Learning how to use conceptual graphs

[Patrick Browne]

I am studying Conceptual Graphs (CGs) with a view to using them in my research as a visual presentation of First Order Logic with equality (FOL=).
I have posted two questions, Question 1  and  Question 2,  to AI StackExchange.

In his seminal book (page 86), Sowa provides a mapping  Φ from CGs to FOL. I also require a mapping Φ inverse. This is more difficult than I first thought due to the differing structuring mechanisms in the sources and targets of the mappings for my particular case. I am using CafeOBJ to present FOL theories, where structuring is based on the Theory of Institutions (TOI).  From my limited knowledge of CGs it seems that the concepts are structured using a Lattice of Theories.  

Obviously, members of this forum would be in a unique position to answer such questions. Any assistance would be greatly appreciated and would help remove my misconceptions.

Regards,
Patrick Browne

[Alex Shkotin]

Hi Patrick,

Very interesting study! What is the motivation for FOL visualization?

Am I right that not every FOL formula has CG representation?

What about rewriting axioms with NOT and EXIST like this

¬∃x ¬part(x,x)

as as far as I know NOT and EXIST available in CG.

What is your project about?  Are you in math or in physics?

In math I am with Euclid: "5. The whole is greater than the part."

Good luck,

Alex 

сб, 1 янв. 2022 г. в 14:46, Patrick Browne <patrickb...@gmail.com>:

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[Patrick Browne]

Alex> What is the motivation for FOL visualization?

My primary motivation for using CGs is the hope that they could provide a simple means of presenting and structuring theories while retaining links to logic.

Such a visual presentation could potentially help explain my underlying CafeOBJ ontologies and programs. My intended audience are earth scientists and Geo-scientists, so I want to avoid to much TOI. 

Alex> Am I right that not every FOL formula has CG representation?

From Sowa's Conceptual Graph Summary: "The ISO standard conceptual graphs express the full semantics of Common Logic (CL)"

Alex>   What about rewriting axioms with NOT and EXIST like this

Alex> ¬∃x ¬part(x,x)

Alex> as as far as I know NOT and EXIST available in CG.

Yes, I am aware of this and the equivalence to  ∀x part(x,x) . But I would like to stick with the common logic use of universal and existential quantifiers.

So I would like to use ∀if possible.

Regards,

Pat

[John F Sowa]

Patrick and Alex,

 

There is no such thing as a one-size-fits all notation for logic.  Some people prefer graphic notations, some prefer linear notations, and some prefer notations that have various computational properties for various purposes.

 

For an overview of  the many notations and the mappings among them, see the slides for the article I presented at the European Semantic Web Conference in June 2020:  http://jfsowa.com/talks/eswc.pdf

 

In those slides, I summarize a wide range of issues about various notations for Common Logic and various subsets.  Among those subsets are first-order logic (FOL), the Semantic Web logics, all of which are subsets of FOL, the TPTP logics (for Thousands of Problems for Theorem Provers, and the logics of the HeTS system , which provides freely downloadable software that can be used to relate all of them to one another and to derive proofs for problems stated in any of them.  Those slides contain many URLs for links to documentation for the many, many issues.

 

In those slides, I recommended four kinds of notations that can be used to represent full Common Logic (and any subset or superset thereof):  (1) CLIP (Common Logic Interface to Predicate Calculus) as  a concise and readable notation that is easy to translate to any of the other notations as well as predicate calculus.  (2) EGs (existential graphs) a very simple, easy-to-learn graphic notation that has the full expressive power of CL and CLIP.  (3)  CGs (conceptual graphs) as extensions of EGs that are designed for mapping to and from natural languages.  (4) CNLs (Controlled natural languages, which are formally defined subsets of the languages that people speak.

 

There is much more to say about all these issues, but I recommend that people read (or at least flip through) the slides in eswc.pdf  for an overview.

 

Patrick:  My primary motivation for using CGs is the hope that they could provide a simple means of presenting and structuring theories while retaining links to logic. Such a visual presentation could potentially help explain my underlying CafeOBJ ontologies and programs. My intended audience are earth scientists and Geo-scientists, so I want to avoid to much TOI.

