Chris, (01)
I agree with you. Note the concluding line. (02)
JFS
>> 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)
CM
> 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)
CM
> 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)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J (010)
|