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Horacio Arlo-Costa Eric Pacuit
 

Summary: Horacio Arl´o-Costa
Eric Pacuit
First-Order Classical
Modal Logic
Abstract. The paper focuses on extending to the first order case the semantical pro-
gram for modalities first introduced by Dana Scott and Richard Montague. We focus on
the study of neighborhood frames with constant domains and we offer a series of new
completeness results for salient classical systems of first order modal logic. Among other
results we show that it is possible to prove strong completeness results for normal sys-
tems without the Barcan Formula (like FOL + K) in terms of neighborhood frames with
constant domains. The first order models we present permit the study of many epistemic
modalities recently proposed in computer science as well as the development of adequate
models for monadic operators of high probability. Models of this type are either difficult
of impossible to build in terms of relational Kripkean semantics.
We conclude by introducing general first order neighborhood frames and we offer a
general completeness result in terms of them which circumvents some well-known prob-
lems of propositional and first order neighborhood semantics (mainly the fact that many
classical modal logics are incomplete with respect to an unmodified version of neighbor-
hood frames). 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

  

Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University

 

Collections: Mathematics