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A Treatise on ManyValued Logics
 Studies in Logic and Computation
, 2001
"... The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with som ..."
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Cited by 84 (5 self)
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The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends
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 271 (16 self)
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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
Manyvalued logic
 Handbook of Philosophical Logic
, 1986
"... ABSTRACT. This paper discusses the general problem of translation functions between logics, given in axiomatic form, and in particular, the problem of determining when two such logics are “synonymous ” or “translationally equivalent. ” We discuss a proposed formal definition of translational equival ..."
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Cited by 66 (1 self)
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ABSTRACT. This paper discusses the general problem of translation functions between logics, given in axiomatic form, and in particular, the problem of determining when two such logics are “synonymous ” or “translationally equivalent. ” We discuss a proposed formal definition of translational equivalence, show why it is reasonable, and also discuss its relation to earlier definitions in the literature. We also give a simple criterion for showing that two modal logics are not translationally equivalent, and apply this to wellknown examples. Some philosophical morals are drawn concerning the possibility of having two logical systems that are “empirically distinct ” but are both translationally equivalent to a common logic. KEY WORDS: modal logic, synonymy, translation 1.
ManyValued Complete Distributivity ∗
, 2006
"... Suppose (Ω, ∗,I) is a commutative, unital quantale. Categories enriched over Ω can be studied as generalized, or manyvalued, ordered structures. Because many concepts, such as complete distributivity, in lattice theory can be characterized by existence of certain adjunctions, they can be reformulat ..."
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Suppose (Ω, ∗,I) is a commutative, unital quantale. Categories enriched over Ω can be studied as generalized, or manyvalued, ordered structures. Because many concepts, such as complete distributivity, in lattice theory can be characterized by existence of certain adjunctions, they can
REPRESENTATIONS OF MANYVALUED ALGEBRAS
"... What is manyvalued logic? The simplest and probably the best answer is the historical one: manyvalued logic is the complex of studies that originated from the papers of ̷Lukasiewicz and Post in the twenties [99, 114]. The idea underlying these studies is to extend the scope of classical logic by c ..."
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What is manyvalued logic? The simplest and probably the best answer is the historical one: manyvalued logic is the complex of studies that originated from the papers of ̷Lukasiewicz and Post in the twenties [99, 114]. The idea underlying these studies is to extend the scope of classical logic
Manyvalued logic and semirings
"... In this paper we describe the relationship between manyvalued logics (in particular Basic logic and ÃLukasiewicz logic) and semirings. We will also give definitions of automata on BLalgebras and MValgebras. 1 ..."
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In this paper we describe the relationship between manyvalued logics (in particular Basic logic and ÃLukasiewicz logic) and semirings. We will also give definitions of automata on BLalgebras and MValgebras. 1
Conjunctions of ManyValued Criteria
"... Working with uncertain information, we often take the advantage of having more than two truth values. This allows us to express different degrees of belief. In fuzzy logic, usually a continuous scalethe real interval [0; 1]is used. There are reasonsboth theoretical and practical (motivated b ..."
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by implementation problems)to restrict to a finite scale of truth degrees, i.e., to a finite chain. In this paper, we study logical operations on finite chains, in particular conjunctions. Using a computer program generating all finitelyvalued fuzzy conjunctions (tnorms), we found several properties
Institutional semantics for manyvalued logics
"... We develop manyvalued logic, including a generic abstract model theory, over a fully abstract syntax. We show that important manyvalued logic model theories, such as traditional firstorder manyvalued logic and fuzzy multialgebras, may be conservatively embedded into our abstract framework. Our ..."
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Cited by 1 (0 self)
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We develop manyvalued logic, including a generic abstract model theory, over a fully abstract syntax. We show that important manyvalued logic model theories, such as traditional firstorder manyvalued logic and fuzzy multialgebras, may be conservatively embedded into our abstract framework. Our
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