.

So perhaps we need a "narrow sense" and a "narrower sense" - or perhaps the "core ontology' "base ontology" for the narrowest sense.  Or some entirely different terms.

On the substance.

The requirement for defined classes is why I  focus on the statemetns/axioms/truths rather than, or at least as well as, the entities.  Again, improved terminology welcome for "definitions and statements of necessary truth"s.  The characteristics in the definition are necessary and sufficient to the entity defined.  "Pneumonia is defined as an inflammation of the parenchyma of the lung with consolidation".   Personally, I would be pragmatic about what definitions we allow, and base it on the application provided they really are necessary and sufficient within the field of discourse. There are others who would be more restrictive.


Yes.  But even the wide sense is insufficient for interpreting the
already overwhelming and rapidly growing amount of natural language data on the WWW.  For an overview of the issues, see
http://www.jfsowa.com/talks/nlu.pdf

But do we want to call all of that natural language data on the WWW "ontology".  If we do, what  are the features  of "ontologies"  that distinguish them from other knowledge resources?  Are "ontologies" language resources or knowledge resources?  I'd rather see the language resources labelled differently - or clearly distinct terms under an umbrella term of "ontology"



Alan


Obrst, Leo J.

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Aug 12, 2016, 9:14:20 AM8/12/16
to ontolo...@googlegroups.com, John F Sowa

Ontologies are knowledge resources. Language gets mixed up in the muddle because semantics (meaning for NL, ways of referring to things of the world) by its nature is connected to ontology (the referents, things of the world). The thing we refer to as a “chair” is that chair-thing, existing in its own right, independent of our way of referring to it.

 

Thanks,

Leo

 

From: ontolo...@googlegroups.com [mailto:ontolo...@googlegroups.com] On Behalf Of Alan Rector
Sent: Friday, August 12, 2016 5:28 AM
To: John F Sowa <so...@bestweb.net>; ontolo...@googlegroups.com
Subject: Re: [ontolog-forum] Applied Ontology Terminology

 


John, Barry, All

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Chris Partridge

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Aug 12, 2016, 9:57:31 AM8/12/16
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Barry,

(Apologies for late reply, just seen this.)
Are these comparable?
In the case of the BoE and Fed - these entities construct the rules that are used in reporting. One has, of course, the more general idea of a Central Bank and central bank reporting. One could argue that there is some kind of grounding going on.
In the case of genes, I do not see how Planet Earth is constructing these - or even another kind of grounding. 
Maybe I am missing something.
BTW agree that there seems to be no need for Planet Earth in your example.

To view this discussion on the web visit https://groups.google.com/d/msgid/ontolog-forum/CAN_82SQ7Qp9MyGwTtx6t3%3DCOZ3LwyJ3fG50%3D4Z0vw38qOOy6Nw%40mail.gmail.com.

Chris Partridge

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Aug 12, 2016, 10:00:28 AM8/12/16
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It is an old argument, but that does not make it wrong.

I think Barry's definition with philosophical terms has a point.
I find it strange that one should want to call something ontology and then have nothing to do with philosophy.
If you want to code in logic, whether common logic or not, there is a long tradition of this - why call it an ontology. (John's suggestion seems to fall into this category)
If you want to design knowledge bases (or whatever), there a long tradition of this, again why call it ontology. (Alan's suggestion seems to fall into the category.)
I think John is right saying there is no agreement on the details of ontology (though the lack of a more general agreement seems so me over-egged). However, there are reasonably well established schools of thought one can work with.

It seems to me that to qualify as an ontology in a way that respects the words origins, one needs to recognize that Leo's talk of 'things of the world' and 'referents' is something traditional ontology/philosophy has an interest - and we can use the work done there. I think it would be helpful to recognize this - maybe talking about philosophically based ontologies - and logic programming 'ontologies' and knowledge base 'ontologies'.
I think it would be very useful to be able to know when something is being offered as an ontology whether or not is has any philosophical ontological input.

Chris




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rrov...@buffalo.edu

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Aug 12, 2016, 10:09:04 AM8/12/16
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QUESTION: What is the perceived or hoped-for utility and benefit of this effort?

CONSIDERATION:
- If one purpose is to form a vocabulary for the applied ontology community to use consistently in whatever medium, then (a) a much wider audience is needed than this list-serve, and (b) reasons for doing so need to be stated.
- Is a self-specified vocabulary for a given community (like this applied onto) wise? Will it run into the same problems of agreement as in the development of any ontology development project?

SUGGESTION: Perhaps instead of trying to assert one sense of each term, this effort (and the website) can (1) catalogue and list the various senses and definitions of them. And then (2) by some community effort (larger than this list-serve) create another unbiased definition in slightly more general terms to possibly encompass that list.


On Thu, Jul 28, 2016 at 4:56 PM, Sandra Lovrenčić <sandra.l...@foi.hr> wrote:
Dear all,

the International Association for Ontology and It's Applications Education Committee previously sent you invitation to help us create a list of applied ontology courses around the world.

We would also like to create a list of terms and their definitions in this field by continuing work of former IAOA Ontology Terminology Sub-committee.
(http://ontolog.cim3.net/wiki/IaoaOntologyTerminology.html)

Their list of terms serves as initial list and is placed on the IAOA Education Wiki. (http://iaoaedu.cs.uct.ac.za/pmwiki.php?n=IAOAEdu.TermList)

If you would like to contribute with new terms and/or their definitions, please send me your proposals (if possible with references) or links to information sources that you find relevant.


