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33
Finiteness in infinitevalued Lukasiewicz logic
, 2000
"... In this paper we deepen Mundici's analysis on reducibility of the decision problem from infinitevalued Lukasiewicz logic L1 to a suitable mvalued Lukasiewicz logic Lm , where m only depends on the length of formulas to be proved. Using geometrical arguments we find a better upper bound for th ..."
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Cited by 5 (1 self)
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In this paper we deepen Mundici's analysis on reducibility of the decision problem from infinitevalued Lukasiewicz logic L1 to a suitable mvalued Lukasiewicz logic Lm , where m only depends on the length of formulas to be proved. Using geometrical arguments we find a better upper bound
The logical content of triangular bases of fuzzy sets in Lukasiewicz infinitevalued logic
"... Continuing to pursue a research direction that we already explored in connection with GödelDummett logic and Ruspini partitions, we show here that Lukasiewicz logic is able to express the notion of pseudotriangular basis of fuzzy sets, a mild weakening of the standard notion of triangular basis. ..."
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Continuing to pursue a research direction that we already explored in connection with GödelDummett logic and Ruspini partitions, we show here that Lukasiewicz logic is able to express the notion of pseudotriangular basis of fuzzy sets, a mild weakening of the standard notion of triangular basis
Recursively Enumerable Prime Theories in InfiniteValued Lukasiewicz Logic are not Uniformly Decidable
"... In infinitevalued Lukasiewicz logic it is wellknown that prime theories do not coincide with maximally consistent (complete) theories. It is said that a theory T is prime if, for every pair of formulas ϕ,ψ either ϕ → ψ ∈ T or ψ → ϕ ∈ T. On the other hand, T is maximally consistent if, whenever ϕ 6 ..."
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In infinitevalued Lukasiewicz logic it is wellknown that prime theories do not coincide with maximally consistent (complete) theories. It is said that a theory T is prime if, for every pair of formulas ϕ,ψ either ϕ → ψ ∈ T or ψ → ϕ ∈ T. On the other hand, T is maximally consistent if, whenever ϕ
Bounded Lukasiewicz Logics
"... Lukasiewicz logics were introduced for philosophical reasons by Jan Lukasiewiczin the 1920s [8] and are among the first examples of manyvalued logics. Currently they are of great importance in several areas of research. Firstly, in fuzzylogic [15], where infinitevalued Lukasiewicz logic ..."
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Lukasiewicz logics were introduced for philosophical reasons by Jan Lukasiewiczin the 1920s [8] and are among the first examples of manyvalued logics. Currently they are of great importance in several areas of research. Firstly, in fuzzylogic [15], where infinitevalued Lukasiewicz logic
Lukasiewicz and Modal Logic
"... . / Lukasiewicz's fourvalued modal logic is surveyed and analyzed. 1 Introduction The Polish philosopher and logician Jan / Lukasiewicz (Lw'ow, 1878  Dublin, 1956) is one of the fathers of modern manyvalued logic, and some of the systems he introduced are presently a topic of deep in ..."
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investigation. In particular his infinitelyvalued logic belongs to the core systems of mathematical fuzzy logic as a logic of comparative truth, cf. [3, 6, 7]. It is interesting to recall that modal notions were present in / Lukasiewicz's motivation from the start. His 1930 paper [13] on manyvalued
Some consequences of compactness in Lukasiewicz Predicate Logic?
"... Abstract. The LośTarski Theorem and the Chang LośSusko Theorem, two classical results in Model Theory, are extended to the infinitevalued Lukasiewicz logic. The latter is used to settle a characterisation of the class of generic structures introduced in the framework of model theoretic forcin ..."
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Abstract. The LośTarski Theorem and the Chang LośSusko Theorem, two classical results in Model Theory, are extended to the infinitevalued Lukasiewicz logic. The latter is used to settle a characterisation of the class of generic structures introduced in the framework of model theoretic
Duality, projectivity, and unification in Lukasiewicz logic and MValgebras
, 2011
"... We prove that the unification type of Lukasiewicz (infinitevalued propositional) logic and of its equivalent algebraic semantics, the variety of MValgebras, is nullary. The proof rests upon Ghilardi’s algebraic characterisation of unification types in terms of projective objects, recent progress ..."
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Cited by 8 (2 self)
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We prove that the unification type of Lukasiewicz (infinitevalued propositional) logic and of its equivalent algebraic semantics, the variety of MValgebras, is nullary. The proof rests upon Ghilardi’s algebraic characterisation of unification types in terms of projective objects, recent progress
On Lukasiewicz's fourvalued modal logic
, 2000
"... . # Lukasiewicz's fourvalued modal logic is surveyed and analyzed, together with # Lukasiewicz's motivations to develop it. A faithful interpretation of it into classical (nonmodal) twovalued logic is presented, and some consequences are drawn concerning its classification and its algeb ..."
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Cited by 3 (0 self)
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. # Lukasiewicz's fourvalued modal logic is surveyed and analyzed, together with # Lukasiewicz's motivations to develop it. A faithful interpretation of it into classical (nonmodal) twovalued logic is presented, and some consequences are drawn concerning its classification and its
Distinguishing nonstandard natural numbers in a set theory within Lukasiewicz logic
, 2007
"... Set theory: H with the comprehension principle within ̷Lukasiewicz infinitevalued logic. A known result: H is ωinconsistent [Y05] i.e. there exists ϕ such that, in any model M of H, • for any standard natural number n, �ϕ(n)�M = 0 holds, • �(∃x ∈ ω) ϕ(x)�M = 1: “ω must contains a nonstandard natu ..."
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Cited by 3 (1 self)
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Set theory: H with the comprehension principle within ̷Lukasiewicz infinitevalued logic. A known result: H is ωinconsistent [Y05] i.e. there exists ϕ such that, in any model M of H, • for any standard natural number n, �ϕ(n)�M = 0 holds, • �(∃x ∈ ω) ϕ(x)�M = 1: “ω must contains a non
F.J.: Fregean algebraic tableaux: Automating inferences in fuzzy propositional logic
 In: Proceedings of the 12th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR’05), SpringerVerlag
, 2005
"... Abstract. We develop a tableau procedure for finding theorems and consequence relations of RPL △ (i.e., ̷L ℵ extended with constants and a determinacy operator). RPL △ includes a large number of proposed truthfunctions for fuzzy logic. Our procedure simplifies tableaux for infinitevalued systems by ..."
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Abstract. We develop a tableau procedure for finding theorems and consequence relations of RPL △ (i.e., ̷L ℵ extended with constants and a determinacy operator). RPL △ includes a large number of proposed truthfunctions for fuzzy logic. Our procedure simplifies tableaux for infinitevalued systems
Results 1  10
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33