In this paper, we show that for any BL-general L-fuzzy automaton (BL-GLFA) there exists a complete deterministic accessible reduced BL-general L-fuzzy automaton that recognizing the behavior of the BL-GLFA. Also, we prove that for any finite realization β, there exists a minimal complete deterministic BL-GLFA recognizing β. We prove any complete deterministic accessible reduced BL-GLFA is a min...

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...

A standard associative graded algebra R over a field k is called Koszul if k admits a linear resolution as an R-module. A (right) R-module M is called Koszul if it admits a linear resolution too. Here we study a special class of Koszul algebras — roughly say, algebras having a lot of Koszul cyclic modules. Commutative algebras with similar properties (so-called algebras with Koszul filtrations)...

We investigate the combinatorics of interpolation in Gödel logic, the propositional logic whose algebraic semantics is the variety of Heyting algebras generated by chains. 1 Motivation In recent work, Busaniche and Mundici prove that Lukasiewicz logic has the Robinson property RP [4], exploiting the geometry of prime filters in the free finitely generated MV-algebra. In this note we recast thei...

A pseudo-addition in BL-algebras is a binary operation that is associative and non commutative. The aim of this paper is to use the notion of pseudo-addition to study the notion of ideal and fuzzy ideal as a natural generalization of that of ideal and fuzzy ideal in MV-algebras. Using a pseudo-addition, we characterize fuzzy ideals and also obtain a concrete description of the fuzzy ideals gene...

We introduce an expansion of Basic Logic (BL) with new connectives which express fixed points of continuous formulas, i.e. formulas of BL whose connectives are among {&,∨,∧}. The algebraic semantics of this logic is studied together with some of its subclasses corresponding to extensions of the above-mentioned expansion. The axiomatic extensions are proved to be standard complete.

This paper studies codes V over GF(4) which have even weights and have the same weight distribution as the dual code FL. Some of the results are as follows. All such codes satisfy VL = 4. (If VI = V, V has a binary basis.) The number of such V's is determined, and those of length <14 are completely classified. The weight enumerator of % is characterized and an upper bound obtained on the minimu...

Ward and Dilworth 1 introduced the concept of residuated lattices as generalization of ideal lattices of rings. The residuated lattice plays the role of semantics for a multiple-valued logic called residuated logic. Residuated logic is a generalization of intuitionistic logic. Therefore it is weaker than classical logic. Important examples of residuated lattices related to logic are Boolean alg...