Best,
Sandra

Faculty of organization and informaticsAssoc. Prof. Sandra Lovrenčić, Ph.D.
University of Zagreb, Faculty of organization and informatics
Pavlinska 2, HR-42000 Varaždin, Croatia
tel: +385 42 390 851; fax: +385 42 213 413; mob: +385 98 243 341
e-mail: sandra.l...@foi.hr
http://www.foi.unizg.hr/eng/staff/sandra.lovrencic


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Ronald Fuller

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Aug 12, 2016, 1:54:10 PM8/12/16
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Whatever the precise definition, it seems clear that an ontology cannot be planned, created, tested or evaluated without considering intent with central importance.  So I can't see how a definition becomes more general by not addressing intent.  Without intent nothing remains to generalize or define.  Peirce's semiotic is all about meaning.  Can meaning exist without intent?

Ron

> Subject: Re: [ontolog-forum] Applied Ontology Terminology
> To: ontolo...@googlegroups.com
> From: so...@bestweb.net
> Date: Wed, 10 Aug 2016 10:38:39 -0400
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Christopher Menzel

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Aug 12, 2016, 2:15:27 PM8/12/16
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You address intent by axiomatizing the items in an ontology's lexicon so as to reflect their intended meanings, as far as that is possible within the constraints of one's chosen formal framework.

-chris

-------- Original message --------
From: Ronald Fuller <rgfu...@hotmail.com>
Date: 8/12/16 1:54 PM (GMT-05:00)
Subject: RE: [ontolog-forum] Applied Ontology Terminology

John F Sowa

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Aug 12, 2016, 2:44:54 PM8/12/16
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Alan, Chris P., Leo, Rob R., Ron F., and Chris M.,

Philosophy is extremely important for anyone who is doing research
on applied ontology and its use in software design and development.
But that does *not* mean that philosophical *jargon* is required.

Alan
> I am arguing for a better vocabulary to at least discuss the issue.
> The term “ontology” has become so blurred as to be often meaningless
> and/or subject to irreconcilable controversies because different
> authors are talking about different things.

I agree. But we need different terms for different purposes:

1. For researchers who analyze the issues and publish papers in AOJ.

2. For teachers of comp. sci. courses to students who have a strong
background in programming, but no background in philosophy.

3. For programmers who link their software to ontology-based tools.

For #1, there should be no limit on what terminology an author may use.

For #2, the primary terminology should be taken from logic. An intro
to the issues in philosophy *and* linguistics *and* lexicography is
desirable. Students should be encouraged to further their study in
any or all of those fields. But they should *not* be required to
master the jargon of those fields -- especially since professional
philosophers have not reached a consensus on the jargon.

For #3, all bets are off. We have no control over what programmers
know or do. Some of them may have taken a course (#2), but an
insignificant fraction would have studied philosophy.

Alan
> I am interested in having a clear vocabulary to discuss different
> aspects of knowledge and its representation.

Chris P.
> I find it strange that one should want to call something ontology
> and then have nothing to do with philosophy.

As I said, philosophy is essential for ontology. But Socrates did
not use any jargon to discuss the most subtle issues of philosophy.
Plato's dialogs, as translated to ordinary NLs, are still the starting
point for introductory philosophy courses.

If you want a more modern example, see Wittgenstein's later philosophy.
He stated his examples and analyses in ordinary language. Yet many
professional philosophers consider him one of the greatest philosophers
of the 20th century.

Since we cannot expect our students to have taken graduate courses
in philosophy, we should not use any jargon that does not occur
in English translations of Plato or Wittgenstein.

Leo
> Language gets mixed up in the muddle because semantics (meaning for NL,
> ways of referring to things of the world) by its nature is connected
> to ontology (the referents, things of the world). The thing we refer
> to as a “chair” is that chair-thing, existing in its own right,
> independent of our way of referring to it.

OK. But I notice that you did not require any philosophical jargon
to make those points. If you find any issue in ontology that you
cannot state without such jargon, please let me know. I'm quite sure
that it could be translated to ordinary English + the terminology
of whatever logic is used for stating the ontology.

Rob
> Is a self-specified vocabulary for a given community (like this
> applied onto) wise? Will it run into the same problems of agreement
> as in the development of any ontology development project?

Ordinary language was sufficient for Plato and Wittgenstein.
If it was good enough for them, it should be good enough for us.
Some discussion about how to use ordinary language may be useful,
but no agreement about terminology is required.

Ron
> Without intent nothing remains to generalize or define. Peirce's
> semiotic is all about meaning. Can meaning exist without intent?

Chris M.
> You address intent by axiomatizing the items in an ontology's lexicon
> so as to reflect their intended meanings, as far as that is possible
> within the constraints of one's chosen formal framework.

I agree. The formal logic is the framework. Thanks to Brentano,
'intent' and 'intentionality' are common terms in English. Therefore,
those words may be used in the informal discussions about the axioms.

John

Ronald Fuller

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Aug 12, 2016, 3:30:24 PM8/12/16
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Information owners (companies) spend a lot of money for people like us to create ontologies and most of the results are problematic.  That is because the ontologies we create reflect not the owners intent, but our perceptions of their intent.   With a complex system it is probably impossible for any owner to make a complete list detailing every nuance of their own intent, so we have to rely instead on incomplete lists of requirements and use our own intuition to fill in the blanks.

Ontology will continue to be problematic until owners become able to directly express their own intent in unambiguous terms -- in other words, in terms of a logical signature.  That is not too much to ask:   Before the late 19th century every person educated at a university studied logic.  In fact logic education is one of the main reasons universities were created in the first place.  Medieval practitioners of commerce were fully able to create their own ontologies which exhibit every characteristic and the full-range of complexities present in modern ontologies.  The did not have the benefit of computers, but they had something far more valuable for the creation of effective ontologies:  a logically-literate merchant class.

