نتایج جستجو برای: integral commutative residuated lattice

تعداد نتایج: 218170  

Journal: :bulletin of the iranian mathematical society 0
m. kondo school of information environment‎, ‎tokyo denki university‎, ‎p.o‎. ‎box 270-1382‎, ‎inzai‎, ‎japan

we consider properties of residuated lattices with universal quantifier and show that, for a residuated lattice $x$, $(x, forall)$ is a residuated lattice with a quantifier if and only if there is an $m$-relatively complete substructure of $x$. we also show that, for a strong residuated lattice $x$, $bigcap {p_{lambda} ,|,p_{lambda} {rm is an} m{rm -filter} } = {1}$ and hence that any strong re...

2016
M. Kondo

A notion of reticulation which provides topological properties on algebras has introduced on commutative rings in 1980 by Simmons in [5]. For a given commutative ring A, a pair (L, λ) of a bounded distributive lattice and a mapping λ : A → L satisfying some conditions is called a reticulation on A, and the map λ gives a homeomorphism between the topological space Spec(A) consisting of prime fil...

2013
JOSÉ GIL-FÉREZ ANTONIO LEDDA CONSTANTINE TSINAKIS Antonio Di Nola C. TSINAKIS

The amalgamation property (AP) is of particular interest in the study of residuated lattices due to its relationship with various syntactic interpolation properties of substructural logics. There are no examples to date of non-commutative varieties of residuated lattices that satisfy the AP. The variety SemRL of semilinear residuated lattices is a natural candidate for enjoying this property, s...

2017
Sándor Jenei

Hahn’s famous structure theorem states that totally ordered Abelian groups can be embedded in the lexicographic product of real groups. Our main theorem extends this structural description to order-dense, commutative, group-like residuated chains, which has only finitely many idempotents. It is achieved via the so-called partial-lexicographic product construction (to be introduced here) using t...

2009
Antonín Dvorák Michal Holcapek

The aim of this paper is to introduce two new types of fuzzy integrals, namely, ⊗-fuzzy integral and →-fuzzy integral, where ⊗ and → are the multiplication and residuum of a complete residuated lattice, respectively. The first integral is based on a fuzzy measure of L-fuzzy sets and the second one on a complementary fuzzy measure of L-fuzzy sets, where L is a complete residuated lattice. Some o...

2014
Michel Marti George Metcalfe

A Hennessy-Milner property, relating modal equivalence and bisimulations, is defined for many-valued modal logics that combine a local semantics based on a complete MTL-chain (a linearly ordered commutative integral residuated lattice) with crisp Kripke frames. A necessary and sufficient algebraic condition is then provided for the class of image-finite models of these logics to admit the Henne...

2017
Wojciech Dzik Sándor Radeleczki

We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law ¬x∨¬¬x = 1, preserves filtering (or directed) unification, that is, the property that for every two unifiers there is a unifier more general then both of them. Contrary to that, often adding new operations to algebras results in changing the unification type. To pr...

2013
Zhudeng Wang Xuejun Liu

In this paper, we introduce the notion of L-topological spaces based on a complete bounded integral residuated lattice and discuss some properties of interior and left (right) closure operators.

Journal: :iranian journal of fuzzy systems 2013
hui han jinming fang

in this paper, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

Journal: :Arch. Math. Log. 2006
Félix Bou Àngel García-Cerdaña Ventura Verdú

The logic of (commutative integral bounded) residuated lattices is known under different names in the literature: monoidal logic [Höh95], intuitionistic logic without contraction [AV00], HBCK [OK85] (nowadays called FLew by Ono), etc. In this paper 1 we study the 〈∨, ∗,¬, 0, 1〉-fragment and the 〈∨,∧, ∗,¬, 0, 1〉-fragment of the logical systems associated with residuated lattices, both from the p...

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