Lukasiewicz logic arrays (LLAs) are analog VLSI circuits structured as trees of continuous-valued implications. First described in 1990, LLAs are now nding uses as applicationspeci c array processors for image processing, fuzzy inference, and robotic control. Yet an early question persists: Why do LLAs work? Intuitively, a small error should build up through successive implications of an arbitr...

In this paper we prove algebraic equivalents of the conservative extension theorems of Lukasiewicz propositional logic to rational Pavelka propositional logic. The results concerns the conservative extension and the very conservative extension of MV-algebras to Pavelka algebras.

In the 1970s, Robin Giles introduced a game combining Lorenzen-style dialogue rules with a simple scheme for betting on the truth of atomic statements, and showed that the existence of winning strategies for the game corresponds to the validity of formulas in Lukasiewicz logic. In this paper, it is shown that ‘disjunctive strategies’ for Giles’s game, combining ordinary strategies for all insta...

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 propose extensions of affine classical linear algebra(ACL-algebra) and many-valued algebra(MV-algebra), the emphasis is being on the latter. MV-algebras are algebraic models of à Lukasiewicz א0-valued logic(à Lא0) and that was established long back in 1958 by C.C. Chang. MV-algebra is recently studied from the angle of fuzzy set theory. Also it is investigated in connection wi...

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...

In this paper we present the theorem prover SBR3 for equational logic and its application in the many-valued logic of Lukasiewicz. We give a new equational axiomatization of many-valued logic and we prove by SBR3 that it is equivalent to the classical equational presentation of such logic given by Wajsberg. We feel that our equational axiomatization of Wajsberg algebras is more suited for autom...

in this paper the concepts of fuzzifying β − irresolute functions and fuzzifying β − compactspaces are characterized in terms of fuzzifying β − open sets and some of their properties are discussed.

Monadic MV –algebras are an algebraic model of the predicate calculus of the Lukasiewicz infinite valued logic in which only a single individual variable occurs. GMV -algebras are a non-commutative generalization of MV -algebras and are an algebraic counterpart of the non-commutative Lukasiewicz infinite valued logic. We introduce monadic GMV -algebras and describe their connections to certain ...