Hi All,
The discussion on category theory has been excellent. My take away is that It has a strong mathematical base but an almost zero level of usage.
Some answers may be found at: https://otterserver.com/category/catalog-for-knowledge-documents/
Tom
Sent from Mail for Windows 10
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The discussion and presentation on ontolog sounds a lot like what has been done for the “DOL” (Distributed Ontology, Model, and Specification Language Specification) standard at OMG. (Not that I understand all the math).
DOL: http://www.omg.org/spec/DOL
Ontolog: http://ontologforum.org/index.php/ConferenceCall_2018_01_24
-Cory
Pat,I count on finite models of Description Logics.Alex2018-01-29 21:49 GMT+03:00 Pat Hayes <pha...@ihmc.us>:AlexI think we are talking at cross purposes. At any rate, you do not seem to be using “model” in the sense of model theory, ie an interpretation which makes a theory true, so I should not comment on your postings any further.Best wishesPat HayesOn Jan 29, 2018, at 7:15 AM, Alex Shkotin <alex.s...@gmail.com> wrote:Pat,We use a finite model of rational numbers - something like the algebra of numbers modulo 10^20.Any DB may be seen as a finite model but not very math.Some finite categories mentioned on the last meeting are finite models for us.What is a model? We may ask it instead of reality and get the same answer. Math models are cheaper than physical and more robust than DBs.Alex2018-01-27 23:54 GMT+03:00 Pat Hayes <pha...@ihmc.us>:
> On Jan 25, 2018, at 7:27 AM, alex.shkotin <alex.s...@gmail.com> wrote:
>
> Hi All!
>
> 1) Sometimes I think it's better not to use word "ontology" at all. And try to substitute "formal theory" or "finite model" instead. And only if some formal text keeps together elements of formal theory and finite model we should use word ontology;-)
Finite model? In what sense of ‘model’? Many formal theories don’t have finite models in the sense of ‘model thoery', and shouldn’t have them. Arithmetic, for instance. But perhaps (?) you mean some other sense of ‘model’ ?
Pat
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In my experience engineers and logicians use the term "model" very differently. Engineers develop models for systems under design or analysis, perhaps in OWL or UML. If formalized the model becomes an axiom set used to reason about the interpretations in the physical or a simulated world. Logicians speak of the interpretations of axiom sets as models. So when this is formalized one has
axiom set <-> engineer's model
logician's model <-> engineer's interpretation. Interpretations include simulations of engineer's models.
- Henson
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In my experience engineers and logicians use the term "model" very differently. Engineers develop models for systems under design or analysis, perhaps in OWL or UML. If formalized the model becomes an axiom set used to reason about the interpretations in the physical or a simulated world. Logicians speak of the interpretations of axiom sets as models. So when this is formalized one has
axiom set <-> engineer's model
logician's model <-> engineer's interpretation. Interpretations include simulations of engineer's models.
- Henson
From: ontolo...@googlegroups.com <ontolog-forum@googlegroups.com> on behalf of Jack Hodges <jhodg...@gmail.com>
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Alex,
I agree with what you are saying. One needs to distinguish between a theory and interpreted statements about the system that the theory is intended to describe.
A typical engineering problem is to modify a product to have some new capability. The typical scenario is to build an engineering model of the product and its operating environment in a modeling language such as UML. One then attempts to determine consequences from the combined product-operation context model and construct simulation code from the model and execute it to better determine the modified system behavior. One also may operate some modified product and collect data for the same purpose. Generally this results in revision and refinement of the engineering model. For an example see https://scholar.google.com/scholar?oi=bibs&cluster=8615220581478398249&btnI=1&hl=en
If you view this engineering activity within a standard logic formalism paradigm, the model is an axiom set, the conclusions derived from the model are statements in the theory of the axiom set, and the simulations, as well as the product operation scenarios are interpretations of the theory.
I am suggesting that the logic paradigm is a good description of the engineering paradigm with of course the change in terminology, e.g., engineering model = axiom set. There are a lot of consequences from adoption of the paradigm. Here are three.
1. The kind of logic used is not given a prior. The kind of logic and form of the theories are determined by the test and evaluation methods accepted in the domain.
2. Physicists and philosophers often think that they are trying to build an axiom set which has a single unique (categorical) interpretation. For engineering the axiom sets that they build to describe systems generally have more valid interpretations than intended. This simply means that part of the engineer’s job is to determine what assumptions need to be added to an axiom set to constrain the possible interpretations to correspond with the physical world.
3. At some stage the engineer may need a meta theory in which he can represent object theories and their interpretations. This is likely the consequence of your statement.
Henson
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Alex,
I agree with what you are saying. One needs to distinguish between a theory and interpreted statements about the system that the theory is intended to describe.
A typical engineering problem is to modify a product to have some new capability. The typical scenario is to build an engineering model of the product and its operating environment in a modeling language such as UML. One then attempts to determine consequences from the combined product-operation context model and construct simulation code from the model and execute it to better determine the modified system behavior. One also may operate some modified product and collect data for the same purpose. Generally this results in revision and refinement of the engineering model. For an example see https://scholar.google.com/scholar?oi=bibs&cluster=8615220581478398249&btnI=1&hl=en
If you view this engineering activity within a standard logic formalism paradigm, the model is an axiom set, the conclusions derived from the model are statements in the theory of the axiom set, and the simulations, as well as the product operation scenarios are interpretations of the theory.
