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...

In this paper a definition of the exploration performed by stochastic algorithms is proposed. It is based on the observation through cluster analysis of the solutions generated during a run. The probabilities associated by an algorithm to solution components are considered. Moreover, a consequent method for quantifying the exploration is provided. Such a measurement is applied toMAX–MIN Ant Sys...

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].

We connect Lukasiewicz logic, a well-established many-valued logic, with weighted logics, recently introduced by Droste and Gastin. We use this connection to show that for formal series with coefficients in semirings derived from MValgebras, recognizability and definability in a fragment of second order Lukasiewicz logic coincide.