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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 217 (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.
An overview of rough set semantics for modal and quantifier logics
 International Journal of Uncertainty, Fuzziness and Knowledgebased Systems
, 2000
"... In this paper, we would like to present some logics with semantics based on rough set theory and related notions. These logics are mainly divided into two classes. One is the class of modal logics and the other is that of quantifier logics. For the former, the approximation space is based on a set o ..."
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Cited by 4 (2 self)
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In this paper, we would like to present some logics with semantics based on rough set theory and related notions. These logics are mainly divided into two classes. One is the class of modal logics and the other is that of quantifier logics. For the former, the approximation space is based on a set of possible worlds, whereas in the latter, we consider the set of variable assignments as the universe of approximation. In addition to surveying some wellknown results about the links between logics and rough set notions, we also develop some new applied logics inspired by rough set theory.
Modal systems based on manyvalued logics
"... We propose a general semantic notion of modal manyvalued logic. Then, we explore the difficulties to characterize this notation in a syntactic way and analyze the existing literature with respect to this framework. ..."
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Cited by 1 (0 self)
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We propose a general semantic notion of modal manyvalued logic. Then, we explore the difficulties to characterize this notation in a syntactic way and analyze the existing literature with respect to this framework.
On the Minimum ManyValued Modal Logic over a Finite
, 811
"... This article deals with manyvalued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated in the residuated lattice (and so defining the minimum mod ..."
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This article deals with manyvalued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated in the residuated lattice (and so defining the minimum modal logic), the ones only evaluated in the idempotent elements and the ones evaluated in 0 and 1. We show how to expand an axiomatization, with canonical truthconstants in the language, of a finite residuated lattice into one of the modal logic, for each one of the three basic classes of Kripke frames. We also provide axiomatizations for the case of a finite MV chain but this time without canonical truthconstants in the language.
NOT FOR PUBLIC RELEASE On the Minimum ManyValued Modal
"... This article deals with manyvalued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated in the residuated lattice (and so defining the minimum mod ..."
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This article deals with manyvalued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated in the residuated lattice (and so defining the minimum modal logic), the ones evaluated in the idempotent elements and the ones evaluated in 0 and 1. We show how to expand an axiomatization, with canonical truthconstants in the language, of a finite residuated lattice into one of the modal logic, for each one of the three basic classes of Kripke frames. We also provide axiomatizations for the case of a finite MV chain but this time without canonical truthconstants in the language. Keywords: Manyvalued modal logic, modal logic, manyvalued logic, fuzzy logic, substructural logic. 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
of the Deutsche Forschungsgemeinschaft. Fuzzy Rough Sets versus Rough Fuzzy Sets An Interpretation and a Comparative Study using Concepts of Modal Logics ∗
, 1998
"... Abstract The starting point of the paper is the (wellknown)observation that the “classical ” Rough Set Theory as introduced by PAWLAK is equivalent to the S5 Propositional Modal Logic where the reachability relation is an equivalence relation. By replacing this equivalence relation by an arbitrary ..."
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Abstract The starting point of the paper is the (wellknown)observation that the “classical ” Rough Set Theory as introduced by PAWLAK is equivalent to the S5 Propositional Modal Logic where the reachability relation is an equivalence relation. By replacing this equivalence relation by an arbitrary binary relation (satisfying certain properties, for instance, reflexivity and transitivity) we shall obtain generalized (crisp!!) rough set theories. Our ideas in the paper are: 1. We replace the crisp reachability relation by a binary fuzzy relation whereas the set to be approximated remains crisp. It is very important that the reachability relation is used as a fuzzy relation, i. e. without introducing and using a cut point. Hence, these lower and upper “fuzzy” approximations of the given crisp set are fuzzy sets, in general. 2. Vice versa, the given set to be approximated is a fuzzy set, but the reachability relation is crisp. Also in this case the lower and the upper “crisp” approximations of the given fuzzy set are again fuzzy sets, in general. 3. Finally, we define a lower and an upper approximation of a fuzzy set using a binary fuzzy relation. It is interesting that this approach coincides with a concept which we have developed for interpreting the modal operators Box and Diamond in the framework of Fuzzy Logic. 1