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Resolution for many-valued logics
2005To achieve efficient proof procedures for quantificational logics with finitely many truth values we extend the classical resolution principle. By generalizing the notion of a semantic tree we demonstrate the completeness of resolution and of some effective refinements.
Matthias Baaz, Christian G. Fermüller
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Lewis Dichotomies in Many-Valued Logics
Studia Logica, 2012In 1979, \textit{H. R. Lewis} [Math. Syst. Theory 13, 45--53 (1979; Zbl 0428.03035)] showed that the computational complexity of the Boolean satisfiability problem dichotomizes, depending on the Boolean operations available to formulate instances: intractable (NP-complete) if negation of implication is definable, and tractable (in P) otherwise ...
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1992
1 Preliminaries.- 2 Many-Valued Propositional Calculi.- 3 Survey of Three-Valued Propositional Calculi.- 4 Some n-valued Propositional Calculi: A Selection.- 5 Intuitionistic Propositional Calculus.- 6 First-Order Predicate Calculus for Many-Valued Logics.- 7 The Method of Finitely Generated Trees in n-valued Logical Calculi.- 8 Fuzzy Propositional ...
Leonard Bolc, Piotr Borowik
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1 Preliminaries.- 2 Many-Valued Propositional Calculi.- 3 Survey of Three-Valued Propositional Calculi.- 4 Some n-valued Propositional Calculi: A Selection.- 5 Intuitionistic Propositional Calculus.- 6 First-Order Predicate Calculus for Many-Valued Logics.- 7 The Method of Finitely Generated Trees in n-valued Logical Calculi.- 8 Fuzzy Propositional ...
Leonard Bolc, Piotr Borowik
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1996
Throughout this chapter, we shall assume that k is a natural number larger than 2. We shall denote the set {0, 1,..., k − 1} by E k . The function f(x n ) = f(x 1, x 2,...,x n ) is called a function of the k-valued logic if, on any tuple α = (α 1, α2,..., α n ) of values of the variables x 1, x 2,..., x n , where α1 ∈ E k , the value f(a) also belongs ...
G. P. Gavrilov, A. A. Sapozhenko
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Throughout this chapter, we shall assume that k is a natural number larger than 2. We shall denote the set {0, 1,..., k − 1} by E k . The function f(x n ) = f(x 1, x 2,...,x n ) is called a function of the k-valued logic if, on any tuple α = (α 1, α2,..., α n ) of values of the variables x 1, x 2,..., x n , where α1 ∈ E k , the value f(a) also belongs ...
G. P. Gavrilov, A. A. Sapozhenko
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2018
Many-valued logics may be distinguished from classical logic on purely semantic grounds. One of the simplifying assumptions on which classical logic is based is the thesis of bivalence, which states that there are only two truth-values – true and false – and every sentence must be one or the other.
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Many-valued logics may be distinguished from classical logic on purely semantic grounds. One of the simplifying assumptions on which classical logic is based is the thesis of bivalence, which states that there are only two truth-values – true and false – and every sentence must be one or the other.
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2000
The study of many-valued logic was initiated by Jan Lukasiewicz around 1920. He started with a three-valued logic, introducing in particular an implication for it (see [Lukasiewicz 1920, 1930] and [Lukasiewicz & Tarski 1930], a selection of Lukasiewicz’s papers can be found in [Borkowski 1970]).
Erich Peter Klement +2 more
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The study of many-valued logic was initiated by Jan Lukasiewicz around 1920. He started with a three-valued logic, introducing in particular an implication for it (see [Lukasiewicz 1920, 1930] and [Lukasiewicz & Tarski 1930], a selection of Lukasiewicz’s papers can be found in [Borkowski 1970]).
Erich Peter Klement +2 more
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1981
I shall endeavour to cover as many branches of many-valued logic and as much of the work done in these branches as space permits. Much must, of course, be omitted, and I should therefore like to refer to an excellent bibliography of many-valued logics by Nicholas Rescher in his book (Many-Valued Logic, McGraw Hill 51893,1969).
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I shall endeavour to cover as many branches of many-valued logic and as much of the work done in these branches as space permits. Much must, of course, be omitted, and I should therefore like to refer to an excellent bibliography of many-valued logics by Nicholas Rescher in his book (Many-Valued Logic, McGraw Hill 51893,1969).
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Many-valued coalgebraic modal logic: One-step completeness and finite model property
Fuzzy Sets and Systems, 2023Churn-Jung Liau
exaly
1993
Abstract The book attempts an elementary exposition of the topics connected with many-valued logics. It gives an account of the constructions being "many-valued" at their origin, i.e. those obtained through intended introduction of logical values next to truth and falsity.
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Abstract The book attempts an elementary exposition of the topics connected with many-valued logics. It gives an account of the constructions being "many-valued" at their origin, i.e. those obtained through intended introduction of logical values next to truth and falsity.
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