Definitions are important because they explain what things mean to people who don't already know.  Any definition of 'ontology' that does not explain to an information owner that their intent must be directly expressed in order to produce the expected result is an incomplete definition, which is useless.



> Subject: Re: [ontolog-forum] Applied Ontology Terminology
> To: ontolo...@googlegroups.com
> From: so...@bestweb.net
> Date: Fri, 12 Aug 2016 14:44:53 -0400
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Ronald Fuller

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Aug 12, 2016, 4:22:17 PM8/12/16
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Thank you Chris.  Please help me understand your meaning here in the context of my own understanding -- which may be mistaken, in which case please correct me.

Ontology deals with 2 kinds of meaning:  1) Tarskian meaning which is purely subjective such as the meaning of a word, and 2) Godelian meaning which is purely objective (at least in an ω-consistent system) such as a logical signature in FOL.

What exactly, in these terms, is an ontology's lexicon?  I think I understand what it means to axiomatize a subjective (Tarskian) element -- you just declare that it is true.  Is that what you mean?  Do you also mean that objective elements can or should be axiomatized in order to reflect their intended meaning?  If so, how exactly to you do that?

Thank you for your patience in clarifying this.

Regards,

Ron



Date: Fri, 12 Aug 2016 14:15:19 -0400

Subject: RE: [ontolog-forum] Applied Ontology Terminology
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rrov...@buffalo.edu

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Aug 12, 2016, 4:28:27 PM8/12/16
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Dr.Sowa is correct in emphasizing lack of consensus in philosophical terms (also in general) and in saying "all those terms are in flux[...] That is not a promising basis for an ISO standard [and arguably this terminology effort]". I would add also no consensus (or answer) to many philosophical questions (of ontology and otherwise). Because many terms,concepts and questions/problems-of-philosophy have a long history with open questions and different views, using some in a restricted way (that may or may not favor a particular applied ontology group) and then fixing it in a terminology is problematic, misleading, and arguably conceptually harmful and confusing to the field and to users of the terms. It would be forcing or imposing a sense on a term whose meaning is inherently fluid, just as language and concepts are.
At the very least, form a new terminology and sense of 'ontology' that is sufficiently general not to impartial to any ontology group.

What Dr.Rector says seems on point for this community. Given the focus of *applied ontology*, the task is not finding out what ontology actually is, but in coming up with a vocabulary. The philosophical baggage should be minimized with respect to applied onto, and a terminology should not bias a particular groups definition.
Some relation to the philosophical origins of ontology may be present in a new definition of 'ontology' BUT that sense must not bias the philosophical assumptions or assumed worldviews of a given top-level ontology or other ontology-development group. And as Christ pointed out, some ontologies are philosophically based, others are not. So, (ii) Some ontologies or developers have no interested in the philosophical background or in infusing their ontology with philosophical senses of terms. So we must not assume that each ontology can be fit in this or that historical or contemporary philosophical ontological account. So in distinguishing different forms of ontology or terms (ontology, philosophical ontology, formal ontology, applied ontology, philosophically-based ontology, etc.), we may better handle the relation to philosophical concepts and inquiry.

Ron is correct in emphasizing intent (of the ontology). A starting point is with the intent of the ontology or application. Being applied ontology, the focus must be on the application, i.e., on solving problems or achieving some computational goal in the given application or domain. However, the importance of logics (the formal systems, not reasoning in general) is overemphasized and given too much importance; furthermore the socio-psychological-historical context is too complex and tangential to get into, but suffice it to say that the dialectic and Socratic concepts are far more significant. And if a lot is being spent on ontology applications, then it is all the more reason to focus on problem-solving (i.e., to do good to the domain and society) and not on infusing (imposing) the philosophical biases of this or that particular ontology group/project/tlo.

Dr.Sowa's points about not using jargon are also valid. The mention of dialetic and Plato are particularly important. 

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Christopher Menzel

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Aug 12, 2016, 4:53:33 PM8/12/16
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On 12 Aug 2016, at 4:22 PM, Ronald Fuller <rgfu...@hotmail.com> wrote:
Ontology deals with 2 kinds of meaning:  1) Tarskian meaning which is purely subjective such as the meaning of a word,

If word meanings were purely subjective communication would be impossible; word meanings must be in very large measure shared (hence objective) no one would have any idea what anyone else means when they use a word. And I don't understand why you associate the idea of purely subjective meaning with Tarski's name given that he's most famous for developing what most would think of as the completely objective, mind-independent semantics of first-order logic.

and 2) Godelian meaning which is purely objective (at least in an ω-consistent system) such as a logical signature in FOL.

The signature of a first-order language is just its uninterpreted lexicon and, hence, represents no notion of meaning at all. There is explicitly no meaning attached to the lexicon of a language; that is the job of a semantical theory like Tarski's. (Again I don't know why you associate this notion with Gödel's name, or with the concept of ω-completeness, which is a proof theoretic notion).

What exactly, in these terms, is an ontology's lexicon?  I think I understand what it means to axiomatize a subjective (Tarskian) element -- you just declare that it is true.  Is that what you mean?

Nope. I mean what is meant in any introductory text on first-order logic. To axiomatize a lexical item is to write down axioms for it. E.g., we typically axiomatize the basic lexicon of number theory — '0', 's' (successor), '+', and '•' — with the axioms of Peano Arithmetic plus the usual axioms for addition and multiplication.

Do you also mean that objective elements can or should be axiomatized in order to reflect their intended meaning?  If so, how exactly to you do that?

Well, by writing down axioms that correctly reflect their intended meanings. For example, in Peano Arithmetic, we intend that '0' denote the first natural number. Hence, we include the axiom "Zero is not the successor of any number", i.e., ¬∃x sx=0. If instead we chose to add an axiom saying that zero is the successor of some number, ∃x sx=0, then we would not have correctly reflected the intended meaning of '0'.