 

Conceptual graphs are primarily designed for mappings between logic and natural languages.  They contain many features that are designed for linguistic issues.  For teaching logic to beginners, EGs are simpler..  For programmers who need a notation that is easy to process. CLIP is more convenient.  For people who want something more readable, CNLs are preferable.

 

Alex> Am I right that not every FOL formula has CG representation?

From Sowa's Conceptual Graph Summary: "The ISO standard conceptual graphs express the full semantics of Common Logic (CL)"

 

Since EGs and CGs can express full CL, they can very easily represent any subset of CL, which includes FOL and all the SW logics.

 

Alex>   What about rewriting axioms with NOT and EXIST like this

Alex> ¬∃x ¬part(x,x)

 

In CLIP, that statement would be written ~[ (∃x) ~(part x x)] .

 

To avoid going beyond the first 128 Unicode characters, it could also be written ~[(Exists x) ~(part x x)].

 

This notation is easy to translate to and from any other linear or graphic notation for logic.

 

The notation ∀x part(x,x) would be written in CLIP as (∀x) (part x x). It could also be written as (Every x) (part x x). Either of these notations could be automatically translated to ~[ (∃x) ~(part x x)] .

 

I'll write more later with references to more detailed discussions of these and other issues. But eswc.pdf is good for an overview.

 

John

[Alex Shkotin]

Patrick,

It is great you are in Geology! Do you have something to read?

Our last results are in [1]. What do you think?

Alex

[1] https://www.researchgate.net/publication/51910491_Towards_OWL-based_Knowledge_Representation_in_Petrology

вс, 2 янв. 2022 г. в 15:03, Patrick Browne <patrickb...@gmail.com>:

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[Alex Shkotin]

John,

Thank you for the important fact that EG and CG are as powerful as FOL. I should write it on my cortex:-)

Let me mention that I am personally for HOL, keeping these facts in my mind:

a) FOL is not enough even for math. For example, let us look in [1] where nx means x+...+x n times (see p.15).

On p.16 we have the definition "An abelian group G is a periodic group iff ∀x∃n≥1 [nx=0]."
And on p.17 we have this nice result: "Therefore, the class of periodic groups cannot be characterized even by the set of first-order axioms - finite or infinite."

b) OWL2 is a subset of HOL language. For example in OWL2 Functional Style, we have proposition [2]

SubClassOf( C1 C2 )
where C1 C2 are unary predicates, i.e. SubClassOf is a binary predicate on unary predicates - this is a HOL language feature.

c) Natural Language is a HOL language by its nature. As we know from Richard Montague. What a pity Barbara Partee forgot to join us. For example, let us look at the proposition we discussed some time ago.

The cat is on the mat.
((the cat) (is on) (the mat)).
"the" is a unary operator,
"on" is a unary operator applied in postfix form - after an argument,
"is" is a binary predicate applied in infix form - between arguments.
If we take canonical function usage (an arguments after function) we get HOL in Functional Style, but boring:
(on(is))((the(cat) the(mat))

Any formal language is fine if we have a processor for this language to work with its statements not manually, but on a computer:-)

But I do not exclude meditation on the diagram;-) I like it! But I know that any diagram from UML to CG can be written in the linear language to be processed on a computer.

As far as I know, CL is expressible on CASL, but not visa versa.

Alex


[1] Part I Model theory, Handbook of mathematical logic, J. Barwise (Ed.), 1977

[2] https://www.researchgate.net/publication/336363623_OWL_2_Functional_Style_operators_from_HOL_point_of_view

пн, 3 янв. 2022 г. в 07:30, John F Sowa <so...@bestweb.net>:

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[Patrick Browne]

Alex> Do you have something to read?

I have no publications in this area, I based my research on GIS papers such as Paper 1 , Paper 2, and Paper 3 .

I am working on improving the Haskell representation which is used in such papers.

Pat

[Patrick Browne]

John,Alex,

JFS> There is no such thing as a one-size-fits all notation for logic.  

Yes. I already have reasonable mechanical presentations of First Order and Equational logics in CafeOBJ, but I need to augment this with simpler more intuitive notation. I was hoping that CGs could provide a simple way to present basic logical sentences, theories, sub-theories, super-theories, and models.

