Standard Gödel Modal Logics

Studia Logica 94 (2):189-214 (2010)
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Abstract

We prove strong completeness of the □-version and the ◊-version of a Gödel modal logic based on Kripke models where propositions at each world and the accessibility relation are both infinitely valued in the standard Gödel algebra [0,1]. Some asymmetries are revealed: validity in the first logic is reducible to the class of frames having two-valued accessibility relation and this logic does not enjoy the finite model property, while validity in the second logic requires truly fuzzy accessibility relations and this logic has the finite model property. Analogues of the classical modal systems D, T, S4 and S5 are considered also, and the completeness results are extended to languages enriched with a discrete well ordered set of truth constants.

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Ricardo Oscar Rodriguez
Universidad de Buenos Aires (UBA)

References found in this work

Modal logic.Alexander Chagrov - 1997 - New York: Oxford University Press. Edited by Michael Zakharyaschev.
Logic with truth values in a linearly ordered Heyting algebra.Alfred Horn - 1969 - Journal of Symbolic Logic 34 (3):395-408.

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