Thank you for your patience in clarifying this.

I'm really not patient at all. :-) That's all I have to say on this, as it is just Ontology 101. There's a great deal of material out there that presents these ideas in great detail. You might have a look at some actual ontologies like Hayes' ontology of liquids or the Process Specification Language PSL.

-chris

Simon Spero

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Aug 12, 2016, 6:14:10 PM8/12/16
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On Aug 12, 2016 4:53 PM, "Christopher Menzel" <chris....@gmail.com> wrote:

>
> If word meanings were purely subjective communication would be impossible; word meanings must be in very large measure shared (hence objective)

Or if the behavior of the other players in situations involving  this word should be generally consistent with your subjective predictions? 🐇😛

>  You might have a look at some actual ontologies like Hayes' ontology of liquids 

Which is available  at http://www.issco.unige.ch/working-papers/Hayes-1978-35.pdf

Relatedly, NPM2 is available at https://www.academia.edu/722721/The_second_naive_physics_manifesto

Simon

Ronald Fuller

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Aug 12, 2016, 6:35:46 PM8/12/16
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Chris,
Tarskian semantics is the absolute highest epitome of subjectivity.  The Stanford Logic Group seems to have decided to completely discard it altogether; see here.  This paper explains that they have difficulty teaching the basic notion of a model to "even the good students" using Tarskian semantics.

A non-interpereted signature absolutely has meaning.  It is expressed by the purely objective syntactic definition of empty functions and relations -- In my line of work (information management) this is the most important kind of meaning.

Godel himself explained that the heuristic principle of his system was "the highly transfinite concept of objective mathematical truth." although he did not use that language in public because he was sensitive to the "philosophical prejudices" of his times.    Syntactic truth conveys meaning just as semantic truth does--sometimes far better.


Subject: Re: [ontolog-forum] Applied Ontology Terminology
Date: Fri, 12 Aug 2016 16:53:29 -0400
To: ontolo...@googlegroups.com
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John F Sowa

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Aug 12, 2016, 11:40:18 PM8/12/16
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On 8/12/2016 6:35 PM, Ronald Fuller wrote:
> Tarskian semantics is the absolute highest epitome of subjectivity.

That statement is nonsense. On these issues, I agree with Chris Menzel.

> The Stanford Logic Group seems to have decided to completely discard
> [Tarski-style model theory]
> altogether; see http://logic.stanford.edu/reports/LG-2006-02.pdf

That paper does *not* discard Tarski-style model theory.

What it does is to propose a set of models that are different from the
ones that are commonly used for FOL. Note the following point on p. 4:
> Herbrand logic differs from first-order logic solely in the structures
> it considers to be models.

In other words, this paper uses a notation that has the same syntax
as FOL. But it uses a different set of models.

The method of evaluation, however, is the same as Tarski's.

Chris M:
> That's all I have to say on this, as it is just Ontology 101.

I agree that on this topic there is nothing more to say.

John

Ronald Fuller

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Aug 13, 2016, 12:03:33 AM8/13/16
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John,  their redefinition of 'model' is just my point.  They define a model as anything that can have a truth value.  No change to FOL syntax.

My point is simple:  A set of empty relations and functions may not convey meaning in a philosophy classroom, but they convey significant meaning in a business database.  Do you disagree?



> Subject: Re: [ontolog-forum] Applied Ontology Terminology
> To: ontolo...@googlegroups.com
> From: so...@bestweb.net
> Date: Fri, 12 Aug 2016 23:40:17 -0400
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John F Sowa

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Aug 13, 2016, 2:39:51 AM8/13/16
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On 8/13/2016 12:03 AM, Ronald Fuller wrote:
> their redefinition of 'model' is just my point.

No. They did not revise the definition of 'model'. What they did
was to specify a different set of models.

Tarski's definition of a model M: A domain D of individuals,
a set of relations and functions among the elements of D,
and an evaluation function that determines the truth values
of sentences about M.

That article you cited did not change the definition of 'model'.
What it did as to specify a different way of defining the domains
and the functions and relations among elements of a domain.

John


Pat Hayes

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Aug 13, 2016, 2:42:02 AM8/13/16
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On Aug 12, 2016, at 3:35 PM, Ronald Fuller <rgfu...@hotmail.com> wrote:

Chris,
Tarskian semantics is the absolute highest epitome of subjectivity.  The Stanford Logic Group seems to have decided to completely discard it altogether; see here.  This paper explains that they have difficulty teaching the basic notion of a model to "even the good students" using Tarskian semantics.

A non-interpereted signature absolutely has meaning.  It is expressed by the purely objective syntactic definition of empty functions and relations -- In my line of work (information management) this is the most important kind of meaning.

Godel himself explained that the heuristic principle of his system was "the highly transfinite concept of objective mathematical truth." although he did not use that language in public because he was sensitive to the "philosophical prejudices" of his times.    Syntactic truth conveys meaning just as semantic truth does--sometimes far better. 

None of the above makes any sense whatsoever. I do not believe that the writer knows what the terms he using actually mean. No purpose will be served by debating this matter, if indeed there is any matter here, any further. 

Pat Hayes

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John F Sowa

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Aug 13, 2016, 2:50:06 AM8/13/16
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On 8/13/2016 2:41 AM, Pat Hayes wrote:
> I do not believe that the writer knows what the terms he uses actually
> mean. No purpose will be served by debating this matter, if indeed there
> is any matter here, any further.

I agree.

