This paper is concerned with the foundations of fuzzy reasoning and its relationships with other logics of uncertainty. The definitions of fuzzy logics are first examined and the role of fuzzification discussed. It is shown that fuzzification of PC gives a known multivalued logic but with inappropriate semantics of implication and various alternative forms of implication are discussed. In the m...

Ontologies play a central role in the development of the semantic web, as they provide precise definitions of shared terms in web resources. One important web ontology language is DAML+OIL; it has a formal semantics and a reasoning support through a mapping to the expressive description logic with the addition of inverse roles. In this paper, we present a probabilistic extension of , called P! ...

Fuzzy answer set programming (FASP) combines two declarative frameworks, answer set programming and fuzzy logic, in order to model reasoning by default over imprecise information. Several connectives are available to combine different expressions; in particular the Gödel and Lukasiewicz fuzzy connectives are usually considered, due to their properties. Although the Gödel conjunction can be easi...

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].

1 The root of this work is on the one hand in Belnap’s four valued paraconsistent logic, and on the other hand on Pavelka’s papers further developed by Turunen. We do not introduce a new non–classical logic but, based on a related study of Perny and Tsoukiás, we introduce paraconsistent semantics of Pavelka style fuzzy sentential logic. Restricted to Lukasiewicz t–norm, our approach and the app...

In this paper an application of the well-known matrix method to an extension of the classical logic to many-valued logic is discussed: we consider an n-valued propositional logic as a propositional logic language with a logical matrix over n truth-values. The algebra of the logical matrix has operations expanding the operations of the classical propositional logic. Therefore we look over the Lu...

In previous work, I have introduced nonmonotonic probabilistic logics under variablestrength inheritance with overriding. They are formalisms for probabilistic reasoning from sets of strict logical, default logical, and default probabilistic sentences, which are parameterized through a value λ∈ [0, 1] that describes the strength of the inheritance of default probabilistic knowledge. In this pap...

Preamble This book written by A. Schumann & F. Smarandache is devoted to advances of non-Archimedean multiple-validity idea and its applications to logical reasoning. Leibnitz was the first who proposed Archimedes' axiom to be rejected. He postulated infinitesimals (infinitely small numbers) of the unit interval [0, 1] which are larger than zero, but smaller than each positive real number. Robi...