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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 273 (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...
Bisimulations and Boolean Vectors
 Advances in Modal Logic
, 2003
"... this paper I show that a shift in the point of view, from Kripke frames to closely related Boolean vector spaces, turns bisimulations from relations to linear mappings having rather nice properties. Monomodal frames give rise to Boolean vector spaces over the familiar twovalued Boolean algebra, wh ..."
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Cited by 9 (0 self)
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this paper I show that a shift in the point of view, from Kripke frames to closely related Boolean vector spaces, turns bisimulations from relations to linear mappings having rather nice properties. Monomodal frames give rise to Boolean vector spaces over the familiar twovalued Boolean algebra, while multimodal frames bring more complex Boolean algebras into the picture. Still, the basic ideas remain the same for both the mono and the multimodal cases. The point of this approach is not to prove new results, but to look at wellknown results in a new way, hoping that a fresh perspective will lead to fresh insights
Deduction in ManyValued Logics: a Survey
 Mathware & Soft Computing, iv(2):6997
, 1997
"... this article, there is considerable activity in MVL deduction which is why we felt justified in writing this survey. Needless to say, we cannot give a general introduction to MVL in the present context. For this, we have to refer to general treatments such as [153, 53, 93]. 2 A classification of man ..."
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this article, there is considerable activity in MVL deduction which is why we felt justified in writing this survey. Needless to say, we cannot give a general introduction to MVL in the present context. For this, we have to refer to general treatments such as [153, 53, 93]. 2 A classification of manyvalued logics according to their intended application
MultiValued Autoepistemic Logic
 Annals of Mathematics and Artificial Intelligence
, 1996
"... We generalize Moore's autoepistemic logic to multivalued autoepistemic logic, where the set of truthvalues can be any complete lattice. Multivalued autoepistemic extensions can be characterized by admissible belief interpretations which are the concrete approximations of extensions and are a ..."
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We generalize Moore's autoepistemic logic to multivalued autoepistemic logic, where the set of truthvalues can be any complete lattice. Multivalued autoepistemic extensions can be characterized by admissible belief interpretations which are the concrete approximations of extensions and are appropriate to be computed and manipulated. We prove that multivalued autoepistemic extensions are exactly the theories of maximal multivalued Kripke models. The class of stratified theories is investigated and it is shown that stratified theories have exactly one multivalued autoepistemic extension. Finally we present a sequent calculus for multivalued logic which serves as a tool for a decision procedure for multivalued autoepistemic logic. 1
Proceedings of the TwentySecond International Joint Conference on Artificial Intelligence Reasoning about Fuzzy Belief and Common Belief: With Emphasis on Incomparable Beliefs
"... We formalize reasoning about fuzzy belief and fuzzy common belief, especially incomparable beliefs, in multiagent systems by using a logical system based on Fitting’s manyvalued modal logic, where incomparable beliefs mean beliefs whose degrees are not totally ordered. Completeness and decidabilit ..."
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We formalize reasoning about fuzzy belief and fuzzy common belief, especially incomparable beliefs, in multiagent systems by using a logical system based on Fitting’s manyvalued modal logic, where incomparable beliefs mean beliefs whose degrees are not totally ordered. Completeness and decidability results for the logic of fuzzy belief and common belief are established while implicitly exploiting the dualitytheoretic perspective on Fitting’s logic that builds upon the author’s previous work. A conceptually novel feature is that incomparable beliefs and qualitative fuzziness can be formalized in the developed system, whereas they cannot be formalized in previously proposed systems for reasoning about fuzzy belief. We believe that belief degrees can ultimately be reduced to truth degrees, and we call this “the reduction thesis about belief degrees”, which is assumed in the present paper and motivates an axiom of our system. We finally argue that fuzzy reasoning sheds new light on old epistemic issues such as coordinated attack problem. 1
Frame Constructions, Truth Invariance and Validity Preservation in ManyValued Modal Logic
"... In this paper we define and examine frame constructions for the family of manyvalued modal logics introduced by M. Fitting in the ’90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting’s original work by considering complete H ..."
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In this paper we define and examine frame constructions for the family of manyvalued modal logics introduced by M. Fitting in the ’90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting’s original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of Hindexed families of generated subframes, disjoint unions and bounded morphisms. Then, we provide an algebraic generalization of the canonical extension of a frame and model, and prove a preservation result inspired from Fitting’s canonical model argument in [7]. The analog of a complex algebra and of a principal ultrafilter is defined and the embedding of a frame into its canonical extension is presented. 1