Friday,
25 February 2005
First-Order Classical
Modal Logic
Horacio
Arlo-Costa, Carnegie Mellon
U. (Philosophy)
12:05 pm, 817R Cathedral of Learning
Abstract: Following Dana Scott’s
‘advice in modal logic’ we extend the so-called neighborhood
semantics of propositional modalities by introducing general
first order neighborhood frames. A general completeness result
for the entire family of first order classical modal logics (encompassing
both normal and non-normal systems) is then proved in terms of first
order neighborhood frames with
constant domains. Therefore the use of varying domains
remains optional but not mandatory in order to characterize standard
systems like FOL + K. This makes possible the natural study
of many modalities that are either hard or impossible to study via
relational semantics (like monadic operators of high probability,
and, more in general, a large family of non-adjunctive modalities
used today in various subfields of Computer Science). We argue
that the semantical program that thus arises surpasses both in expressivity
and adequacy the standard Kripkean approach (even when it comes
to the study of first order normal systems).
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