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

Ricardo Oscar Rodriguez
Universidad de Buenos Aires (UBA)
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.
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
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DOI 10.1007/s11225-010-9230-1
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References found in this work BETA

Modal Logic.Alexander Chagrov - 1997 - Oxford University Press.
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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Citations of this work BETA

Fuzzy Logic.Petr Hajek - 2008 - Stanford Encyclopedia of Philosophy.
Fuzzy Intensional Semantics.Libor Běhounek & Ondrej Majer - 2018 - Journal of Applied Non-Classical Logics 28 (4):348-388.

View all 9 citations / Add more citations

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