John

Christopher Menzel

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Aug 13, 2016, 6:13:09 PM8/13/16
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[This is not to be construed as a continuation of the original discussion in this thread but rather simply an interesting ancillary point about the connection between Tarski semantics and Herbrand semantics.]
To put John's point a bit differently: the term "model" — or better, "interpretation" — in mathematical logic has a broad, general meaning, viz., a well-defined, mathematically rigorous assignment of semantic values (defined over a given set) to the elements of an uninterpreted formal language. These in turn will be used by the overarching semantic theory to assign appropriate semantic values to the syntactically complex constructions defined by the grammar of the language. Different semantic theories define different notions of model. Tarskian semantics defines the familiar notion for first-order logic. The Herbrand semantics defined by Hinrichs and Genesereth defines a different notion. But H&G no more "redefine" what a (Tarskian) model is than an artist "redefines" Starry Night by painting a new picture.

In fact, it's easy to see (unless I've missed something from my quick look at H&G) that you can map an Herbrand model H for a language L directly onto a Tarski model M, e.g., the domain of M consists of the ground terms of L (this will ensure the domain is at most denumerable), the semantic value of every ground term is itself (this will yield the unique-names condition), the extension of every n-place predicate π of L in M is the set of n-tuples ⟨t1,...,tn⟩ such that π(t1,...,tn) ∈ H, and so on. So Herbrand models can actually be viewed simply as a special case of Tarski models.

-chris

Pat Hayes

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Aug 14, 2016, 11:13:25 AM8/14/16
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Which was exactly how Herbrand first proved what is now called Goedel's completeness theorem, in his 1938 doctoral thesis.

Pat


-chris


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Christopher Menzel

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Aug 14, 2016, 12:59:50 PM8/14/16
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On Aug 14, 2016, at 11:13 AM, Pat Hayes <pha...@ihmc.us> wrote:
>> ...
>> In fact, it's easy to see (unless I've missed something from my quick look at H&G) that you can map an Herbrand model H for a language L directly onto a Tarski model M, e.g., the domain of M consists of the ground terms of L (this will ensure the domain is at most denumerable), the semantic value of every ground term is itself (this will yield the unique-names condition), the extension of every n-place predicate π of L in M is the set of n-tuples ⟨t1,...,tn⟩ such that π(t1,...,tn) ∈ H, and so on. So Herbrand models can actually be viewed simply as a special case of Tarski models.
>
> Which was exactly how Herbrand first proved what is now called Goedel's completeness theorem, in his 1938 doctoral thesis.

Interesting. I should know the history here better. It's often called "Gödel's completeness theorem" quite appropriately, of course, since Gödel was the first to prove completeness in his 1930 dissertation albeit, without the benefit of Tarski's seminal work (notably his 1933 paper on truth in formalized languages), relying on more or less intuitive notions of truth and satisfiability. Given the obvious similarities between Herbrand models and the term models that Henkin introduced to prove his now standard proof of completeness, I'm wondering how similar Herbrand's proof is to Henkin's. Do you happen to know, Pat?

-chris

Ronald Fuller

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Aug 14, 2016, 1:30:07 PM8/14/16
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What Pat points out should be a reminder that model theory is deeply connected with proof theory.  Logic deals with 2 notions of truth: 1) the kind someone defines, and 2) the kind expressed in truth tables.  I think this distinction is important to the issue of ontology, and I don't think discussing it should be met with dismissiveness or ridicule.  It should go without saying that people of varying backgrounds will perceive and describe things differently..  if this forum presupposes a PhD in math, cs, or philosophy then you should state that up front.


Subject: Re: [ontolog-forum] Applied Ontology Terminology
Date: Sun, 14 Aug 2016 08:13:15 -0700
To: ontolo...@googlegroups.com

Christopher Menzel

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Aug 14, 2016, 2:31:19 PM8/14/16
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On Aug 14, 2016, at 12:30 PM, Ronald Fuller <rgfu...@hotmail.com> wrote:
What Pat points out should be a reminder that model theory is deeply connected with proof theory.

Well, no, not in general, in classical logic at any rate. Conceptually, they are completely different. The model theory for a class of languages is defined independently of any notion of proof for those languages and it is in fact an independent question entirely whether the model theoretic notion of logical consequence for a given class of languages is even capable of being expressed in a complete proof theory. (Second-order consequence, notably, cannot be so expressed.) That is why the completeness theorem for first-order logic is so significant. It does indeed reveal a deep connection between the model theory for first-order languages and (as it is usually proved) a corresponding proof theory, but it is, as it were, a surprise, simply because there is no reason a priori why logical consequence and provability should turn out to be coextensive. (There is a wonderful quote by George Boolos about this: “The equation of first-order validity with provability effected by the completeness theorem would be miraculous if it weren't so familiar.”)

Logic deals with 2 notions of truth: 1) the kind someone defines, and 2) the kind expressed in truth tables.  I think this distinction is important to the issue of ontology, and I don't think discussing it should be met with dismissiveness or ridicule.

I don’t believe anyone has ridiculed you, but if you sense any dismissiveness it is because you are making claims like the above in which you make reference to extensively studied fields like model theory and proof theory and well-understood concepts like ω-completeness, but which you yourself have not studied enough for your claims to make clear sense. Case in point: the fact that you think the two notions of truth you cite above exhaust (or in the first case, have much of anything to do with) the notion of truth in logic shows in particular that you haven’t even studied the basic model theory of first-order logic (i.e., so-called Tarskian semantics); truth tables are only used for defining truth in the model theory for propositional logic. The fact that first-order models can be infinite renders truth tables of only limited (and inessential) use in first-order logic.

It should go without saying that people of varying backgrounds will perceive and describe things differently.  if this forum presupposes a PhD in math, cs, or philosophy then you should state that up front.

