NDLI: First-Order Classical Modal Logic

Content Provider	Springer Nature Link
Author	Arló Costa, Horacio Pacuit, Eric
Copyright Year	2006
Abstract	The paper focuses on extending to the first order case the semantical program 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 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 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 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 [40].We conclude by introducing general first order neighborhood frames with constant domains and we offer a general completeness 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 incomplete with respect to an unmodified version of either neighborhood or relational frames). We argue that the semantical program that thus arises offers the first complete semantic unification of the family of classical first order modal logics.
Starting Page	171
Ending Page	210
Page Count	40
File Format	PDF
ISSN	00393215
Journal	Studia Logica
Volume Number	84
Issue Number	2
e-ISSN	15728730
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2006-11-09
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	First-order modal logic neighborhood semantics general frames Computational Linguistics Mathematical Logic and Foundations Logic
Content Type	Text
Resource Type	Article
Subject	Logic History and Philosophy of Science

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