JFS> For an overview of  the many notations and the mappings among them, see the slides
I have studied the slides. My work is aimed at producing a set of research tools for use in ontological research in the domain of Geographic Information.
I do not consider the actual deployment of systems. Instead I focus on the construction of ontologies and the development of simple prototype programs based on those ontologies.  This approach is in line with a long tradition of algebraic specification within GI-Science (e.g. A Paper from Werner Kuhn ).
DOL is an obvious approach to ontologies, models, and specifications but for my purpose it lacks the directly executable initial algebras of CafeOBJ.
CafeOBJ provides a sorted first order theorem prover similar to PROVER9, which approximates Common Logic, together with an executable order sorted algebra (OSA). I am trying to retain much of the simplicity of the current approach that uses Haskell as an ontology design language.

The Questions:
I think that my problems in Question 1 and Question 2 stem from my lack of understanding the meanings of the terms concept, type, theory, and model in the context CGs. For further posts, I will try to develop a better contextual understanding these terms.

Regards,

Pat

[Alex Shkotin]

Pat,

Ontology on Haskell sounds very interesting for my weekend:-) Is there any chance to look at it?

It is a pity your domain is Geography - not Geology!

Anyway, do you keep in mind to convert your ontology to OWL2 and add to https://obofoundry.org/? 

As now they have a situation like this http://www.ontobee.org/search?ontology=OMIT&keywords=Geograph&submit=Search+terms

Regards,

Alex

вт, 4 янв. 2022 г. в 15:54, Patrick Browne <patrickb...@gmail.com>:

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[Matteo Bianchetti]

Hi Alex, 

I am unable to check out the reference to Barwise's book but you can develop the whole theory of groups in ZFC which is a FOL theory (with infinitely many axioms because of Comprehension). Could you explain what Barwise meant by that sentence? 

Even more interestingly, in this list, I frequently read about comparing FOL and HOL. However, the two notions are partly ambiguous. FOL means that you can quantify over individuals only, but nothing prevents you to take individuals to be sets (i.e. properties and relations). This is why, in ZFC (again, a FOL theory), we can prove the categoricity of a Dedekind-Peano structure (a structure saying that 0 is a number and not the successor of any number; the successor function is 1-1; and, if a subset S of the domain contains 0 and the successor of every number, then the domain is a subset of S). The key is that the last condition (the induction axiom) is a first-order axiom in ZFC even if it quantifies over sets. However, if you take numbers as individuals and exclude sets, you cannot write the induction axiom and, in FOL, you need infinitely many induction schemata. For this reason, in this context, you lose categoricity in FOL and you can regain it in HOL.

This is an interesting read. I myself do not know enough about this and will be happy to get more insights from others, but the bottom line is that just saying FOL and HOL without saying what counts as individuals and sets is not enough to compare the two types of logic.

Many thanks,

Matteo

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[Alex Shkotin]

Hi Matteo,

I have this book in Russian translation on my bookshelf and I think the initial English version is this [1]. 

But let me point that I am not developing something - I just cited a theorem. If you would like to refute this theorem in ZFC it would be great.

About HOL and FOL we should keep separately logic and language. But tomorrow:-)

And maybe CL is just kind of HOL;-) 

Maybe it is possible to say that any language with numbers is more or less HOL one.

Alex

[1] https://www.worldcat.org/title/handbook-of-mathematical-logic/oclc/2347202

вт, 4 янв. 2022 г. в 17:32, Matteo Bianchetti <mttb...@gmail.com>:

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[Matteo Bianchetti]

Hi Alex, 

Thanks. I was only asking what the meaning of "characterized in FOL" was in that theorem. Anyway, I found the 1993 version of that book and on p. 9 it says what you quoted above (replacing "period" with "torsion"). If I understand, what Barwise points out is similar to the Induction axiom (or schema). It is a single FOL axiom if you count sets as individuals. Similarly, in the period (torsion) formula, one quantifies over the set of natural numbers ( is a shortcut for , where is another shortcut for a set being the domain of a Dedekind-Peano structure). This is first-order in ZFC. Happy if someone can explain more or better though.

Many thanks,

Matteo 

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[doug foxvog]

On Mon, 3 Jan 2022 at 04:53, Alex Shkotin <alex.s...@gmail.com> wrote:

>...

> c) Natural Language is a HOL language by its nature. As we know from
> Richard Montague. What a pity Barbara Partee forgot to join us. For
> example, let us look at the proposition we discussed some time ago.
> The cat is on the mat.
> ((the cat) (is on) (the mat)).

