Theory matrices (for modal logics) using alphabetical monotonicity

Studia Logica 52 (2):233 - 257 (1993)
In this paper I give conditions under which a matrix characterisation of validity is correct for first order logics where quantifications are restricted by statements from a theory. Unfortunately the usual definition of path closure in a matrix is unsuitable and a less pleasant definition must be used. I derive the matrix theorem from syntactic analysis of a suitable tableau system, but by choosing a tableau system for restricted quantification I generalise Wallen's earlier work on modal logics. The tableau system is only correct if a new condition I call alphabetical monotonicity holds. I sketch how the result can be applied to a wide range of logics such as first order variants of many standard modal logics, including non-serial modal logics.
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DOI 10.1007/BF01058390
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References found in this work BETA
Raymond M. Smullyan (1968). First-Order Logic. New York [Etc.]Springer-Verlag.
J. W. Lloyd (1987). Foundations of Logic Programming. Journal of Symbolic Logic 52 (1):288-289.
Melvin Fitting (1972). Tableau Methods of Proof for Modal Logics. Notre Dame Journal of Formal Logic 13 (2):237-247.

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