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Calculi for Many-Valued Logics
Logica Universalis, 2021We present a number of equivalent calculi for many-valued logics and prove soundness and strong completeness theorems. The calculi are obtained from the truth tables of the logic under consideration in a straightforward manner and there is a natural duality among these calculi. We also prove the cut elimination theorems for the sequent-like systems.
Kaminski, Michael, Francez, Nissim
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Fundamenta Informaticae, 1991
Two families of many-valued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite many-valued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be many-valued. Gentzen sequent calculi are given
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Two families of many-valued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite many-valued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be many-valued. Gentzen sequent calculi are given
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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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Designing in many-valued logic
Proceedings of the Second International Conference on Intelligent Processing and Manufacturing of Materials. IPMM'99 (Cat. No.99EX296), 1999The analysis described is based on the many-valued logic of Lukasiewitcz (1970). It leads to the construction of a simple design model when the analysis cannot be based upon a two-valued logic. The reference is based on the semantics of Kripke, immersion in a definite possible world, and on the process of verification and confirmation of Carnap.
DONNARUMMA A, PAPPALARDO, Michele
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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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1981
The term ‘many-valued logic’ is most often used to denote logics which are constructed by means of introduction of additional truth-values, while classical logic is construed as a two-valued logic (cf. “Sentence logic” §1.1).
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The term ‘many-valued logic’ is most often used to denote logics which are constructed by means of introduction of additional truth-values, while classical logic is construed as a two-valued logic (cf. “Sentence logic” §1.1).
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