Finite models constructed from canonical formulas

Journal of Philosophical Logic 36 (6):605 - 640 (2007)
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Abstract

This paper obtains the weak completeness and decidability results for standard systems of modal logic using models built from formulas themselves. This line of work began with Fine (Notre Dame J. Form. Log. 16:229-237, 1975). There are two ways in which our work advances on that paper: First, the definition of our models is mainly based on the relation Kozen and Parikh used in their proof of the completeness of PDL, see (Theor. Comp. Sci. 113-118, 1981). The point is to develop a general model-construction method based on this definition. We do this and thereby obtain the completeness of most of the standard modal systems, and in addition apply the method to some other systems of interest. None of the results use filtration, but in our final section we explore the connection

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2009-01-28

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Larry Moss
Indiana University

Citations of this work

Complete additivity and modal incompleteness.Wesley H. Holliday & Tadeusz Litak - 2019 - Review of Symbolic Logic 12 (3):487-535.
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DEL-sequents for progression.Guillaume Aucher - 2011 - Journal of Applied Non-Classical Logics 21 (3-4):289-321.

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References found in this work

Modal Logic: Graph. Darst.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - New York: Cambridge University Press. Edited by Maarten de Rijke & Yde Venema.
An introduction to modal logic: the Lemmon notes.E. J. Lemmon - 1977 - Oxford: Blackwell. Edited by Dana S. Scott.
Normal forms in modal logic.Kit Fine - 1975 - Notre Dame Journal of Formal Logic 16 (2):229-237.
Decidability of S4.1.Krister Segerberg - 1968 - Theoria 34 (1):7-20.
An Introduction to Modal Logic.E. J. Lemmon, Dana Scott & Krister Segerberg - 1979 - Journal of Symbolic Logic 44 (4):653-654.

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