One aspect that has been poorly studied in multiple-valued logics, and in particular in Lukasiewicz logics, is the generation of instances of varying difficulty for evaluating, comparing and improving satisfiability solvers. In this paper we present a new class of clausal forms, called Lukasiewicz (L-)clausal forms, motivate their usefulness, study their complexity, and report on an empirical i...

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...

Ontologies play a crucial role in the development of the Semantic Web as a means for defining shared terms in Web resources. They are formulated in web ontology languages, which are based on expressive description logics. Significant research efforts are recently directed towards representing and reasoning with uncertainty and vagueness in ontologies for the Semantic Web. In this paper, we give...

The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)’s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Lukasiewicz, modal logics that admit the ru...

The aim of this paper is to explore the class of intermediate logics between the truth-preserving Lukasiewicz logic L and its degree-preserving companion L≤. From a syntactical point of view, we introduce some families of inference rules (that generalize the explosion rule) that are admissible in L≤ and derivable in L and we characterize the corresponding intermediate logics. From a semantical ...

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...

Prolog is a programming language based on a restricted subset of classical rst order predicate logic. In order to overcome some problems of classical logic to handle imperfect human knowledge, we provide a formal framework for a Lukasiewicz logic based Prolog system. The use of Lukasiewicz logic with its connection to Ulam games enables us to deal with partial inconsistencies by interpreting th...