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Re: [ontolog-forum] Next steps in using ontologies as standards

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Tue, 6 Jan 2009 14:11:10 -0600
Message-id: <D8CB88D0-C8CA-402E-BDF5-705813C622A9@xxxxxxxx>
On Jan 6, 2009, at 1:34 PM, Patrick Cassidy wrote:
> NO, FOL is a syntax,    (01)

Not so.  Really importantly not so.  In fact, it is *semantics* that  
makes FOL FOL.  It is of course required that a first-order language  
have a certain type of syntax that includes a minimal set of  
connectives, the apparatus of quantification, and a certain  
recursively defined class atomic and molecular sentences (though even  
here there is great variability -- see the grammar of Common Logic,  
where this variability is explicitly built in).  But what makes a  
logical framework -- i.e., a language plus a semantics -- first-order  
is the fact that it has certain semantic properties (specifically --  
not that it matters much here -- by what is known as Lindström's  
Theorem, compactness and the downward Löwenheim-Skolem properties).    (02)

> and a basic vocabulary is critical.    (03)

Yes, but the only critical basic vocabulary is the purely logical  
vocabulary of boolean operators and quantifiers.    (04)

> I think that optimally the FO needs to include the semantic  
> primitives,    (05)

Again, assuming by a semantic primitive you mean a syntactic item  
that, relative to the semantics, cannot be defined in terms of any  
other syntactic items, the semantic primitives of FOL consist of (some  
subset of) the purely logical vocabulary.  If you are talking about  
NON-logical primitives, then I think what you have in mind are the  
basic constants and predicates of a first-order *theory* that are  
intended to represent concepts from some intended domain.  The only  
way to establish that they are indeed primitive is to look at the  
axioms of the theory and determine whether or not they are definable  
(in the formal sense) in terms of other constants and predicates in  
the theory.    (06)

> otherwise people will create relations that have the same terms and  
> different meanings, and different terms for the same meaning, and  
> there will be no automatic way to recognize the similarities or  
> differences.    (07)

That's just what we have axioms for, no?    (08)

> But if all domain terms (and domain ontology elements) are logically  
> specified using the same set of semantic primitives, the machine  
> will be able to automatically properly interpret the domain  
> representations, because it knows how to properly interpret the  
> primitives.    (09)

These are stormy waters, as you well know.  Strictly speaking,  
machines can't interpret anything.  All they can do is process  
syntax.  That's why we have to write axioms for them to process (via  
automated reasoners) that do a reasonably complete job of representing  
the information we want them to represent.    (010)

> This is not a trivial issue that can be dismissed with offhand  
> comments.  It is at the core of what it means to represent meanings,  
> and it should be seriously investigated by a project involves most  
> of the most knowledgeable ontologists, and some representation of  
> potential users -- especially natural language researchers.    (011)

Well, it seems to me that this is what logical AI since the early days  
has been all about (though I think the bulk of NL research has had  
other fish to fry.)    (012)

> I ask the question again: is it not at least interesting, if not (as  
> I believe) of central importance to the practice of ontological  
> engineering to learn whether a necessary and sufficient inventory of  
> semantic primitives can in fact be identified?    (013)

That depends a lot on what they are supposed to be necessary and  
sufficient *for*, but think your question is simply whether it is  
reasonable to think that there could be a single, comprehensive  
foundational ontology upon which all other ontologies could be  
usefully built.  While I can imagine *formally* what it would mean to  
have such an ontology -- a single theory of time/space/matter/motion/ 
properties/<YourFavoriteFundamentalConceptHere> of which all other  
ontologies are extensions -- I think Ed and others have raised  
reasonable doubts about whether it is a realistic prospect.    (014)

-chris    (015)

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