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ManyValued Modal Logics
 Fundamenta Informaticae
, 1992
"... . Two families of manyvalued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite manyvalued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds a ..."
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Cited by 272 (16 self)
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. Two families of manyvalued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite manyvalued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be manyvalued. Gentzen sequent calculi are given for both versions, and soundness and completeness are established. 1 Introduction The logics that have appeared in artificial intelligence form a rich and varied collection. While classical (and maybe intuitionistic) logic su#ces for the formal development of mathematics, artificial intelligence has found uses for modal, temporal, relevant, and manyvalued logics, among others. Indeed, I take it as a basic principle that an application should find (or create) an appropriate logic, if it needs one, rather than reshape the application to fit some narrow class of `established' logics. In this paper I want to enlarge the variety of logics...
ManyValued Modal Logics II
 Fundamenta Informaticae
, 1992
"... Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible  in other words each of the experts has their own Kripke model in ..."
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Cited by 34 (0 self)
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Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible  in other words each of the experts has their own Kripke model in mind (subject, of course, to the dominance relation that may hold between experts). How will they assign truth values to sentences in a common modal language, and on what sentences will they agree? This problem can be reformulated as one about manyvalued Kripke models, allowing manyvalued accessibility relations. This is a natural generalization of conventional Kripke models that has only recently been looked at. The equivalence between the manyvalued version and the multiple expert one will be formally established. Finally we will axiomatize manyvalued modal logics, and sketch a proof of completeness.
A Simple Modal Encoding of Propositional Finite ManyValued Logics
"... We present a method for testing the validity for any finite manyvalued logic by using simple transformations into the validity problem for von Wright’s logic of elsewhere. The method provides a new original viewpoint on finite manyvaluedness. Indeed, we present a uniform modal encoding of any fin ..."
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We present a method for testing the validity for any finite manyvalued logic by using simple transformations into the validity problem for von Wright’s logic of elsewhere. The method provides a new original viewpoint on finite manyvaluedness. Indeed, we present a uniform modal encoding of any finite manyvalued logic that views truthvalues as nominals. Improvements of the transformations are discussed and the translation technique is extended to any finite annotated logic. Using similar ideas, we conclude the paper by defining transformations from the validity problem for any finite manyvalued logic into TAUT (the validity problem for the classical propositional calculus). As already known, this sharply illustrates that reasoning within a finite manyvalued logic can be naturally and easily encoded into a twovalued logic. All the manyone reductions in the paper are tight since they require only time in O(n.log n) and space in O(log n). Keywords: finite manyvalued logic, modal logic of elsewhere, manyone reduction 1
ManyValued Modal Logics II Melvin
, 2004
"... Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible — in other words each of the experts has their own Kripke model in mi ..."
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Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible — in other words each of the experts has their own Kripke model in mind (subject, of course, to the dominance relation that may hold between experts). How will they assign truth values to sentences in a common modal language, and on what sentences will they agree? This problem can be reformulated as one about manyvalued Kripke models, allowing manyvalued accessibility relations. This is a natural generalization of conventional Kripke models that has only recently been looked at. The equivalence between the manyvalued version and the multiple expert one will be formally established. Finally we will axiomatize manyvalued modal logics, and sketch a proof of completeness. 1