This is a problematic way of treating "on". On is an operator for "the
mat", not for "is". The "is" here is a binary operator relating the
subject to the object.
(is-located (the cat) (on (the mat))).

Note we could broaden the English to
"The cat is in the hall on the mat."
(is-located (the cat) (and (in (the hall)) (on (the mat))).
If we reverse the prepositions, the meaning is different, locating the mat
as being in the hall. The above sentence allows the mat to be partially
in the hall, so the meanings are different.

"The cat is on the mat in the hall."
(is-located (the cat)
(on (the-with-property !mat (is-located !mat (in (the hall))).

> "the" is a unary operator,
> "on" is a unary operator applied in postfix form - after an argument,

I beg to differ. "on" is a prefix unary operator, with the value of the
operation being a location - above and touching its argument.

-- doug foxvog

> "is" is a binary predicate applied in infix form - between arguments.
> If we take canonical function usage (an arguments after function) we get
> HOL in Functional Style, but boring:
> (on(is))((the(cat) the(mat))

> ...
> Alex

>>> <http://www.jfsowa.com/cg/cgif.htm>:

[Patrick Browne]

 Hi,

 I have posted some additional questions concerning the basic representation of logical sentences  and "structuring" of Conceptual Graphs (Q1,Q2,Q3,Q4) to various StackExchange forums.

 Perhaps someone from this forum could comment or answer these questions within the StackExchange forum itself.

 This may help spread knowledge on ontological topics to a wider audience.
 
 Regards,
 Pat

[Robert Goldman]

A little nitpicking:

On Monday, January 3, 2022 at 3:53:51 AM UTC-6 alex.shkotin wrote:

b) OWL2 is a subset of HOL language. For example in OWL2 Functional Style, we have proposition [2]

SubClassOf( C1 C2 )
where C1 C2 are unary predicates, i.e. SubClassOf is a binary predicate on unary predicates - this is a HOL language feature.

I take it from the above that you don't mean simply  "OWL2 is a subset of HOL language." which is trivially true, but that you are claiming that OWL2 lies inside HOL but outside FOL.

I don't believe that this claim is correct, based on the above. If "SubClassOf(C1 C2)" is simply shorthand/a macro for ∀x C1(x) → C2(x) then this is not second order logic. In order for it to be second order, we would need to be able to quantify over classes/predicates, so we would need to be able to say something like "∀C Foo(C) → SubClassOf(C FooClass)" which I do not believe we can do in OWL.

My understanding is that OWL is, in fact a subset of FOL, but I can't point to a citation; this isn't really my field of expertise.

[Pascal Hitzler]

OWL DL is indeed (mostly) a fragment of first-order predicate logic with
counting quantifiers.

If you need a reference:

Pascal Hitzler, Markus Krötzsch, Sebastian Rudolph
Foundations of Semantic Web Technologies.
Textbooks in Computing, Chapman and Hall/CRC Press, 2010.

Pascal.

On 1/5/2022 9:54 AM, Robert Goldman wrote:
>
> A little nitpicking:
>
> On Monday, January 3, 2022 at 3:53:51 AM UTC-6 alex.shkotin wrote:
>
>
> b) OWL2 is a subset of HOL language. For example in OWL2 Functional
> Style, we have proposition [2]
> SubClassOf( C1 C2 )
> where C1 C2 are unary predicates, i.e. SubClassOf is a binary
> predicate on unary predicates - this is a HOL languagefeature.
>
>
> I take it from the above that you don't mean simply  "OWL2 is a subset
> of HOL language." which is trivially true, but that you are claiming

> that OWL2 lies inside HOL but /outside /FOL.

