Gary,
Unfortunately, you don't provide links to either Marcus's talk or your own. This means it's impossible to quickly delve deeper, with just one click. Let me answer from a general perspective.
The question for genAI is: does it have a model of the world?
The question for IT-ontology is: does it contain a model of the world?
In both cases, the number one question is: what world are we talking about?
If it's a small world, like the ISS or Tiangong, then knowledge about it can fit in both genAI and IT-ontology.
Let W be some world. For example, it could be the world of a coffee shop for a robot waiter.
What are the criteria for IT-ontology, genAI, or robot-software to have a model of the world W?
That's the question.
Antithesis: IT-ontology can contain a model of the world.
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Marco,
Thank you. The beauty of IT-ontology is its formal representation of any knowledge. Moreover, "formal" simply means "mathematical." Mathematical representations of knowledge about the world are highly developed in physics and other sciences and technologies. IT-ontology formalizes the texts that accompany scientific and engineering knowledge using mathematical logic.
At the same time, IT-ontology can easily contain any mathematical formulas and algorithms. And, of course, any facts (A-box) about a given world.
On the other hand, genAI is a trainable black box. And if we say "there's no model of the world," the trainers respond, "We'll teach it right now."
And as I wrote, "What are the criteria for IT-ontology, genAI, or robot software to have a model of the world W?"
We can take these criteria from the GB-C slide[1] or from GM text.
And see if they can be implemented in IT-ontology.
I believe so.
From the model theory perspective you mentioned, I believe finite models will suffice, but somewhere nearby will be algorithms. May be in Wolfram system 📯
[1]

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Marco,
It is interesting that in your version of the document (2004) they have "world" 31 times. But in newer version (2014) - 0 times.
And it is interesting that in the former they have in Glossary:
"World (n.) (with the:) (i) The actual world. (with a:) (ii) A way that the actual world might be arranged. (iii) An interpretation (iv) A possible world.
(The metaphysical status of 'possible worlds' is highly controversial. Fortunately, one does not need to commit oneself to a belief in parallel universes in order to use the concept in its second and third senses, which are sufficient for semantic purposes.)"
Anyway the main question is not a math object (they use Model theory), but reference to reality from this math object.
As for genAI, my knowledge is very superficial.
Best,
Alex
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Amit,
Judging by the "the "WorldModel" is defined as an internal representation consisting of ontologies, domain-specific knowledge, and rules used to process digital media and enhance search." here you think the same as Gary, who started this thread.
I am still thinking that we can keep "domain-specific knowledge, and rules" in IT-ontology. Taking into account for example the definition of Nicola Guarino as most comprehensive.
As for the idea itself, we should at least start with Laplace: "Pound, J. (trans.) (1809) The System of the World, 2 vols, London: Richard Phillips
_ The System of the World (v.1)
_ The System of the World (v.2)
"
Alex
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John,
Any language, even natural language, is a rough approximation of reality, designed to capture the essence, i.e., to abstract correctly.
On the other hand, English is a fairly formal language. See (PDF) English is a HOL language message #1X.
Of course, formal representation is the final phase of knowledge processing. First, knowledge must be systematized and concentrated. Systematization consists of extracting the most important units of knowledge from the text: definitions, axioms, hypotheses, proofs. Concentration consists of storing these units in frameworks in the languages in which people were able to formulate them.
Here's an example of an axiom in a framework.
https://docs.google.com/spreadsheets/d/1gThpt1P8iulIl5SXfoekUiMg-562oiLfhHQYQjjg_y4/edit?gid=0#gid=0
Note that all languages are equal in a framework. Modern ontologies written in OWL2 contain all other languages in annotations, which is logically incorrect.
Anyone who needs definitions specifically in OWL2 should simply extract them, in the required quantity, from the framework.
On the other hand, any text (textbook, article, presentation) using terms from the framework should reference the framework, or better yet, directly the knowledge units.
Modern, separately stored ontologies are knowledge references.
Alex
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Doug,
https://standards.clarin.eu/sis/views/view-spec.xq?id=SpecOpenCyc has https://cyc.com/platform/opencyc/ but it does not work.
Is this https://github.com/asanchez75/opencyc a good reference?
A system of interconnected terms with definitions is a backbone of any theory.
It is interesting that it has a value without axioms - the source of a theory.
Alex
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Marco,
I haven't looked into this, and of course, if there's an entailment, it's worth looking into.
I'll just note for now that when we study the language itself and its semantics, rather than the semantics of what can be written in it, it's worth first looking at its keywords:
https://www.w3.org/TR/rdf-syntax-grammar/#section-Namespace
"The RDF namespace IRI (or namespace name) is http://www.w3.org/1999/02/22-rdf-syntax-ns# and is typically used in XML with the prefix rdf although other prefix strings may be used. The RDF Vocabulary is identified by this namespace name and consists of the following names only:
Syntax names — not concepts
RDF Description ID about parseType resource li nodeID datatype
Class names
Seq Bag Alt Statement Property XMLLiteral List
Property names
subject predicate object type value first rest _n
where n is a decimal integer greater than zero with no leading zeros.
Resource names
nil"
There's something to think about - very interesting keywords:
Seq Bag Alt Statement Property XMLLiteral List subject predicate object type value first rest _n nil
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Doug,
This distinction between terms and facts in DL-ontology is the distinction between a T-box and an A-box. As Gary mentioned.
Gary is silent, and I think we've discussed this topic enough.
🕉️
Alex
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