|From:||Christopher Menzel <cmenzel@xxxxxxxx>|
|Date:||Thu, 26 Jan 2012 18:31:42 +0100|
On Thu, Jan 26, 2012 at 4:40 PM, Adrian Walker <adriandwalker@xxxxxxxxx> wrote:
Hi John, Chris, and Pat,
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.
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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