It presupposes no such thing and there are any number of people who contribute to this forum who don’t have PhDs. The forum does presuppose that, when you make claims about important concepts and disciplines in mathematics and logic, you understand them well enough for your claims to make reasonably clear sense.

Cheers,

-chris 

Ronald Fuller

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Aug 14, 2016, 9:25:02 PM8/14/16
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Ok, let me put it a different way:  I think it would be nice if ontology included terms to make it easy to refer to those two kinds of truth.  Maybe others too if you'd like..  I didn't mean that list to be exhaustive.  And of course truth tables are not the only way to express that kind of truth.  If there are already terms to easily express this please let me know.

Tarski and Church used the terms "objective" and "subjective" to discuss distinctions between science and the underlying logic, although neither explained their use of the terms (see here).   Those terms might be useful in ontology.   Maybe they are already used.. I just haven't seen them in many circumstances where I thought they (or something similar) might be helpful. 


Subject: Re: [ontolog-forum] Applied Ontology Terminology
Date: Sun, 14 Aug 2016 13:31:14 -0500
To: ontolo...@googlegroups.com
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Ronald Fuller

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Sep 7, 2016, 2:02:54 PM9/7/16
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Chris, Pat, John, Alex -- or anyone who understands ω-consistant theory well, please tell me if the following statements are correct:
  1. the idea of ω-consistancy can apply to systems (such as FOL) as well as to theories within a system (a theory being a set of statements)
  2. If a system is ω-consistant, that means any true statement made within that system cannot be contradicted by any other true statement with the same system
  3. In an ω-inconsistant system, it is possible to construct true statements that contradict each other
  4. FOL is ω-consistant
  5. All statements made within FOL are ω-consistant


Thank you.  I'd really appreciate any correction or comment about this.


Regards,


Ron





Subject: Re: [ontolog-forum] Applied Ontology Terminology
Date: Sat, 13 Aug 2016 18:13:04 -0400
To: ontolo...@googlegroups.com
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Christopher Menzel

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Sep 7, 2016, 3:30:31 PM9/7/16
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Chris, Pat, John, Alex -- or anyone who understands ω-consistant theory well, please tell me if the following statements are correct:

Let's get the spelling right first: "consistent".
  1. the idea of ω-consistancy can apply to systems (such as FOL) as well as to theories within a system (a theory being a set of statements)
Well, "systems" does not have a well-defined, broadly-used conventional meaning, so you'd have to provide one; as I use it, I usually just mean "theory" (in some logical framework). But, strictly speaking, FOL, for a given language L, is a theory — one with no proper axioms — so "theory" is all you need for your question. That aside, at a minimum, the concept of ω-consistency only applies to theories in the language of arithmetic (or, at least, theories in which a certain amount of arithmetic is interpretable). Otherwise you can't even express the concept. I suppose, if you don't require any more than that one's theory is in the language of arithmetic, then FOL in that language, qua theory, is ω-consistent, since it's only capable of proving logical truths. So it obviously won't prove anything that would only be true in a non-standard model of arithmetic.
  1. If a system is ω-consistant, that means any true statement made within that system cannot be contradicted by any other true statement with the same system
ω-consistency has to do with provability, not with truth. ω-consistency implies consistency, so obviously you aren't going to be able to prove statements that contradict each other in an ω-consistent theory.
  1. In an ω-inconsistant system, it is possible to construct true statements that contradict each other.
Only if the system is inconsistent per se — which wouldn't be interesting. The only interesting ω-inconsistent systems are consistent.
  1. FOL is ω-consistant
Under the conditions noted above.
  1. All statements made within FOL are ω-consistant
ω-consistency is a property of theories, not statements.

-cm

Ronald Fuller

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Sep 7, 2016, 5:56:04 PM9/7/16
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Thank you Chris,

So when Godel said the following, was he not referring to ω-consistency?  Is the notion of truth he discusses here the same as that described by Tarski?

"it should be noted that the heuristic principle of my construction of undecidable number theoretical proposition in the formal systems of mathematics is the highly transfinite concept of 'objective mathematical truth', as opposed to demonstrability [...] which with it was generally confused before my own and Tarski's work. Again, the use of this transfinite concept eventually leads to finitary provable results, for example, the general theorems about the existence of undecidable propositions in consistent formal systems."

Ron


From: chris....@gmail.com
Subject: Re: [ontolog-forum] Applied Ontology Terminology
Date: Wed, 7 Sep 2016 15:30:19 -0400
To: ontolo...@googlegroups.com


Chris, Pat, John, Alex -- or anyone who understands ω-consistant theory well, please tell me if the following statements are correct:

Let's get the spelling right first: "consistent".
  1. the idea of ω-consistancy can apply to systems (such as FOL) as well as to theories within a system (a theory being a set of statements)
Well, "systems" does not have a well-defined, broadly-used conventional meaning, so you'd have to provide one; as I use it, I usually just mean "theory" (in some logical framework). But, strictly speaking, FOL, for a given language L, is a theory - one with no proper axioms - so "theory" is all you need for your question. That aside, at a minimum, the concept of ω-consistency only applies to theories in the language of arithmetic (or, at least, theories in which a certain amount of arithmetic is interpretable). Otherwise you can't even express the concept. I suppose, if you don't require any more than that one's theory is in the language of arithmetic, then FOL in that language, qua theory, is ω-consistent, since it's only capable of proving logical truths. So it obviously won't prove anything that would only be true in a non-standard model of arithmetic.
  1. If a system is ω-consistant, that means any true statement made within that system cannot be contradicted by any other true statement with the same system
ω-consistency has to do with provability, not with truth. ω-consistency implies consistency, so obviously you aren't going to be able to prove statements that contradict each other in an ω-consistent theory.
  1. In an ω-inconsistant system, it is possible to construct true statements that contradict each other.
Only if the system is inconsistent per se - which wouldn't be interesting. The only interesting ω-inconsistent systems are consistent.
  1. FOL is ω-consistant
Under the conditions noted above.
  1. All statements made within FOL are ω-consistant
ω-consistency is a property of theories, not statements.

