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Classical Gentzentype Methods in Propositional ManyValued Logics
 In Fitting, M., & Orlowska, E. (Eds.), Theory and Applications in MultipleValued Logics
, 2002
"... A classical Gentzentype system is one which employs twosided sequents, together with structural and logical rules of a certain characteristic form. A decent Gentzentype system should allow for direct proofs, which means that it should admit some useful forms of cut elimination and the subformula p ..."
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Cited by 6 (2 self)
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property. In this tutorial we explain the main difficulty in developing classical Gentzentype systems with these properties for manyvalued logics. We then illustrate with numerous examples the various possible ways of overcoming this difficulty. Our examples include practically all 3valued logics
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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. 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
Temporal and modal logic
 HANDBOOK OF THEORETICAL COMPUTER SCIENCE
, 1995
"... We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic. ..."
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Cited by 1300 (17 self)
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We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
GentzenType Systems, Resolution And Tableaux
 Journal of Automated Reasoning
, 1993
"... Introduction In advanced books and courses on logic (e.g. [Sm], [BM]) Gentzentype systems or their dual, tableaux, are described as techniques for showing validity of formulae which are more practical than the usual Hilberttype formalisms. People who have learnt these methods often wonder why the ..."
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Cited by 36 (13 self)
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Introduction In advanced books and courses on logic (e.g. [Sm], [BM]) Gentzentype systems or their dual, tableaux, are described as techniques for showing validity of formulae which are more practical than the usual Hilberttype formalisms. People who have learnt these methods often wonder why
Gentzentype Refutation Systems for ThreeValued Logics ⋆
"... Abstract. While the purpose of a conventional proof calculus is to axiomatise the set of valid sentences of a given logic, a refutation system, or complementary calculus, is concerned with axiomatising the invalid sentences. Instead of exhaustively searching for counter models for some sentence, ref ..."
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, refutation systems establish invalidity by deduction and thus in a purely syntactic way. Such systems are relevant not only for prooftheoretic reasons but also for realising deductive systems for nonmonotonic logics. In this paper, we introduce Gentzentype refutation systems for two basic threevalued
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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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
A Framework for Defining Logics
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1993
"... The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of ariti ..."
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Cited by 807 (45 self)
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The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system
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 34 (0 self)
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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
Abduction in Logic Programming
"... Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over th ..."
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Cited by 616 (76 self)
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Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over
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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ideas 1.1 From classical to manyvalued logic Logical systems in general are based on some formalized language which includes a notion of well formed formula, and then are determined either semantically or syntactically. That a logical system is semantically determined means that one has a notion
Results 1  10
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