The multi-valued logic of Lukasiewicz is a substructural logic that has been widely studied and has many interesting properties. It is classical, in the sense that it admits the axiom schema of double negation elimination, [DNE]. However, our understanding of Lukasiewicz logic can be improved by separating its classical and intuitionistic aspects. The intuitionistic aspect of Lukasiewicz logic ...

In this paper we give a characterization of all the interpretations of the varieties of bounded distributive lattices, De Morgan algebras and Lukasiewicz algebras of order m in the variety of Lukasiewicz algebras of order n. In the case of distributive lattices we give a structure theorem that is generalized to De Morgan algebras and to Lukasiewicz algebras of order m. In the last two cases we ...

Moisil logic, having as algebraic counterpart Lukasiewicz-Moisil algebras, provides an alternative way to reason about vague information based on the following principle: a many-valued event is characterized by a family of Boolean events. However, using the original definition of Lukasiewicz-Moisil algebra, the principle does not apply for subalgebras. In this paper we identify an alternative a...

in this paper, we study the finitely many constraints of the fuzzyrelation inequality problem and optimize the linear objectivefunction on the region defined by the fuzzy max-product operator.simplification operations have been given to accelerate theresolution of the problem by removing the components having noeffect on the solution process. also, an algorithm and somenumerical and applied exa...

We investigate admissible rules of Lukasiewicz multi-valued propositional logic. We show that admissibility of multiple-conclusion rules in Lukasiewicz logic, as well as validity of universal sentences in free MV -algebras, is decidable (in PSPACE ).

In the framework of propositional Lukasiewicz logic, a suitable notion of implicit definability, tailored to the intended real-valued semantics and referring to the elements of its domain, is introduced. Several variants of implicitly defining each of the rational elements in the standard semantics are explored, and based on that, a faithful interpretation of theories in Rational Pavelka logic ...

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 ...

In this paper we propose clustering methods based on weighted quasiarithmetic means of T -transitive fuzzy relations. We first generate a T -transitive closure R from a proximity relation R based on a max-T composition and produce a T -transitive lower approximation or opening RT from the proximity relation R through the residuation operator. We then aggregate a new T -indistinguishability fuzz...