I am suggesting that the logic paradigm is a good description of the engineering paradigm with of course the change in terminology, e.g., engineering model = axiom set. There are a lot of consequences from adoption of the paradigm. Here are three.
1. The kind of logic used is not given a prior. The kind of logic and form of the theories are determined by the test and evaluation methods accepted in the domain.
2. Physicists and philosophers often think that they are trying to build an axiom set which has a single unique (categorical) interpretation. For engineering the axiom sets that they build to describe systems generally have more valid interpretations than intended. This simply means that part of the engineer’s job is to determine what assumptions need to be added to an axiom set to constrain the possible interpretations to correspond with the physical world.
3. At some stage the engineer may need a meta theory in which he can represent object theories and their interpretations. This is likely the consequence of your statement.
Henson
From: ontolo...@googlegroups.com <ontolog-forum@googlegroups.com> on behalf of Alex Shkotin <alex.s...@gmail.com>
Sent: Wednesday, January 31, 2018 7:02 AM
To: ontolog-forum
Subject: Re: [ontolog-forum] 2 ideas after our last meeting (2018.1.24)
Henson,
interpretation for logicians as I know is a function (usually recursive one) how to calculate some logical formulas on some math system (first of all - algebraic, second - categoric). If all axioms give True, the system is a model of this axioms.In Description Logics, they call an axiom anything from a theory statement (like "any human is mortal") to system statement (like "Socrates is a human.").Keeping theory and system statements separately should be very useful IMHO.
Alex
2018-01-30 22:41 GMT+03:00 henson graves <henson...@hotmail.com>:
In my experience engineers and logicians use the term "model" very differently. Engineers develop models for systems under design or analysis, perhaps in OWL or UML. If formalized the model becomes an axiom set used to reason about the interpretations in the physical or a simulated world. Logicians speak of the interpretations of axiom sets as models. So when this is formalized one has
axiom set <-> engineer's model
logician's model <-> engineer's interpretation. Interpretations include simulations of engineer's models.
- Henson
From: ontolo...@googlegroups.com <ontolo...@googlegroups.com> on behalf of Jack Hodges <jhodg...@gmail.com>
Henson,
A good analysis. Also consider the “forward engineering” scenario. For physical items this could be 3D printing a design. For a software system this could be producing software artifacts (A.K.A. Model Driven Architecture – MDA).
In both cases there is a “source model” (set of axioms) and a set of “production rules”, which can be thought of as “production axioms”.
There is an interesting difference between physical and software production – the 3D printed item is the final “real thing” in the world. Produced software is, of course, a real thing in the world but is also, essentially, a set of axioms describing the data and processes the software will process (this assumes software can be accepted as a set of axioms). So we have the “source model” (set of axioms) transformed by a transformation model/rule (set of axioms) producing software (set of axioms) that act on statements about the world. Those “statements about the world” are what logicians typically call models! Perhaps they are all models.
Of course the source model (set of axioms) can also be processed by a different set of axioms for the simulation paradigm you describe. That the same model can be interpreted with different axioms for different purposes points to the need for unifying semantics.
-Cory
From: ontolo...@googlegroups.com [mailto:ontolo...@googlegroups.com]
On Behalf Of henson graves
Sent: Wednesday, January 31, 2018 10:22 AM
To: ontolog-forum <ontolo...@googlegroups.com>
Subject: Re: [ontolog-forum] 2 ideas after our last meeting (2018.1.24)
Alex,
Alex,
The fact that different communities use the same terminology for very different things should not be the show stopper that it seems to be in this forum. Logicians have one set of terminology, engineers have another. They use the word model for different things. Since I occasionally talk to people of both communities, I often use the words engineering model or descriptive model for what engineers talk about and interpretation of a model for what logicians mean when they say model.
John,
Of course it doesn't make sense to talk about the axioms of a model in the Tarskian sense, but the way that engineers use the word model such as the design model for an aircraft, the design is an axiom set, and the intepretations are; model in the Tarskian sense of the word.
Henson
I have spent considerable building design and analysis models in various UML languages for both aircraft and molecules. I have also spent some time using OWL to build the same kind of "models" of aircraft and molecules. Of course these models are called axiom sets in OWL. My purpose was to see if OWL could be used in engineering model development as OWL of course provides reasoning and the UML languages do not. I was doing the same kind of activity in both cases. Same activity and artifacts, but different names.
The important thing to me seems to realize that the same activity is going own in both domains with different names. It seems not a point of real interest that the same names are used for different concepts.
I know pretty much what one finds in a book on model theory. It doesn't change what I am saying.
Henson
On Jan 31, 2018, at 11:19 AM, henson graves <henson...@hotmail.com> wrote:... It seems not a point of real interest that the same names are used for different concepts….
