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Re: [ontolog-forum] Constructs, primitives, terms

To: Ontolog-forum <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Tue, 13 Mar 2012 20:02:58 +0100
Message-id: <35A16B18-3BAC-4CE0-ACB8-FE2A9153A300@xxxxxxxx>
Am Mar 13, 2012 um 5:45 PM schrieb John F. Sowa:
> ...
> CM
>> I suppose we can make something up, e.g., models M1 and M2 of theory
>> G are inconsistent with each other if there is some sentence A in
>> the language of G (obviously not a theorem of G) to which M1 and M2
>> assign different truth values.
> Yes. I prefer to talk about the set of ground-level facts in a database
> as a model of the theory expressed by the conjunction of all the DB
> definitions and constraints (axioms).  Whenever you add a new axiom,
> you reduce the set of permissible models (i.e., databases) that
> that can satisfy that theory.    (01)

Maybe I'm not understanding, but I don't see how this works. I assume
a ground-level fact is just, logically speaking, an atomic sentence. (?)
On that assumption, I assume further that by the ground-level facts being 
a model, you mean that you can construct a model where the interpretation
of a predicate F is just the set of a n-tuples <a1,…,an> such that 
"Fa1…an" is a ground-level fact. But now suppose that one of my axioms
is "∃xGx" but there are no ground-level facts of the form "Ga". "∃xGx" is
not true in the model you construct from the ground-level facts.    (02)

-chris    (03)

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