On Aug 3, 2010, at 5:29 PM, Obrst, Leo J. wrote:
> John, Chris,
>
> Is this the same as guarded quantification? (01)
It's sort of a limiting case. The term "guarded quantification" is usually
used in the context of rather advanced studies in modal logic, finite model
theory, etc where the issue of complexity vs expressibility comes to the fore.
The idea in these contexts is typically to add guarded quantifiers to some
fragment of first-order logic (yielding a so-called "guarded fragment" of FOL)
and explore its computational and model theoretic properties. In the
definition of typed quantification that I gave, I put no restrictions on the
formulas that can serve as the "guard" F in a guarded quantifier. In the study
of guarded fragments, the complexity of the guard F is highly relevant. In
some contexts, for example, the guards might be restricted to atomic formulas. (02)
There has been a great deal of research recently on guarded fragments in the
study of modal logic (which, recall, can be represented as fragments of FOL),
which has made them quite relevant to the study of OWL (as OWL can itself be
represented as a modal logic). (03)
Pat did some work on guarded fragments a while ago and might be able to add
more here. (04)
-chris (05)
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