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

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Wed, 14 Mar 2012 08:38:46 -0500
Message-id: <4F609F66.40303@xxxxxxxxxxx>
Chris,    (01)

I agree with you.   Note the concluding line.    (02)

>> 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.    (03)

> 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.    (04)

Yes.  That is what I meant:  any Tarski-style model can be represented
by a set of positive or negative atomic sentences.    (05)

Since relational DBs don't express negated tuples, the closed=world
assumption is the default -- negation is represented by absence.    (06)

> 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.    (07)

If you have an axiom (i.e., constraint) that is not true when evaluated
in terms of your DB, then your DB violates that constraint -- i.e., it's
not a model of the axioms.    (08)

John    (09)

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