-cm


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Alex Shkotin

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Sep 8, 2016, 4:12:53 AM9/8/16
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Ron,

I use FOL for First Order Language - a family of very simple context free languages to write axioms and theorems for a lot of math theories.

May be it's better to use FOLL:-)

Alex


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Christopher Menzel

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Sep 8, 2016, 5:24:32 AM9/8/16
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That usage of "FOL" might be fine for your personal diary, Alex, but it is definitely going to lead to misunderstanding in a lot of discussions!

Also, smallish point, there are perfectly good first-order languages that are not context free, e.g., those that disallow vacuous quantifiers and free variables. Those are pretty common in intro logic texts.

-chris
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Pat Hayes

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Sep 8, 2016, 5:43:59 AM9/8/16
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2016-09-07 21:02 GMT+03:00 Ronald Fuller <rgfu...@hotmail.com>:
Chris, Pat, John, Alex -- or anyone who understands ω-consistant theory well, please tell me if the following statements are correct:
  1. the idea of ω-consistancy can apply to systems (such as FOL) as well as to theories within a system (a theory being a set of statements)
Um..not in a direct way, no. Omega-consistency refers to theories of arithmetic which at least have enough of a signature to refer to numbers (ie numerals), so don't really apply to the bare logic as such. But of course one might use this form of words to indicate that any such theory couched in FOL was w-consistent, for example.

  1. If a system is ω-consistant, that means any true statement made within that system cannot be contradicted by any other true statement with the same system
That is what plain old 'consistent' means. Omega-consistent means that you can't prove P(n) for every number n, but also prove that exists (n) not P(n) or equivalently, not forall (n) P(n).
  1. In an ω-inconsistant system, it is possible to construct true statements that contradict each other
Again, that is simple inconsistency. The omega-inconsistent situation is the one I just described where something is true of all the integers considered individually, but the universal statement (forall (n)...) is false. A theory can be w-inconsistent but consistent: some nonstandard arithmetics are, for example. 
  1. FOL is ω-consistant
I think this is meaningless, understood strictly.
  1. All statements made within FOL are ω-consistant
Definitely not. There are first-order theories of arithmetic that allow nonstandard models and are omega-inconsistent. But in any case, its trivial to make an inconsistent theory in FOL, eg P(a) & not P(a). 

Pat

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Christopher Menzel

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Sep 8, 2016, 12:05:36 PM9/8/16
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On 8 Sep 2016, at 5:43 AM, Pat Hayes <pha...@ihmc.us> wrote:
2016-09-07 21:02 GMT+03:00 Ronald Fuller <rgfu...@hotmail.com>:
Chris, Pat, John, Alex -- or anyone who understands ω-consistant theory well, please tell me if the following statements are correct:
  1. the idea of ω-consistancy can apply to systems (such as FOL) as well as to theories within a system (a theory being a set of statements)
Um..not in a direct way, no. Omega-consistency refers to theories of arithmetic which at least have enough of a signature to refer to numbers (ie numerals), so don't really apply to the bare logic as such. But of course one might use this form of words to indicate that any such theory couched in FOL was w-consistent, for example.

Right, the usual context for speaking of ω-consistency is a theory with a enough arithmetic to code its proof theory. But, as I noted in my reply, as long as you've got a language L with the numerals, the definition of ω-consistency makes sense even with regard to the "theory" of arithmetic that has no proper axioms — i.e., first-order logic in L — and you get its ω-consistency as a trivial consequence of the fact that (by definition) no sentence true only in nonstandard models is a logical truth.
  1. FOL is ω-consistant
I think this is meaningless, understood strictly.

Yes, if one stipulates that ω-consistency only applies to theories containing a certain amount of arithmetic.

  1. All statements made within FOL are ω-consistant
Definitely not. There are first-order theories of arithmetic that allow nonstandard models and are omega-inconsistent.

I said in my reply to this question that the notion of ω-consistency only applies to theories, not statements, which is true if (as I think is most standard) you define theories to be closed under consequence (hence infinite). But a theory can also be identified with its proper axioms, in which case a single statement could be viewed as a theory. In that case, Pat is right, as there are finitely axiomatizable theories T of arithmetic (hence single statements — just conjoin the axioms of T) that, qua theories, are ω-inconsistent, e.g., where R is (the conjunction of the axioms of) Robinson Arithmetic, the statement R ∧ ¬Con(⟨R⟩), where "Con(⟨R⟩)" is the consistency sentence for R.

-chris

Alan Rector

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Sep 12, 2016, 11:02:53 AM9/12/16
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Barry, John, All

I am just getting back and catching up.  Delighted to see all the discussion.

Of all the many subthreads, I think the exchange below comes closest to the heart of the issues I am trying to raise. 

On Tue, Aug 9, 2016 at 4:43 PM, John F Sowa <so...@bestweb.net> wrote:
On 8/7/2016 11:24 AM, Barry Smith wrote:
…

As a clear, general, and flexible definition, I suggest:

"A knowledge base has three components:  a logic for specifying the
form of what can be expressed, an ontology for specifying the subject
domain, and a database for collecting information about individuals
that exist or may exist within the specified domain."

This definition covers most, if not all current ontologies, DBs, and
KBs.  It imposes no restrictions on the choice of logic, the choice
of definitions and axioms in the ontology, the contents of the DB,
or the choice of philosophical jargon for talking about ontology.