Alex,
The fact that different communities use the same terminology for very different things should not be the show stopper that it seems to be in this forum. Logicians have one set of terminology, engineers have another. They use the word model for different things. Since I occasionally talk to people of both communities, I often use the words engineering model or descriptive model for what engineers talk about and interpretation of a model for what logicians mean when they say model.
I don't see that Cory needs to change his terminology e.g., MDA. One doesn't have to conflate or confuse the concepts once one understands what is going on. What I have outlined is completely consistent with the Tarskian view point, and with what one finds in books on model theory.
I agree that engineer's models (aka axiom sets) are often somewhat different from the ones that logicians typically deal with and the interpretation theory (logician's model theory) has some interesting aspects that Cory mentions. But that only raises interesting issues for ontology discussion.
Henson
From: ontolo...@googlegroups.com <ontolog-forum@googlegroups.com> on behalf of Alex Shkotin <alex.s...@gmail.com>
Sent: Wednesday, January 31, 2018 9:58 AM
To: ontolog-forum
Subject: Re: [ontolog-forum] 2 ideas after our last meeting (2018.1.24)
Henson,
for me "the model is an axiom set" is not a good point of view as this should be a very special kind of axioms. It's better for me to think (as Tarski:-) that the model is math-structure satisfying some axioms.W need a special language to build math-structures by the way.What kind of math-structures engineers use to model their production it's another matter, but this structures (for example labeled graphs) are finite with numbers:-)
Alex
2018-01-31 18:21 GMT+03:00 henson graves <henson...@hotmail.com>:
Alex,
I agree with what you are saying. One needs to distinguish between a theory and interpreted statements about the system that the theory is intended to describe.
A typical engineering problem is to modify a product to have some new capability. The typical scenario is to build an engineering model of the product and its operating environment in a modeling language such as UML. One then attempts to determine consequences from the combined product-operation context model and construct simulation code from the model and execute it to better determine the modified system behavior. One also may operate some modified product and collect data for the same purpose. Generally this results in revision and refinement of the engineering model. For an example see https://scholar.google.com/scholar?oi=bibs&cluster=8615220581478398249&btnI=1&hl=en
If you view this engineering activity within a standard logic formalism paradigm, the model is an axiom set, the conclusions derived from the model are statements in the theory of the axiom set, and the simulations, as well as the product operation scenarios are interpretations of the theory.
I am suggesting that the logic paradigm is a good description of the engineering paradigm with of course the change in terminology, e.g., engineering model = axiom set. There are a lot of consequences from adoption of the paradigm. Here are three.
1. The kind of logic used is not given a prior. The kind of logic and form of the theories are determined by the test and evaluation methods accepted in the domain.
2. Physicists and philosophers often think that they are trying to build an axiom set which has a single unique (categorical) interpretation. For engineering the axiom sets that they build to describe systems generally have more valid interpretations than intended. This simply means that part of the engineer’s job is to determine what assumptions need to be added to an axiom set to constrain the possible interpretations to correspond with the physical world.
3. At some stage the engineer may need a meta theory in which he can represent object theories and their interpretations. This is likely the consequence of your statement.
Henson
From: ontolo...@googlegroups.com <ontolo...@googlegroups.com> on behalf of Alex Shkotin <alex.s...@gmail.com>
John
My view of your diagram is very close to yours. But the inability to recognize how engineering terminology has evolved in the last 50 years, perhaps improperly from your point of view, is causing an immense amount of unnecessary confusion. One wonders if propagating confusion is the point of this thread.
To attempt to explain the difference in terminology, how it arose, and see how engineers are beginning to employ a standard logic paradigm as depicted in your diagram consider the following engineering creation myth.
People in ancient times, before say 1985 proceeded pretty much like you describe. People use test and verbal language to describe things they want to build or analyze. They then often built prototypes often on reduced scale which most everybody called models. So far everything is exactly as you say. Then something happened over a course of the next several years. The engineers started replacing their verbal and text description with artifacts in languages such as UML and OWL. This didn’t happen overnight and was not successful overnight. The reasons should be of great interest to logicians and KRR folks. But after year 2000 things changed. Now these artifacts are becoming the authoritative source of information.
Reasoning from the artifacts are used to make design decisions; they are used to generate simulations which help understand properties of systems under design or analysis. Engineers called these new artifacts “models” which is certainly not in keeping with the terminology of the Tarskian tradition. Some engineers have realized that these artifacts, which they call models, are axiom sets or can be embedded as axiom sets in logic. The result of doing so gives some well-known tools from logic to apply to questions of correctness of reasoning and validity of simulations (interpretations in synthetic worlds). This development promises to fundamentally change the way engineering is done on a daily basis.
Unfortunately some people with a logic background get confused about the different use of terminiology, e.g., engineering model as axiom set and logical model as interpretation. Perhaps engineers should be chastised for calling their artifacts models, but they do. Perhaps “ model driven analysis”, “model based system engineering”, and “Unified Modeling Language” should be forced to change their names. Historically the engineering artifacts were as you describe. But now the term model is generally used in the engineering community to mean the diagrams which translate to axioms or are directly axiom sets. As I have said the interpretations of the engineering models are Tarskian models for the appropriate logic.
