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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...
Probabilistic and TruthFunctional ManyValued Logic Programming
 IN PROCEEDINGS OF THE 29TH IEEE INTERNATIONAL SYMPOSIUM ON MULTIPLEVALUED LOGIC
, 1998
"... We introduce probabilistic manyvalued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic manyvalued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problems that a ..."
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Cited by 14 (9 self)
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We introduce probabilistic manyvalued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic manyvalued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problems that are Pcomplete for classical logic programs are shown to be coNPcomplete for probabilistic manyvalued logic programs. We then focus on manyvalued logic programming in Pr ? n as an approximation of probabilistic manyvalued logic programming. Surprisingly, manyvalued logic programs in Pr ? n have both a probabilistic semantics in probabilities over a set of possible worlds and a truthfunctional semantics in the finitevalued Łukasiewicz logics Łn . Moreover, manyvalued logic programming in Pr ? n has a model and fixpoint characterization, a proof theory, and computational properties that are very similar to those of classical logic programming. We especially introduce the proof...
Lp, A Logic for Representing and Reasoning with Statistical Knowledge
, 1990
"... This paper presents a logical formalism for representing and reasoning with statistical knowledge. One of the key features of the formalism is its ability to deal with qualitative statistical information. It is argued that statistical knowledge, especially that of a qualitative nature, is an importa ..."
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Cited by 11 (0 self)
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This paper presents a logical formalism for representing and reasoning with statistical knowledge. One of the key features of the formalism is its ability to deal with qualitative statistical information. It is argued that statistical knowledge, especially that of a qualitative nature, is an important component of our world knowledge and that such knowledge is used in many different reasoning tasks. The work is further motivated by the observation that previous formalisms for representing probabilistic information are inadequate for representing statistical knowledge. The representation mechanism takes the form of a logic that is capable of representing a wide variety of statistical knowledge, and that possesses an intuitive formal semantics based on the simple notions of sets of objects and probabilities defined over those sets. Furthermore, a proof theory is developed and is shown to be sound and complete. The formalism offers a perspicuous and powerful representational tool for stat...
ManyValued FirstOrder Logics with Probabilistic Semantics
 In Proceedings of the Annual Conference of the European Association for Computer Science Logic, 1998, volume 1584 of LNCS
, 1998
"... . We present nvalued firstorder logics with a purely probabilistic semantics. We then introduce a new probabilistic semantics of nvalued firstorder logics that lies between the purely probabilistic semantics and the truthfunctional semantics of the nvalued / Lukasiewicz logics / Ln . Within t ..."
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Cited by 8 (6 self)
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. We present nvalued firstorder logics with a purely probabilistic semantics. We then introduce a new probabilistic semantics of nvalued firstorder logics that lies between the purely probabilistic semantics and the truthfunctional semantics of the nvalued / Lukasiewicz logics / Ln . Within this semantics, closed formulas of classical firstorder logics that are logically equivalent in the classical sense also have the same truth value under all nvalued interpretations. Moreover, this semantics is shown to have interesting computational properties. More precisely, nvalued logical consequence in disjunctive logic programs with nvalued disjunctive facts can be reduced to classical logical consequence in n \Gamma 1 layers of classical disjunctive logic programs. Moreover, we show that nvalued logic programs have a model and a fixpoint semantics that are very similar to those of classical logic programs. Finally, we show that some important deduction problems in nvalued logic ...
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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Cited by 8 (1 self)
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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
Tutorial: Complexity of ManyValued Logics
 In Proc. 31st International Symposium on MultipleValued Logics, IEEE CS Press, Los Alamitos
, 2001
"... this article selfcontained. ..."
DT  An Automated Theorem Prover for MultipleValued FirstOrder Predicate Logics
 In Proc. 26th International Symposium on MultipleValued Logics
, 1996
"... We describe the automated theorem prover "Deep Thought" ( d DT ). The prover can be used for arbitrary multiplevalued firstorder logics, provided the connectives can be defined by truth tables and the quantifiers are generalizations of the classical universal resp. existential quantifiers. d DT h ..."
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Cited by 2 (0 self)
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We describe the automated theorem prover "Deep Thought" ( d DT ). The prover can be used for arbitrary multiplevalued firstorder logics, provided the connectives can be defined by truth tables and the quantifiers are generalizations of the classical universal resp. existential quantifiers. d DT has been tested with many interesting multiplevalued logics as well as classical firstorder predicate logic. d DT uses a freevariable semantic tableau calculus with generalized signs. For the existential tableaurules two liberalized versions are implemented. The system utilizes a static index to control the application of axioms as wells as the search for applicable rules. A dynamic lemma generation strategy and various heuristics to control the tableau expansion and branch closure are integrated into d DT . Theoretically, contradiction sets of arbitrary size can be discovered to close a branch. 1 Introduction Deep Thought ( d DT ) is an automated theorem prover which is able to cope wi...
Preservation of interpolation by fibring
 In Carnielli et al. [2004a
"... The method of fibring for combining logics as originally proposed by Gabbay [13, 14], includes some other methods as fusion [29] as a special case. Albeit fusion is the best developed mechanism, mainly in what concerns preservation of properties as ..."
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Cited by 1 (1 self)
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The method of fibring for combining logics as originally proposed by Gabbay [13, 14], includes some other methods as fusion [29] as a special case. Albeit fusion is the best developed mechanism, mainly in what concerns preservation of properties as
Towards a Theory of Conservative Computing
, 2003
"... We extend the notion of conservativeness, given by Fredkin and Toffoli in 1982, to generic gates whose input and output lines may assume a finite number d of truth values. A physical interpretation of conservativeness in terms of conservation of the energy associated to the data used during the comp ..."
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Cited by 1 (1 self)
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We extend the notion of conservativeness, given by Fredkin and Toffoli in 1982, to generic gates whose input and output lines may assume a finite number d of truth values. A physical interpretation of conservativeness in terms of conservation of the energy associated to the data used during the computation is given. Moreover, we define conservative computations, and we show that they naturally induce a new NP–complete decision problem. Finally, we present a framework that can be used to explicit the movement of energy occurring during a computation, and we provide a quantum implementation of the primitives of such framework using creation and annihilation operators on the Hilbert space C d, where d is the number of energy levels considered in the framework. 1