The term" fuzzy logic," as it is understood in this book, stands for all aspects of representing
and manipulating knowledge based on the rejection of the most fundamental principle of …

Originating as an attempt to provide solid logical foundations for fuzzy set theory, and
motivated also by philosophical and computational problems of vagueness and imprecision …

Fuzzy logics are many-valued logics that are well suited to reasoning in the context of
vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse …

This article deals with many-valued modal logics, based only on the necessity operator, over
a residuated lattice. We focus on three basic classes, according to the accessibility relation …

Since the mid-1980s, quantales have found an increasing interest in various areas of
mathematics. This development has its origin in ideas coming from non-commutative …

This article introduces, studies, and applies a new system of logic which is called 'HYPE'. In
HYPE, formulas are evaluated at states that may exhibit truth value gaps (partiality) and truth …

We introduce a new class of algebras called EQ-algebras. An EQ-algebra has three basic
binary operations (meet, multiplication and a fuzzy equality) and a top element. These …

The book presents a thoroughly elaborated logical theory of generalized truth-values
understood as subsets of some established set of (basic) truth values. After elucidating the …

We introduce a systematic procedure to transform large classes of (Hilbert) axioms into
equivalent inference rules in sequent and hypersequent calculi. This allows for the …

The present chapter is aimed at giving a conceptual exposition of the mathematical
principles underlying Sahlqvist correspondence theory. These principles are argued to be …