So while your diagram is ok, the gloss is incomplete in my opinion. The real unfortunate aspect is it seems to preclude logicians from understanding how engineering is beginning to almost be applied logic. I would like for logicians to understand this scenario and contribute to the developments in logic, model theory needed to obtain specific benefits from using this well-known paradigm as expressed in your diagram, as opposed to chasing one’s tail regarding the use of the word “model”.
Henson
Cory,
I have a real problem with this:
> In both cases there is a “source model” (set of axioms) and a set of “production rules”, which can be thought of as “production axioms”.
“Production rules” are transformation rules. The significant question for transformations is: What properties of the source do they preserve in the image? And, to some extent, their preservation capability may be limited by the differences in nature between the source milieu and the target milieu. A precise mathematical vector maps to an imperfect graphical display and to an even more imperfect physical cut line or deposition line. And as Pat pointed out, a mapping from an n-ary fact to RDF does not maintain the integral sense when viewed as a set of triples; that sense must be imposed on the RDF graph, but it is not present in the RDF milieu per se.
So, in what sense are “production”/”transformation” rules “axioms”? What is the nature of the logic in which they are “true”? The truth seems to be only that the target image is a representation of the source. And those are the kind of axioms we often call “simple facts”. The interesting axioms are those that enable one to reason about behaviors of the target entities in the target milieu from the facts and axioms that describe the behaviors of the source entities in the source milieu. That is: the preservation axioms and the mutation axioms (what is predictably different).
I have spent a large part of my life developing rule-based transformations in software (which is the nature of 90% of all software) and in machine control. They are all “algorithmic”, but it is not clear that any of them is “axiomatic”. And it is really important not to confuse those concepts.
-Ed
Jack,
If you start one, sign me up!
Sincerely,
Rich Cooper,
Rich Cooper,
Chief Technology Officer,
MetaSemantics Corporation
MetaSemantics AT EnglishLogicKernel DOT com
( 9 4 9 ) 5 2 5-5 7 1 2
From: ontolo...@googlegroups.com [mailto:ontolo...@googlegroups.com] On Behalf Of Jack Hodges
Sent: Friday, February 02, 2018 7:16 AM
To: ontolo...@googlegroups.com
Subject: Re: [ontolog-forum] 2 ideas after our last meeting (2018.1.24)
I would be interested in a moderated forum devoted to semantics and engineering. Perhaps a companion forum to ontolog so that these interesting philosophical, theoretical, and historical discussions can take place, here, and topics which are engineering specific can take place there, trying to keep them independent as much as practical.
Jack
Sent from my iPad
On Jan 30, 2018, at 11:41 AM, henson graves <henson...@hotmail.com> wrote:
In my experience engineers and logicians use the term "model" very differently. Engineers develop models for systems under design or analysis, perhaps in OWL or UML. If formalized the model becomes an axiom set used to reason about the interpretations in the physical or a simulated world. Logicians speak of the interpretations of axiom sets as models. So when this is formalized one has
axiom set <-> engineer's model
logician's model <-> engineer's interpretation. Interpretations include simulations of engineer's models.
- Henson
From: ontolo...@googlegroups.com <ontolo...@googlegroups.com> on behalf of Jack Hodges <jhodg...@gmail.com>
Ed,
Cory’s comments about axioms and production rules can be interpreted in the following way.
Engineering is transitioning from constructing artifacts in natural language to artifacts in UML and OWL. However, as axiom sets these artifacts are very weak as they generally have a lot more models (interpretations) than their constructors intended. Only gradually have engineers understood the implicit assumptions needed to constrain the valid models to what is intended. It takes a lot of work to identify and formalize this implicit knowledge. Some of us view these assumptions as the context of the axiom set. This usage of context is consistent with its use in logic and lambda calculus and other places.
What Cory refers to as production rules are rules used to construct simulation models for engineering and to generate code from “incomplete” artifacts used to generate software. These rules add information to the artifacts. However, this info should be and can be formalized and made part of the axiom set. This is necessary if one wants to reason correctly from the axiom sets to their interpretations. This is now a concern in engineering.
I don't think this view is really inconsistent with what you say.
Henson
On Feb 2, 2018, at 10:10 AM, John F Sowa <so...@bestweb.net> wrote:Pat and Mary-Anne,
I changed the subject line to include notes by both of you.
PJH["Pat's position"], which is not a ‘position’, but simply a fact.
Whoa! A fact about what? The physical world? Some publication?
If the latter, please cite the source. It was certainly not Tarski.
Note the title of Tarski's original paper (1933): "The concept of
truth in formalized languages." For example, "Schnee ist weiß"
if and only if snow is white. But then he said that the issues
about natural languages and the world are too vague and complex.
That paper only addressed the right-hand side (RHS) of mthworld.gif.
For the LHS, see the informal philosophical paper by Tarski (1944):
http://jfsowa.com/logic/tarski.pdf
PJHYour diagram is seriously misleading because it takes the matter
of how a ‘model’ (in any sense) can be approximation to a reality
– issues of degrees of precision, tolerance, approximation, accuracy
and so forth – outside the semantic framework of formal ontologies
and their semantics altogether.
I believe that the correct term is 'metalevel', not 'outside’.
