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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 ..."
Abstract

Cited by 218 (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 22 (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.
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 ..."
Abstract
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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
The Temporal Calculus
"... We consider the problem of defining conditional objects (a I b), which would allow one to regard the conditional probability Pr(alb ) as a probability of a welldefined event rather than as a shorthand for Pr(ab)/Pt(b). The next issue is to define boolean combinations of con ditional objects, a ..."
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We consider the problem of defining conditional objects (a I b), which would allow one to regard the conditional probability Pr(alb ) as a probability of a welldefined event rather than as a shorthand for Pr(ab)/Pt(b). The next issue is to define boolean combinations of con ditional objects, and possibly also the operator of further conditioning.
The Temporal Calculus of Conditional Objects and Conditional Events
, 2008
"... We consider the problem of defining conditional objects (ab), which would allow one to regard the conditional probability Pr(ab) as a probability of a welldefined event rather than as a shorthand for Pr(ab) / Pr(b). The next issue is to define boolean combinations of conditional objects, and poss ..."
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We consider the problem of defining conditional objects (ab), which would allow one to regard the conditional probability Pr(ab) as a probability of a welldefined event rather than as a shorthand for Pr(ab) / Pr(b). The next issue is to define boolean combinations of conditional objects, and possibly also the operator of further conditioning. These questions have been investigated at least since the times of George Boole, leading to a number of formalisms proposed for conditional objects, mostly of syntactical, prooftheoretic vein. We propose a unifying, semantical approach, in which conditional events are (projections of) Markov chains, definable in the threevalued extension (TLTL) of the past tense fragment of propositional linear time logic (TL), or, equivalently, by threevalued counterfree Moore machines. Thus our conditional objects are indeed stochastic processes, one of the central notions of modern probability theory.