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Re: [ontolog-forum] OWL Well Defined Semantics (was: Terminology...)

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Thu, 26 Jan 2012 18:31:42 +0100
Message-id: <CAO_JD6O0R2FGuioz-EqzDkztStcurvzgWztiznC2wejGftyRaQ@xxxxxxxxxxxxxx>
On Thu, Jan 26, 2012 at 4:40 PM, Adrian Walker <adriandwalker@xxxxxxxxx> wrote:
Hi John, Chris, and Pat,

The following kind of got lost under a wrong subject heading on Ontolog, and I'm wondering whether you have time to comment please.

Ed Barkmeyer wrote:

At least with OWL the models have well-defined formal semantics,...

Please correct me if I'm wrong, but I'm under the impression that OWL shares with full first order logic the property of having in general more than one model for a given set of clauses.

Sure, but to say the semantics is well-defined is only to say that, WITHIN a given interpretation, there is no semantic ambiguity; every term has a definite denotation, every predicate a definite extension, every sentence a definite truth value. Obviously, though, terms can denote different things, predicates can have different extensions and, hence, sentences can have different truth values and, intuitively, mean different things from one interpretation to another.
If so, there's ambiguity about what it should be possible to deduce, and the formal semantics is therefore (in a practical sense) not well-defined.

That does not follow; the fact that a set of sentences has different models alters nothing about what can be deduced from that set in first-order logic (or OWL). Indeed, because FOL is semantically complete, deducibility from a set Γ of sentences correlates exactly with what remains true across different models of Γ — φ is deducible from Γ if and only if φ is true in every model of Γ. There is nothing ambiguous about that.

Does this answer your question?


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