Some excerpts from Tarski (1944), sections 20, 21, and 22:The most natural and promising domain for the applications of
theoretical semantics is clearly linguistics — the empirical study
of natural languages...
The relation between theoretical and descriptive semantics is analogous
to that between pure and applied mathematics, or perhaps to that between
theoretical and empirical physics... another important domain for
possible applications of semantics is the methodology of science; this
term is used here in a broad sense so as to embrace the theory of
science in general... The semantics of scientific language should be
simply included as a part in the methodology of science... One of the
main problems of the methodology of empirical science consists in
establishing conditions under which an empirical theory or hypothesis
should be regarded as acceptable...
As regards the applicability of semantics to mathematical sciences and
their methodology, i.e., to metamathematics, we are in a much more
favorable position than in the case of empirical sciences.
Formal mathematics is the only field for which Tarski (1944) claimed
that his definition of truth was directly applicable.
He didn't deny
that it could be extended, but his discussion implied that extensions
would be in the "methodology" -- i.e., metalevel.
PJHI have never seen anyone, including your good self, explain how
we can even begin to talk about the proposed relationship between
‘formal models’ and reality, if our semantic theories – that is,
model theories – stop before these matters can even be brought
into their scope.
It's a two-step mapping: In 1933, Tarski specified the RHS of
mthworld.gif. In 1944, he discussed the then current methodologies
for the LHS and admitted that they weren't formal.
I doubt that he
would approve of making them formal by magic: Waving your hand and
declaring "Presto-zingo, my domain consists of things in the world.”
That statement is OK as a hypothesis, but it's not an observation.
If you want a one-step mapping, look at fuzzy logic.
... I don't believe that the LHS can ever be
completely formal, because no system of measurement can be perfect.
MAWa cool formalisation of symbol grounding
http://www.benjaminjohnston.com.au/papers/formal.pdf
Symbol grounding addresses the LHS of mthworld.gif. Page 5
of the article discusses the informal issues:Representation units may or may not have any particular semantic
interpretation, and may be manipulated by rules (such as interaction
with the environment or hyper-computational systems) that are beyond
formal definition.
Yes. For humans, symbols are grounded by what Peirce called
"the gates" of perception and purposive action. Methods of
pattern recognition and robotics address those two gates, but
none of them can be completely formal at the points of contact.
On Feb 4, 2018, at 9:51 AM, John F Sowa <so...@bestweb.net> wrote:On 2/2/2018 6:43 PM, Pat Hayes wrote:Tarki’s account of truth conditions, now usually referred to
as ‘model theory’, characterizes the domain of an interpretation
as being a non-empty set containing the referents of symbols.
The *only* condition imposed by the theory on this set is that
it be non-empty... Ergo, it applies when the set contains real-
world entites. QED.
Nothing prevents you from having a set that consists of physical
entities. I'm just saying that such a set could not be the domain
of a Tarski-style model, but it might be isomorphic to the domain.
If you derive a model *for* a set of axioms, that model will consist
of mathematical objects.
If you derive it *from* observations of
the world, you get data that you can store in a computer. It might
resemble, represent, or be analogous to something in the world,
but a set of data is not physical.
As a simple example, let's take an axiom for which we don't
need a computer or even pencil and paper:
Axiom: There are three people in Pat Hayes' living room.
If you are one of them, I'm sure that you could verify that the
axiom is true of the current state just by looking. Testing that
axiom would be trivial.
But there is something between that axiom and the physical situation:
the occipital lobes in the back of your head, where a "mental image"
of the room and things in it is formed. There are also the temporal
lobes that recognize some things called people, the parietal lobes
for matching patterns, and the frontal lobes for reasoning, counting,
and saying "Yes!”
As you said above, "the domain of an interpretation [is] a non-empty
set containing the referents of symbols." For that example, the set
of referents are the people and the room.
But the image of those
referents and the process of verifying the axiom are performed on
patterns in your head. Psychologists such as Johnson-Laird would
call those patterns a "mental model”.
For a more complex theory and situation, you would need a more
elaborate specification, aided by pencil and paper or a computer.
That spec would be more specific than the axioms. It would contain
"data", such as diagrams, measurements, lists of parts and subparts...
Whether you call it a mental model, an engineering model, or a
Tarski-style model, there is always something data-like between
your axioms and the physical things or situation.
QED.
John
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> <Blocks.pdf>
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On Feb 5, 2018, at 11:29 AM, Gary Berg-Cross <gberg...@gmail.com> wrote:Pat, John, Nicola:To observe the obvious from time to time there are phrases used in these discussions (mathematical entities as one, I think) where there is a substantial potential for lines of argument to diverge based on what assumptions they come with.
But I did wonder if a big one is the meaning of the phrase "semantic mapping" in Pat's sentence below:Pat > Yes, of course the interpretation mapping itself is not part of the world being described: it is the semantic mapping from language expressions into that world. I hope nobody interpreted any thing I have said as disagreeing with this.Is this a mapping from the formal model or from a mental model?
It seems that John allows for both meanings from which the mapping is possible and Pat is using this more restrictively to the formal model.
