On skolems (was: Re: existential answers to queries (was: Re: on behalf of sandro))

From: Pat Hayes (phayes@ai.uwf.edu)
Date: 10/25/01

I think talking about skolems is a red herring. If the KB has skolems 
in it, then as far as the QE is concerned they are just functions; 
their status as skolems is invisible. And as far as generating 
skolems during the query process, that is simply invalid, and 
shouldn't be allowed to happen. The only logical distinctions we need 
to draw are between terms that can have values bound to them in the 
query-answering process (universals in the KB and existentials in the 
query, speaking purely logically) and those that cannot (all 
constants and names; existentials in the KB and universals in the 
query), and which of the former are considered to be the 
answer-binding-places (a subset of the existentials in the query, 
usually.) The only real complication over logical QA is that in our 
case the KB and the QE have disjoint scopes, and it is never valid to 
take an existential variable name outside its scope. The querying 
process basically hands the query to the KB and says: prove this. 
That puts the query temporarily inside the KB's scope, but if a query 
variable gets bound to an existential in the KB, then it must not 
hand that binding back to the QE; hence the <blank> complication. 
(This isn't just post-processing stuff: it would be logically invalid 
to do that. )

Notice that handing back <blank> is not handing back a skolem.  Its 
like saying 'a frog' without calling it Fred. (You could say that it 
is a kind of licence to the QE to create its own skolem, but that 
would be misleading. Such name creation would be independent of the 
query-answering. If an reasoning engine wants to create names for 
things, it can do that; but that's its private business, not 
something that arises from a transaction with another agent.)


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