文档介绍：Horacio Arlo-Costa´ First-Order Classical
Eric Pacuit 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 in the first part of
the paper a series of pleteness results for salient classical systems of first order
modal logic. Among other results we show that it is possible to prove plete-
ness results for normal systems 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 puter science as well as
the development of adequate models for monadic operators of high probability. Mod-
els of this type are either difficult of impossible to build in terms of relational Kripkean
semantics [40].
We conclude by introducing general first order neighborhood frames with constant do-
mains and we offer a pleteness result for the entire family of classical first order
modal systems in terms of them, circumventing some well-known problems of propositional
and first order neighborhood semantics (mainly the fact that many classical modal logics
are plete with respect to an unmodified version of either neighborhood or relational
frames). We argue that the semantical program that thus arises offers the plete
semantic unification of the family of classical first order modal logics.
Keywords: First-Order Modal Logic, Neighborhood Semantics, General Frames.
1. Introduction
Dana Scott and Richard Montague proposed in 1970 (independently, in [47]
and [44] respectively) a new semantic framework for the study of modalities,
which today tends to be known as neighborhood semantics.
A neighborhood frame is a pair hW, Ni, where W is a set of states,
W
or worlds, and N : W → 22 is a neighborhood function which associates
a set of neighborhoods with ea