Much attention is focused on the relationship between rough sets and many-valued modal logic to deal with approximate reasoning. This paper discusses graded puts forward G(S5). Secondly, by employing operators that correspond operations in G(S5), we introduce concept of upper lower truth degrees a logical formula. Then, propose conditional degrees. Several basic interesting properties are addre...

The last three decades have witnessed major advances in many-valued logic and related fields. The theory of Łukasiewicz logic and Chang’s MV-algebras has flourished, establishing profound connections with other fields of mathematics; Petr Hájek’s framework for mathematical fuzzy logic has met with remarkable success, bringing into focus the central rôle of residuation; and the algebraic analysi...

Fuzzy Description Logics (FDLs) have been introduced to reason about vague or imprecise knowledge in application domains. In recent years, reasoning in many FDLs based on infinitely many values has been proved to be undecidable [3,15] and systematic studies have been undertaken on this topic [8]. On the other hand, every finite-valued FDL that has been studied in the recent literature has not o...

Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in knowledge bases. We present a paraconsistent many-valued logic with a simple and n...

In classical propositional logic over finitely many variables no automorphism has any stochastic property, because the dual space is a finite discrete set. In this paper we show that the situation for the infinite-valued Lukasiewicz logic is radically different, by exhibiting a family of Bernoulli automorphisms over two variables. As dynamical systems, these are piecewiselinear area-preserving ...

Classically, two propositions are logically equivalent precisely when they are true under the same logical valuations. Also, two logical valuations are distinct if, and only if, there is a formula that is true according to one valuation, and false according to the other. By a real-valued logic we mean a many-valued logic in the sense of Petr Hájek that is complete with respect to a subalgebra o...

We continue a series of papers on a family of many-valued modal logics, a family whose Kripke semantics involves many-valued accessibility relations. Earlier papers in the series presented a motivation in terms of a multiple-expert semantics. They also proved completeness of sequent calculus formulations for the logics, formulations using a cut rule in an essential way. In this paper a novel cu...

A core tool for granular modeling is the use of linguistic rules, e.g. in fuzzy control approaches. We provide the reader with basic mathematical tools to discuss the behavior of system of such linguistic rules. These mathematical tools range from fuzzy logic and fuzzy set theory, through the consideration of fuzzy relation equations, up to discussions of interpolation strategies and to the use...