J. Vaz De Carvalho and T. Almada in A generalization of the Lukasiewicz algebras, Studia Logica 69 (2001), 329-338 introduced the variety Ln , m ≥ 1, n ≥ 2, of m–generalized Lukasiewicz algebras of order n as a generalization of Lukasiewicz algebras of order n and a particular case of Ockham algebras. In this note, bearing in mind the important role that weak implication played in the study of ...

We construct explicit bases of single-conclusion and multiple-conclusion admissible rules of propositional Lukasiewicz logic, and we prove that every formula has an admissibly saturated approximation. We also show that Lukasiewicz logic has no finite basis of admissible rules.

We define the Lukasiewicz transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an MV-algebra. Then we describe the “ Lukasiewicz Transform Based” ( LTB) algorithm for image processing, demonstrating its applicability.

This paper studies the linguistic truth value domain (AX) based on finite monotonous hedge algebra and then we extend lukasiewicz algebra on [0, 1] to linguistic lukasiewicz algebra on linguistic truth value domain (AX), in an attempt to propose a general resolution for linguistic many-valued logic based on hedge moving rules and linguistic lukasiewicz algebra for linguistic reasoning. Its theo...

We show that the set of valid formulas in Lukasiewicz predicate logic is a complete Π 2 set. We also show that the classically valid formulas are exactly those formulas in the classical language whose fuzzy value is 1/2. Lukasiewicz’ infinite valued logic can be seen as a particular “implementation” of fuzzy logic. The set of possible “truth values” (or, in another interpretation, degrees of ce...

We consider propositional logic. Three-valued logics are old: the first one is Lukasiewicz three valued logic from 1920 [8]. Gödel in [5] from 1932 studied a hierarchy of finite-valued logics, containing Gödel three-valued logic. Our main interest pays to Kleene three-valued logic [6]. Other threevalued logics will not be considered here. Let us agree that the three truth values are 0, 1 2 , 1 ...

This paper is devoted to construction of fuzzy preference relations and to showing how this construction is connected with Lukasiewicz filters and TL-evaluators. We will study also extensions of Lukasiewicz filters on subsets of some X 6= ∅ to TL-evaluators on the system (lattice) of fuzzy functions f : X → [0, 1].