Berstel and Pin have characterized local languages by introducing local automaton. In this paper fuzzy local language is introduced and the fuzzy local languages recognized by partial fuzzy local automata in max-min and min-max compositions are studied. Some closure properties of fuzzy local languages are provided. Mathematics Subject Classification: 68Q45

In this paper we investigate the propositional logic of standard algebras for Hájek’s Basic Fuzzy Logic BL in a language expanded with propositional constants for the idempotent elements delimiting the L-, G-, and Π-components of the algebra. We start from a fixed standard BL-algebra; introduce new propositional constants; present a suitable set of axioms; investigate completeness results; and ...

This paper presents a tableau calculus for finding a model for a set-satisfiable finite set of formulas of a fuzzy logic BL△∼, a fuzzy logic BL with additional Baaz connective △ and the involutive negation ∼, if such a model exists. The calculus is a generalisation of a tableau calculus for BL, which is based on the decomposition theorem for a continuous t-norm. The aforementioned tableau calcu...

An interpretation of lattice-valued logic, defined by Titani, in basic fuzzy logic, defined by Hájek, is presented. Moreover, Titani’s axioms of lattice-valued set theory are interpreted in fuzzy set theory, under slight modifications of the fuzzy set theory axiomatics.

BL-algebras are algebraic structures corresponding to Hajek’s basic fuzzy logic. The aim of this paper is analyze the structure using commutative rings. Due computational considerations, we interested in finite case. We present new ways generate rings and provide summarizing statistics. Furthermore, investigated BL-rings, i.e., whose lattice ideals can be equipped with a BL-algebra. A character...

In [1] the authors considered finitely-valued modal logics with Kripke style semantics where both propositions and the accessibility relation are valued over a finite residuated lattice. Unfortunately, the necessity operator does not satisfy in general the normality axiom (K). In this paper we focus on the case of finite chains, and we consider a different approach based on introducing a multim...

Bounded residuated lattice ordered monoids (R -monoids) are a common generalization of pseudo-BL-algebras and Heyting algebras, i.e. algebras of the non-commutative basic fuzzy logic (and consequently of the basic fuzzy logic, the Łukasiewicz logic and the non-commutative Łukasiewicz logic) and the intuitionistic logic, respectively. In the paper we introduce and study classes of filters of bou...

An algebra M = (M ; ,∨,∧,→, 0, 1) of type 〈2, 2, 2, 2, 0, 0〉 is called a bounded commutative R`-monoid iff (i) (M ; , 1) is a commutative monoid, (ii) (M ;∨,∧, 0, 1) is a bounded lattice, and (iii) x y ≤ z ⇐⇒ x ≤ y → z, (iv) x (x → y) = x ∧ y, for each x, y, z ∈ M . In the sequel, by an R`-monoid we will mean a bounded commutative R`-monoid. (Note that bounded commutative R`-monoids are just bo...