John

On 9 Aug 2016, at 22:17, Barry Smith <phis...@buffalo.edu> wrote:

John
We are not defining 'knowledge base"
...

My starting place is that in order to have an agreed  terminology for Applied Ontology we need an agreed terminology for discussing kinds of knowledge and knowledge representation sufficient for, but not limited to, ontology.  The task is not to solve all the issues, but it is to provide a vocabulary with which to discuss them - or even to discuss with other groups who may use some of the same words differently.

Supporting points...


a) We may not be trying to define ‘knowledge base” but we are trying to define “Applied Ontology” and many “Applied Ontologies” are applied in, or in conjunction with,  “Knowledge bases”

b) Empirically, many people are confusing “ontology” and “knowledge base”.  Certainly this is my experience in many tutorials and discussions in biomedicine. I often even hear odd neologisms such as “non-ontological knowledge” without any clarity on what is, and isn’t, “ontological.”  In addition, the Gruber definition of  “conceptualisation of a domain' is still widely quoted, and is open to the interpretation that “ontology” and “knowledge base” are synonyms.   If we think that this is too broad or too vague, then we need to say why in ways that are operationally useful in a terminology that we can explain.

c) From the discussion thread, many contributors, definitely including Barry and, if I understand rightly, also John, as well as myself, would use “ontology” for something narrower than a knowledge base, i.e. would reject a broad interpretation some put on Gruber’s ambiguous words.

d) If we accept something like John's characterisation in which the ontology clearly forms only part of a knowledge base, If we are to discuss why an ontology is needed, the role of the ontology, and what is included in and excluded from it, we need a consistent vocabulary.  

e) Specifically, In constructing knowledge bases for biomedical applications, a large amount of the knowledge is in the form of generalisations - “The treatment for X includes…”, “The symptoms of X include, etc.”  Often these statements are phrased as “is-a” statements: “Y is a treatment for X”, etc.  These statements make up a large part of the information that WHO wanted to include as an annex to the International Classification of Diseases.  Explaining that they are not “ontological” is made more difficult because we don’t have an agreed name and characterisation for them.  I suggest “Generalisations” as less loaded with prior baggage than other terms I have tried, but would gladly hear other suggestions if they led to some broader agreement.

f) “Generalisations" in this sense grade into other sorts of troublesome statements, e.g. of typicality and normative status on the one hand - the heart is normally/typically on the left side of the body - and “may” on the other, “Candida may cause pneumonia”.  We also need to distinguish the notion of “not impossible” - e.g. “might” - “xicillus might cause pneumonia.”  Perhaps meaning something like  'Pneumonia caused by Xicillus” is not impossible.

g) The most widely available and standardised technologies for open-world and closed world are best suited to different information and tasks and often cause confusion when used for others - OWL and DLs open world view for the indefeasible necessary knowledge of definitions and universals; databases, logic programming and other closed world formalisms to generalisations, contingencies, and most facts.  For example,  “How do I say ‘may’ in OWL?” is a common question in tutorials.  There are several possible answers, ranging from “you don’t”, to "say it in a database/logic programme using the entities from your OWL ontology”, to various work-arounds and/or hybrid architectures.  But the starting point has to be that the understanding of the differences between the sorts of knowledge to be represented, e.g. that, for example, "Meningococcus infection may cause a rash” is different from “Meningococcus is a kind of gram negative bacterium” or “Meningitis is defined as an inflammation of the meninges (one of the membrane layers covering the brain and spinal cord)”  

h) Discussion of how best to represent the knowledge requires the ability to be more precise about what each of these sorts of statements is intended to mean.  For example, does ‘may” in any given context mean just "not impossible” - which might be represented by showing that such a statement would be satisfiable - or something stronger - e.g. that the statement is true sufficiently often that we ought to be aware of the possibility.  Or perhaps something best represented by the inverse, e.g. “This type of rash is typically (necessarily?) caused by meningococcus” - where the deictic “this” might point to an image or criteria for distinguishing the rash.  Any terminology for Applied Ontology ought  ought to fit with a wider terminology for discussing knowledge and knowledge representation which allows us to discuss the  intended meaning of statements for an application and whether or not it is captured effectively by alternative representations.

i) And to have that discussion we of course need to have an agreed terminology for the different different sorts of  knowledge representation technology and formalisms available.

Hope we can make progress towards some of these goals.

Regards

Alan


The definition of 'ontology' that is at issue is the one expounded upon in the https://mitpress.mit.edu/building-ontologies book. I will of course be happy to amend it to accommodate future innovations, in true scientific spirit, when you tell me what they are. 
BS

On Tue, Aug 9, 2016 at 4:43 PM, John F Sowa <so...@bestweb.net> wrote:
On 8/7/2016 11:24 AM, Barry Smith wrote:
> The Smith-Ceusters definition on the Wiki confines ontologies to
> “Universals”

Such a restriction is anathema in science.  It's important to define
individual terms precisely.  But no definition of an entire field should
be so narrow that it rules out current practices and future innovations.

As a clear, general, and flexible definition, I suggest:

"A knowledge base has three components:  a logic for specifying the
form of what can be expressed, an ontology for specifying the subject
domain, and a database for collecting information about individuals
that exist or may exist within the specified domain."

This definition covers most, if not all current ontologies, DBs, and
KBs.  It imposes no restrictions on the choice of logic, the choice
of definitions and axioms in the ontology, the contents of the DB,
or the choice of philosophical jargon for talking about ontology.

John


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-------------------
Alan Rector
Professor of Medical Informatics (emeritus)
School of Computer Science
University of Manchester
Manchester M13 9PL, UK

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