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).