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On Feb 5, 2018, at 10:32 PM, John F Sowa <so...@bestweb.net> wrote:Pat, Nicola, and Gary,
I believe that the following “blast"
is correct.
PatThe interpretation function is a mathematical construct in a semantic
metatheory. It does not need to have any method, formal or otherwise,
to “do” anything. It need not even be a computable function. We aren’t
talking about computer science here: there isn't any “accessing”
involved in the semantic theory.
Yes. A model may be infinite.
But it must be formally specified
by the kinds of mathematical methods
used to specify possibly infinite
sets and structures -- for example, the method of deriving a model from
a set of axioms.
But that derivation cannot give you a physical set.
At best, it will give you a set of symbols that may refer to the
elements in a physical set.[JFS] Tarski (1944) mentioned "mathematics and theoretical physics"
as suitable fields for applying formal semantics. (Section 6)
In Section 20, he discussed the difference between "empirical research"
and "theoretical semantics". The difference is that the empirical
(experimental) research is "concerned only with natural languages
and that theoretical semantics applies to these languages only with
certain approximation" -- as my mthworld.gif diagram shows.
[Pat] What Tarski means here is that the natural language involved is
itself too complicated for his semantic theory to apply to it exactly.
Natural language, even when used in science, has semantic content which
cannot be fully captured by simple model theory.
No. That is not what Tarski said or implied. In fact, Tarski said
that NLs were *easier* to deal with than "natural sciences, such as
physics, biology, etc." Some excerpts:
[Section 20] The most natural and promising domain for the application
of theoretical semantics is clearly linguistics...
It is perhaps unnecessary to say that semantics cannot find any direct
applications in natural sciences such as physics, biology, etc.; for
in none of these sciences are we concerned with linguistic phenomena...
[Section 21] Besides linguistics, another important domain for
possible applications of semantics is the methodology of science;
this term is used here in a broad sense so as to embrace the theory
of science in general. Independent of whether a science is conceived
merely as a system of statements or as a totality of certain statements
and human activities, the study of scientific language constitutes an
essential part of the methodological discussion of a science...
One of the main problems of the methodology of empirical science
consists in establishing conditions under which an empirical theory
or hypothesis should be regarded as acceptable.
That methodology involves metalanguage about how to derive information
by observation and experimentation and using that info to specify the
axioms for which a model of the world may be derived.
Now let me go back to the following claim from a week ago
PatYour diagram is seriously misleading because it takes the matter
of how a ‘model’ (in any sense) can be approximation to a reality
– issues of degrees of precision, tolerance, approximation, accuracy
and so forth – outside the semantic framework of formal ontologies
and their semantics altogether.
No. See the above points by Tarski (1944): Theoretical physics is
a suitable domain for formal semantics, but "It is perhaps unnecessary
to say that semantics cannot find any direct applications in natural
sciences such as physics, biology, etc.”
By "natural science", he means the practice of observing, analyzing,
formulating hypotheses, testing them, and repeat. That is the
"methodology of science". The results of that methodology are the
theories of theoretical physics, which is suitable for formal semantics.
Pat[How can we] even begin to talk about the proposed relationship
between ‘formal models’ and reality, if our semantic theories –
that is, model theories – stop before these matters can even be
brought into their scope.
Very simply. Tarski used ordinary language supplemented with GOFFOL
(Good Old Fashioned FOL) to present his publications about model theory.
In his 1944 paper, he talked about these issues in a very informal way.
For related comments by Halmos, Einstein, Polya, Euler, and Laplace,
see slides 3 to 8 of http://jfsowa.com/talks/ppe.pdf
NicolaThe simple theory shown in the example is intended to axiomatize
the relation “on” holding among blocks... However, the theory can’t
distinguish between the actual real-world situations shown to the right.
That example illustrates the points that Tarski made about empirical
science. At that level of detail, The English description is just as
precise as the FOL formulas. But the real world is a continuum that
allows uncountably many options. The vagueness is not the fault of NLs,
but of any attempt to limit continuity to discrete options.
GaryIs this a mapping from the formal model or from a mental model?
It seems that John allows for both meanings from which the mapping
is possible and Pat is using this more restrictively to the formal
model.
I'll let Pat answer for himself. I'll go with the mathematician
Paul Halmos who said, in a passage I quoted on slide 3 of ppe.pdf,Mathematics — this may surprise or shock some — is never deductive
in its creation. The mathematician at work makes vague guesses,
visualizes broad generalizations... the deductive stage, writing
the result down, and writing its rigorous proof are relatively
trivial once the real insight arrives.
I would say that what goes on in the mathematician's head could be
called a "mental model". See the later slides in ppe.pdf.
Re mthworld.gif: After rereading Tarski (1944), I'm more convinced
than ever that my diagram is consistent with that article:
http://jfsowa.com/logic/tarski.htm
Pat, if you're not convinced, please quote any passage by Tarski
that conflicts with the diagram.
John
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John
John and Mary-Anne,
John wrote:
For "commonsense ontologies", the situation is far worse than
physics. That's why we have been talking about contexts.
In the summit talks, speakers have stated various definitions.
But when you analyze them, they all have a similar implication:
"A context is whatever you or somebody else says it is."
