David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Studia Logica 84 (2):171 - 210 (2006)
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 .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
|Keywords||First-order modal logic neighborhood semantics general frames|
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References found in this work BETA
Saul A. Kripke (1963). Semantical Considerations on Modal Logic. Acta Philosophica Fennica 16 (1963):83-94.
Isaac Levi (1996). For the Sake of the Argument: Ramsey Test Conditionals, Inductive Inference, and Nonmonotonic Reasoning. Cambridge University Press.
Timothy Williamson (1998). Bare Possibilia. Erkenntnis 48 (2/3):257--73.
Melvin Fitting, R. Mendelsohn & Roderic A. Girle (2002). First-Order Modal Logic. Bulletin of Symbolic Logic 8 (3):429-430.
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