>
> I don't believe that this claim is correct, based on the above. If
> "SubClassOf(C1 C2)" is simply shorthand/a macro for ∀x C1(x) → C2(x)
> then this is not second order logic. In order for it to be second order,
> we would need to be able to quantify over classes/predicates, so we
> would need to be able to say something like "∀C Foo(C) → SubClassOf(C
> FooClass)" which I do not believe we can do in OWL.
>
> My understanding is that OWL is, in fact a subset of FOL, but I can't
> point to a citation; this isn't really my field of expertise.
>

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--
Pascal Hitzler
Lloyd T. Smith Creativity in Engineering Chair
Director, Center for AI and Data Science
Kansas State University http://www.pascal-hitzler.de
http://www.daselab.org http://www.semantic-web-journal.net

[Robert Goldman]

A quick follow up:

From "A prototypical OWL Full Reasoner based on First-Order Reasoning" by Michael Schneider:

"Translation into First-Order Logic. Since the semantic conditions of OWL 2 Full have the form of FOL formulae, its semantics can directly be axiomatisized  [sic] as a FOL theory. Further, every RDF graph can be written as a FOL axiom consisting of a conjunction of ternary atomic formulae, with existentially quantified variables for the blank nodes. The details of the translation can be found in [7]. As a concrete FOL syntax, we use the TPTP language [8], which is understood by the majority of existing FOL reasoners" (p. 2)

I would have thought it would be trivial to find a clear statement like this somewhere on the W3C site, but either it's not there, or my search skills were not sufficient to find it.

[Robert Goldman]

Right, and OWL Full is also a subset of FOL. I don't know off-hand if it is a proper subset or not.

[Pascal Hitzler]

I'm not sure if anybody other than Michael ever really looked at that,
to be honest.

Even just looking at RDFS as a logic is at least - weird, and OWL Full
includes all of RDFS. I'm not sure that perceiving OWL Full as a
language that can be somehow converted into predicate logic is all that
helpful. In the end, you can express any formal language (and many more
things) somehow using a formal logic. But this doesn't mean that the
perspective is always particularly useful.

Pascal.

On 1/5/2022 10:09 AM, Robert Goldman wrote:
> A quick follow up:
>

> From " <goog_1488095950>A prototypical OWL Full Reasoner based on
> First-Order Reasoning"
> <http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.306.7179&rep=rep1&type=pdf>

> by Michael Schneider:
>
> "Translation into First-Order Logic. Since the semantic conditions of
> OWL 2 Full have the form of FOL formulae, its semantics can directly be
> axiomatisized  [sic] as a FOL theory. Further, every RDF graph can be
> written as a FOL axiom consisting of a conjunction of ternary atomic
> formulae, with existentially quantified variables for the blank nodes.
> The details of the translation can be found in [7]. As a concrete FOL
> syntax, we use the TPTP language [8], which is understood by the
> majority of existing FOL reasoners" (p. 2)
>
> I would have thought it would be trivial to find a clear statement like
> this somewhere on the W3C site, but either it's not there, or my search
> skills were not sufficient to find it.
>
>
> On Wednesday, January 5, 2022 at 9:54:23 AM UTC-6 Robert Goldman wrote:
>
>
> A little nitpicking:
>
> On Monday, January 3, 2022 at 3:53:51 AM UTC-6 alex.shkotin wrote:
>
>
> b) OWL2 is a subset of HOL language. For example in OWL2
> Functional Style, we have proposition [2]
> SubClassOf( C1 C2 )
> where C1 C2 are unary predicates, i.e. SubClassOf is a binary
> predicate on unary predicates - this is a HOL languagefeature.
>
>
> I take it from the above that you don't mean simply  "OWL2 is a
> subset of HOL language." which is trivially true, but that you are

> claiming that OWL2 lies inside HOL but /outside /FOL.

>
> I don't believe that this claim is correct, based on the above. If
> "SubClassOf(C1 C2)" is simply shorthand/a macro for ∀x C1(x) → C2(x)
> then this is not second order logic. In order for it to be second
> order, we would need to be able to quantify over classes/predicates,
> so we would need to be able to say something like "∀C Foo(C) →
> SubClassOf(C FooClass)" which I do not believe we can do in OWL.
>
> My understanding is that OWL is, in fact a subset of FOL, but I
> can't point to a citation; this isn't really my field of expertise.
>

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[Pascal Hitzler]

I'm not so sure about the "subset". It's perhaps a subset somewhat in
the sense in which C++ is a subset of machine code :)

Pascal.

On 1/5/2022 10:10 AM, Robert Goldman wrote:
> Right, and OWL Full is /also /a subset of FOL. I don't know off-hand if
> it is a /proper/ subset or not.