John
Another way to put this is that the observer is subjective, and the ontologizer is subjective, and the context selected by either is strongly affected by their individual experiences, yet ontologies are expected to be universal, objective, transferrable. Bad assumption in the first place.
Sincerely,
Rich Cooper,
Rich Cooper,
Chief Technology Officer,
MetaSemantics Corporation
MetaSemantics AT EnglishLogicKernel DOT com
( 9 4 9 ) 5 2 5-5 7 1 2
http://www.EnglishLogicKernel.com
From: ontolo...@googlegroups.com [mailto:ontolo...@googlegroups.com] On Behalf Of Mary-Anne Williams
Sent: Monday, February 12, 2018 12:47 PM
To: ontolo...@googlegroups.com
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John and Mary-Anne,
John wrote:
For "commonsense ontologies", the situation is far worse than
physics. That's why we have been talking about contexts.
In the summit talks, speakers have stated various definitions.
But when you analyze them, they all have a similar implication:
"A context is whatever you or somebody else says it is."
John
Another way to put this is that the observer is subjective, and the ontologizer is subjective, and the context selected by either is strongly affected by their individual experiences, yet ontologies are expected to be universal, objective, transferrable. Bad assumption in the first place.
Sincerely,
Rich Cooper,
Rich Cooper,
Chief Technology Officer,
MetaSemantics Corporation
MetaSemantics AT EnglishLogicKernel DOT com
( 9 4 9 ) 5 2 5-5 7 1 2
http://www.EnglishLogicKernel.com
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Mary-Anne,
So, given that we agree on the subjectivity of all participants in ontology, perhaps we should treat ontology as an art, rather than as a scientific, or universal, representation of knowledge. The influence of an ontology's author is very personal, very much in tune with that person's experience. The same is true of literature, art, music, and the many expressions of human knowledge.
Sincerely,
Rich Cooper,
Rich Cooper,
Chief Technology Officer,
MetaSemantics Corporation
MetaSemantics AT EnglishLogicKernel DOT com
( 9 4 9 ) 5 2 5-5 7 1 2
http://www.EnglishLogicKernel.com
From: ontolo...@googlegroups.com
[mailto:ontolo...@googlegroups.com] On Behalf Of Mary-Anne Williams
Sent: Monday, February 12, 2018 2:01 PM
To: ontolo...@googlegroups.com
Subject: Re: [ontolog-forum] Models and symbol grounding
I agree Rich.
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art is science and conversely!
Mary-Anne,
That link:
https://www.lucs.lu.se/spinning/categories/dynamics/Williams/surprise
brings up a blank browser window, but nothing more than that. Perhaps the URL needs correction?
Sincerely,
Rich Cooper,
Rich Cooper,
Chief Technology Officer,
MetaSemantics Corporation
MetaSemantics AT EnglishLogicKernel DOT com
( 9 4 9 ) 5 2 5-5 7 1 2
http://www.EnglishLogicKernel.com
From:
ontolo...@googlegroups.com [mailto:ontolo...@googlegroups.com] On
Behalf Of Mary-Anne Williams
Sent: Monday, February 12, 2018 3:08 PM
To: ontolo...@googlegroups.com
Subject: Re: [ontolog-forum] Models and symbol grounding
On 13 February 2018 at 10:04, Mary-Anne Williams <Mary...@themagiclab.org> wrote:
art is science and conversely!
On 13 February 2018 at 09:17, Rich Cooper <metase...@englishlogickernel.com> wrote:
Mary-Anne,
So, given that we agree on the subjectivity of all participants in ontology, perhaps we should treat ontology as an art, rather than as a scientific, or universal, representation of knowledge. The influence of an ontology's author is very personal, very much in tune with that person's experience. The same is true of literature, art, music, and the many expressions of human knowledge.
Sincerely,
Rich Cooper,
Rich Cooper,
Chief Technology Officer,
MetaSemantics Corporation
MetaSemantics AT EnglishLogicKernel DOT com
( 9 4 9 ) 5 2 5-5 7 1 2
http://www.EnglishLogicKernel.com
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Mary-Anne,
That link:
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Mary-Anne,
I got a blank browser window when I went to that URL, but I followed your paper through to another link:
https://link.springer.com/article/10.1007/s10458-009-9082-0
which is informative, from your other writings. The "grounding" you describe is called "ground truth" in US military systems that represent situations of interest, in areas of interest. You pointed out the link from information to reality that is so slippery to straighten out.
Sincerely,
Rich Cooper,
Rich Cooper,
Chief Technology Officer,
MetaSemantics Corporation
MetaSemantics AT EnglishLogicKernel DOT com
( 9 4 9 ) 5 2 5-5 7 1 2
http://www.EnglishLogicKernel.com
From:
ontolo...@googlegroups.com [mailto:ontolo...@googlegroups.com] On
Behalf Of Mary-Anne Williams
Sent: Monday, February 12, 2018 3:08 PM
To: ontolo...@googlegroups.com
Subject: Re: [ontolog-forum] Models and symbol grounding
On 13 February 2018 at 10:04, Mary-Anne Williams <Mary...@themagiclab.org> wrote:
art is science and conversely!
