Chris, (01)
I agree with you. Note the concluding line. (02)
JFS
>> I prefer to talk about the set of groundlevel 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)
CM
> Maybe I'm not understanding, but I don't see how this works. I assume
> a groundlevel fact is just, logically speaking, an atomic sentence. (?)
> On that assumption, I assume further that by the groundlevel 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 ntuples<a1,…,an> such that
> "Fa1…an" is a groundlevel fact. (04)
Yes. That is what I meant: any Tarskistyle 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)
CM
> But now suppose that one of my axioms
> is "∃xGx" but there are no groundlevel facts of the form "Ga". "∃xGx" is
> not true in the model you construct from the groundlevel 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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