> <https://groups.google.com/d/msgid/ontolog-forum/7c78b665-73c4-41bd-8de5-cb6b83bb172cn%40googlegroups.com?utm_medium=email&utm_source=footer

> <https://groups.google.com/d/msgid/ontolog-forum/7c78b665-73c4-41bd-8de5-cb6b83bb172cn%40googlegroups.com?utm_medium=email&utm_source=footer>>.
>
>
> --
> Pascal Hitzler
> Lloyd T. Smith Creativity in Engineering Chair
> Director, Center for AI and Data Science
> Kansas State University http://www.pascal-hitzler.de

> <http://www.pascal-hitzler.de>
> http://www.daselab.org <http://www.daselab.org>
> http://www.semantic-web-journal.net
> <http://www.semantic-web-journal.net>

>
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[Robert Goldman]

On 5 Jan 2022, at 10:17, 'Pascal Hitzler' via ontolog-forum wrote:

> I'm not so sure about the "subset". It's perhaps a subset somewhat in
> the sense in which C++ is a subset of machine code :)

Exactly! Michael's translation (I am assuming it is correct) from OWL
Full to FOL shows that OWL Full is a subset of FOL, but does not show
th e converse, that FOL is contained in OWL Full...

This sounds like an interesting question but... not what I am paid to
work on!

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[John F Sowa]

Re the many, many notations for logic:  Please note the eswc.pdf slides, which discuss the OMG standard for DOL, which relates a wide range of logics, including the many representations for the Semantic Web and for the formalized versions of UML:  http://jfsowa.com/talks/eswc.pdf

 

The OMG standard for DOL is far more important for interoperability than the ISO standard for ontology.  I strongly urge people to review it.  Section 2 of the eswc.pdf slides provides a short overview of DOL and references.

 

I have been tied up with other issues, and I'll send another note on this topic later.

 

John

[Elisa Kendall]

John -

Thanks very much for the support for DOL.  We have started working on revisions, so if you or anyone who reviews it has feedback for us, you can send it to me directly or to iss...@omg.org, citing the DOL standard (and section if possible) to raise an issue against it. It is freely available at https://www.omg.org/spec/DOL/.  The specification document, metamodel, and an informative ontology are all posted there.  There is also a recent presentation that talks about DOL and the HETS implementation, among other things, from last March at https://ontocommons.eu/sites/default/files/tm.pdf.

DOL and Hets - Tools for modular and heterogeneous ontologies DOLandHets-Toolsformodularand heterogeneousontologies TillMossakowski University of Magdeburg, Germany 2021-03-19 TillMossakowski DistributedOntology,ModelandSpecificationLanguage(DOL) 2021-03-19 1 ontocommons.eu

Also, we have recently published a standard for APIs for Knowledge Platforms, which is ontology driven and extends the DOL ontology.  Although it was approved for publication in March of last year, I'm not certain whether it and the related files (including ontologies, YAML files, IDL, etc.) are publicly available outside of members.  The APIs have been implemented at Mayo Clinic and Fraunhofer, and the specification is currently in what we call finalization.  See https://www.omg.org/spec/API4KP/.  We believe this is another really important piece of the puzzle, and would appreciate feedback on it as well.  A number of issues are outstanding, though, many of which are related to streamlining and simplifying the APIs and ontologies, so I would not consider it to be "baked" yet.  If anyone is interested and cannot get access via the link, above, please let me know.

Best regards,

Elisa

---

From: ontolo...@googlegroups.com <ontolo...@googlegroups.com> on behalf of John F Sowa <so...@bestweb.net>
Sent: Wednesday, January 5, 2022 12:47 PM
To: ontolo...@googlegroups.com <ontolo...@googlegroups.com>
Subject: Re: [ontolog-forum] Notations for Logic (was Learning how to use CGs

 

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[Alex Shkotin]

Very proper. This is why we have a practice to write FOL in annotations of OWL2-ontologies. see slide 18: "Common practice: annotate OWL ontologies with informal FOL" in the presentation given by @Elisa Kendall below or here

ср, 5 янв. 2022 г. в 19:10, Robert Goldman <rpgo...@gmail.com>:

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[Alex Shkotin]

Hi Patrick,

The place you choose is not very suitable - they deleted my comment. 