On 13 February 2018 at 09:17, Rich Cooper <metase...@englishlogickernel.com> wrote:
Mary-Anne,
So, given that we agree on the subjectivity of all participants in ontology, perhaps we should treat ontology as an art, rather than as a scientific, or universal, representation of knowledge. The influence of an ontology's author is very personal, very much in tune with that person's experience. The same is true of literature, art, music, and the many expressions of human knowledge.
Sincerely,
Rich Cooper,
Rich Cooper,
Chief Technology Officer,
MetaSemantics Corporation
MetaSemantics AT EnglishLogicKernel DOT com
( 9 4 9 ) 5 2 5-5 7 1 2
http://www.EnglishLogicKernel.com
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John, you said
Note the word 'goal'. That is something that can be stated in formal
terms (e.g., a sentence in a version of logic or clearly written NL).
Another word that I recommend is 'intention'. That word can be
defined as "A goal that guides the actions by some agent."
In mKR, I refer to the purpose of an action, e.g.
I do go to the store with purpose = { I do buy od food; };
The word ‘purpose’ can be defined as “the reason that something is done”.
Purpose is a property of an action.
It is a word that is used in everyday English.
Relative onticity
Contextual emergence has been originally conceived as a relation between levels of descriptions, not levels of nature: It addresses questions of epistemology rather than ontology. In agreement with Esfeld (2009), who advocated that ontology needs to regain more significance in science, it would be desirable to know how ontological considerations might be added to the picture that contextual emergence provides.
A network of descriptive levels of varying degrees of granularity raises the question of whether descriptions with finer grains are more fundamental than those with coarser grains. The majority of scientists and philosophers of science in the past tended to answer this question affirmatively. As a consequence, there would be one fundamental ontology, preferentially that of elementary particle physics, to which the terms at all other descriptive levels can be reduced.
But this reductive credo also produced critical assessments and alternative proposals. A philosophical precursor of trends against a fundamental ontology is Quine's (1969) ontological relativity. Quine argued that if there is one ontology that fulfills a given descriptive theory, then there is more than one. It makes no sense to say what the objects of a theory are, beyond saying how to interpret or reinterpret that theory in another theory. Putnam (1981, 1987) later developed a related kind of ontological relativity, first called internal realism, later sometimes modified to pragmatic realism.
On the basis of these philosophical approaches, Atmanspacher and Kronz (1999) suggested how to apply Quine's ideas to concrete scientific descriptions, their relationships with one another, and with their referents. One and the same descriptive framework can be construed as either ontic or epistemic, depending on which other framework it is related to: bricks and tables will be regarded as ontic by an architect, but they will be considered highly epistemic from the perspective of a solid-state physicist.
Coupled with the implementation of relevance criteria due to contextual emergence (Atmanspacher 2016), the relativity of ontology must not be confused with dropping ontology altogether. The "tyranny of relativism" (as some have called it) can be avoided by identifying relevance criteria to distinguish proper context-specific descriptions from less proper ones. The resulting picture is more subtle and more flexible than an overly bold reductive fundamentalism, and yet it is more restrictive and specific than a patchwork of arbitrarily connected model fragments.
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John
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John
Hi Matthias,
Interesting paper, but I'm confused about equation 12. I encoded this in the attached ontology. I also added an axiom to state that delusions must be about something, otherwise equations 11 and 12 don't carry any force (a delusion that is not about anything would be equivalent to a unicorn delusion, since it's not about anything that isn't a unicorn).
Using this ontology, if I state that horned horses don't exist, then unicorn delusions become unsatisfiable. I don't think that's your intent or the intent of even the kind of weak-tea realism I subscribe to, in which the world of our scientific ontologies are buffered from any kind of phantasmagoric ontology (which may not even be logically consistent). When you try and put these things on the same footing, axioms and unsatisfiability 'leaks' from one 'world' to another.
This is the ontology in manchester syntax:
Prefix: : <http://unicorn.org/>
Ontology: <http://unicorn.org>
ObjectProperty: isAbout
ObjectProperty: hasPart
Class: Horn
Class: Delusion SubClassOf: isAbout some owl:Thing
Class: UnicornDelusion EquivalentTo: Delusion and isAbout only (Horse and hasPart some Horn)
Class: Horse DisjointWith: hasPart some Horn
This is the explanation of unsatisfiability in HermiT:
Note that it gets worse if you add instances, e.g. my own delusion about my pink unicorn:
Individual: MyUnicornDelusion Types: Delusion and isAbout only (Horse and hasPart some Horn)
This results in the whole ontology being inconsistent. i.e. the only consistent worlds are ones in which our delusions are about real things.
Apologies if I'm missing something, but was this your intent?
FWIW I'm not sure there is a use case for reasoning about fantasy entities. The most straightforward thing is to keep direct representations of unicorns and imaginary homeopathic processes out of scientific ontologies, and to have a lightweight minimally axiomatized ontologies of delusions, fiction etc if they are required (e.g. for a psychiatric ontology).
I enjoyed the paper, though I'm glad the bio-ontology community has moved on from unicorns and onto more pragmatic concerns.
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