Studia Logica 59 (2):249-269 (1997)

Abstract
A possible world structure consist of a set W of possible worlds and an accessibility relation R. We take a partial function r(·,·) to the unit interval [0, 1] instead of R and obtain a Kripke frame with graded accessibility r Intuitively, r(x, y) can be regarded as the reliability factor of y from x We deal with multimodal logics corresponding to Kripke frames with graded accessibility in a fairly general setting. This setting provides us with a framework for fuzzy possible world semantics. The basic propositional multimodal logic gK (grated K) is defined syntactically. We prove that gK is sound and complete with respect to this semantics. We discuss some extensions of gK including logics of similarity relations and of fuzzy orderings. We present a modified filtration method and prove that gK and its extensions introduced here are decidable.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1023/A:1004956418185
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Modal Logic: An Introduction.Brian F. Chellas - 1980 - Cambridge University Press.
Counterfactuals.David Lewis - 1974 - Tijdschrift Voor Filosofie 36 (3):602-605.
In so Many Possible Worlds.Kit Fine - 1972 - Notre Dame Journal of Formal Logic 13 (4):516-520.

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