Anyway I think this may be interesting for you.

see here

Alex

ср, 5 янв. 2022 г. в 15:59, Patrick Browne <patrickb...@gmail.com>:

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[Patrick Browne]

Alex,

As I said in a previous post, the use of DOL/HETS is an obvious approach to multiple representations in the  ontological domain,  but for my purpose it lacks the directly executable initial algebras of CafeOBJ. Also it does not directly address the "structuring"  questions posed in (Q1,Q2,Q3,Q4).   Perhaps I am expecting too much from the basic CG notation and perhaps the structuring task should be carried out in a metal-language such as  graph-homomorphisms. Here is an example from Chein and Mugnier :

My computational, logical, and proof system is CafeOBJ which uses the Theory of Institutions (TOI-1,TOI-2, TOI-3) for the type of structuring  mentioned in (Q1,Q2,Q3,Q4).  I use two logics FOL and Equational Logic (EL). I am happy with the basic FOL/EL <-> CG mappings. So, I will probably use some "homemade" notation to relate CGs to TOI  for visual structuring diagrams . 

Regards,

Pat

[John F Sowa]

Elisa,

 

Thanks for the URL for the slides by Tilll Mosakowski:  

 

DOL and HETS: Tools for modular and heterogeneous ontologies,

https://ontocommons.eu/sites/default/files/tm.pdf

Note to everybody:  I strongly recommend Till's  info about DOL and HETS (Heterogeneous Tool Set).  The HeTS tools support the many notations for logic, including the TPTP logic for Thousands of Problems for Theorem Provers. 

 

The TPTP tools, many of which are available for free download are far and away faster than the tools designed for the Semantic Web.  The idea of lobotomizing logics (i.e., forcing them to be decidable)  does noting for performance.

 

For more info, see the note below by Elisa, and the copy of my original note below that.

 

John

---

From: "Elisa Kendall" <eken...@thematix.com>
Sent: Wednesday, January 5, 2022 5:07 PM

To: "ontolo...@googlegroups.com" <ontolo...@googlegroups.com>
Subject: Re: [ontolog-forum] Notations for Logic (was Learning how to use CGs

John -

 

Thanks very much for the support for DOL.  We have started working on revisions, so if you or anyone who reviews it has feedback for us, you can send it to me directly or to iss...@omg.org, citing the DOL standard (and section if possible) to raise an issue against it. It is freely available at https://www.omg.org/spec/DOL/.  The specification document, metamodel, and an informative ontology are all posted there.  There is also a recent presentation that talks about DOL and the HETS implementation, among other things, from last March at https://ontocommons.eu/sites/default/files/tm.pdf.

DOL and Hets - Tools for modular and heterogeneous ontologies

DOLandHets-Toolsformodularand heterogeneousontologies TillMossakowski University of Magdeburg, Germany 2021-03-19 TillMossakowski DistributedOntology,ModelandSpeci?cationLanguage(DOL) 2021-03-19 1 ontocommons.eu

[Ronald Stamper]

THIS SEEMS TO HAVE BEEN LOST.  APOLOHIRD IF BEEING RESENT.  [SORRY: P99R SIGHT]

Dear Patruc,  Personally, unless working on fiction, I ask “Please take my by the hand and show me what you are talking about.”  The arcs and edges connecting your nodes will also elicit a simian request, because there is then a good chance the graph will tell us something interesting about the world, unless, of course, the part of the world you are concerned with, happens the associations in the minds of each person who supplies those links. You could fold the links favoured by people from different sub .  

On 1 Jan 2022, at 11:46, Patrick Browne <patrickb...@gmail.com> wrote:

I am studying Conceptual Graphs (CGs) with a view to using them in my research as a visual presentation of First Order Logic with equality (FOL=).
I have posted two questions, Question 1  and  Question 2,  to AI StackExchange.

In his seminal book (page 86), Sowa provides a mapping  Φ from CGs to FOL. I also require a mapping Φ inverse. This is more difficult than I first thought due to the differing structuring mechanisms in the sources and targets of the mappings for my particular case. I am using CafeOBJ to present FOL theories, where structuring is based on the Theory of Institutions (TOI).  From my limited knowledge of CGs it seems that the concepts are structured using a Lattice of Theories.  

Obviously, members of this forum would be in a unique position to answer such questions. Any assistance would be greatly appreciated and would help remove my misconceptions.

Regards,
Patrick Browne

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