We develop the general theory of RMV-algebras, which are essentially unit intervals in Riesz spaces with strong unit. Since the variety of RMV-algebras is generated by [0, 1], we get an equational characterization of the real product on [0,1] interpreted as scalar multiplication.

In this paper we build upon previous works of Hájek and Vychodil on the axiomatization of truthstressing and depressing hedges as expansions of BL logic by new unary connectives. They show that their logics are chain-complete, but standard completeness is only proved for the expansions over Gödel logic....

Equality algebras has recently been introduced. A subclass of equality algebras, called equivalential equality algebras is closely related to BCK-algebras with meet. We show that the variety of equality algebras has nice properties: We shall investigate their congruences and filters and prove that the...

In this paper, extension of the EQ-logic by the connective is introduced. The former is a new kind of many-valued logic which based on EQ-algebra of truth values, i.e. the algebra in which fuzzy equality is the fundamental operation and implication is derived from it. First, we extend the EQ-algebra...

We introduce an axiomatic extension of H¨ohle's Monoidal Logic called Semi­divisible Monoidal Logic, and prove that it is complete by showing that semi­divisibility is preserved in MacNeille completion. Moreover, we introduce Strong semi­ divisible Monoidal Logic and conjecture that a predicate formula...

This paper presents a generalization of many particular results about special types of filters (e.g., (positive) implicative, fantastic) on algebras of nonclassical (mostly fuzzy) logics. Our approach is rooted in the framework of Abstract Algebraic Logic, and is based on the close connection between...

We define the notion of a canonical Gödel system in the framework of single-conclusion hypersequent calculi. A corresponding general (nondeterministic) Gödel valuation semantics is developed, as well as a (non-deterministic) linear intuitionistic Kripke-frames semantics. We show that every canonical...

We define the fuzzy description logic ALCHNM based on the t-norm of Nilpotent Minimum and we prove its reduction to the crisp description logic ALCH. Hence we prove decidability results for ALCHNM.

This paper studies the possibility to deal with partial functions in fuzzy type theory. Among various ways how to represent them we chose introduction of a special value "undefined" laying outside the corresponding domain. In FTT, we can quite naturally utilize the description operator by extending its...

Fuzzy sets are widely used to model vague properties. According to a common understanding, a fuzzy set represents the degrees of similarity of precisely specified objects with the prototypes of the considered vague property. We propose a logic based on this idea, using an entailment relation which was...

Presented are preliminary results on ordinary-style and graded-style completeness results for fuzzy attribute logic with models constrained by fuzzy closure operators with hedges.

Solving systems of equations (even linear ones) in standard fuzzy arithmetic may be a problem. We suggest an alternative approach which transfers the task to a linear space where the solution may be standard. Fuzzy intervals form a proper subset (in fact, a cone) in this linear space.