共查询到20条相似文献,搜索用时 31 毫秒
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Lattice implication algebra is an algebraic structure that is established by combining lattice and implicative algebra. It originated from the study on lattice-valued logic. In this paper, we characterize two special classes of lattice implication algebra, namely, subdi-rectly irreducible and directly indecomposable lattice implication algebras. Some important results are obtained. 相似文献
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Fuzzy蕴涵代数的素MP-滤子空间(英文) 总被引:1,自引:0,他引:1
In this paper,the topological space(PFMP(X),T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T0-space if X with condition(P).Secondly,we restricted T to the set of all maximal MP-filters MFMP(X) of X and concluded that(PFMP(X),T |PFMP(X) )is a compact T2 space if X with conditions(P) and(S). 相似文献
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In this paper,some necessary and sufficient conditions that a finite lattice implication algebra is simple are established.Specially,it is proved that a finite lattice implication algebra L is simple if and only if (L,≤) is a chain,if and only if there exists the unique dual atom in L.Also,it is given that a finite lattice implication algebra with order of a prime number is simple. 相似文献
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Manuel Abad Cecilia Rossana Cimadamore José Patricio Díaz Varela 《Central European Journal of Mathematics》2009,7(2):299-309
In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable
monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give
a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic
implication algebras and the category of monadic implication spaces.
相似文献
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This paper introduced the concept of L-fuzzy sub lattice implication algebra and discussed its properties. Proved that the intersection set of a family of L-fuzzy sub lattice implication algebras is a L-fuzzy sub lattice implication algebra, that a L-fuzzy sub set of a lattice implication algebra is a L-fuzzy sub lattice implication algebra if and only if its every cut set is a sub lattice implication algebra, and that the image and original image of a L-fuzzy sub lattice implication algebra under a lattice implication homomorphism are both L-fuzzy sub lattice implication algebras. 相似文献
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多值逻辑是人工智能中一个重要的研究方向。为了进一步深入研究多值逻辑,特别是真值基于格上的多值逻辑,文献「1」提出并提建立了格蕴涵代数这一逻辑代数结构,进而研究了对应的格值逻辑系统。本文则集中讨论了一类较特殊但也较广泛的格蕴涵代数,即内射的格蕴涵代数,深入探讨了这类代数和一些性质并给出了其特征结构的刻画。 相似文献
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蕴涵格及其Fuzzy拓扑表现定理 总被引:27,自引:0,他引:27
以L-Lindenbaum代数为背景,引入了蕴涵格与正则蕴涵格的概念,讨论了其基本性质,引入了Fuzzy蕴涵空间的概念,为点集拓扑学中零维空间概念的推广.建立了正则蕴涵格的Fuzzy蕴涵空间表现定理,以此为基础可以给出著名的Stone表现定理的另一种证明. 相似文献
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In this paper,the concepts of product and factorization of lattice implication algebra areproposed,the relation between lattice implication product algebra and its factors and some properties oflattice implication product algebras are discussed. 相似文献
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OntheCharacteristicofProperLatticeImplicationAlgebras¥XuYang;QinKeyun(SouthwestJiaotongUniversity)(HenanNormalUniversity)Abst... 相似文献
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蕴涵格的滤子及同余关系 总被引:2,自引:0,他引:2
在蕴涵格中引和了蕴涵滤子的概念,讨论了蕴涵滤子的一些基本性质,并由此建立了由素蕴涵滤子决定的同余关系及其商蕴涵格,以便为Fuzz推理建立了严格的逻辑基础作些必要的准备。 相似文献
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Generalized Esakia spaces are the topological duals of bounded implicative semilattices in the duality studied by G. Bezhanishvili and R. Jansana. We study the relation between a Hilbert algebra and the generalized Esakia space dual to its free implicative semilattice extension. To establish the relation we introduce a category whose objects are a generalized Esakia space together with a family of clopen up-sets that constitutes a subalgebra of the implication fragment of the Heyting algebra of the up-sets of the generalized Esakia space. 相似文献
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Sobriety in Terms of Nets 总被引:2,自引:0,他引:2
Philipp Sünderhauf 《Applied Categorical Structures》2000,8(4):649-653
Sobriety is a subtle notion of completeness for topological spaces: A space is sober if it may be reconstructed from the lattice of its open subsets. The usual criterion to check sobriety involves either irreducible closed subsets or completely prime filters of open sets. This paper provides an alternative possibility, thus trying to make sobriety easier to understand. We define the notion of observative net, which, together with an appropriate convergence notion, characterizes sobriety. As the filter approach does not involve just usual (topological) convergence, this is not an instance of the classical net-filter translation in general topology. 相似文献
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Sergio A. Celani Leonardo M. Cabrer Daniela Montangie 《Central European Journal of Mathematics》2009,7(3):463-478
In this paper we introduce a special kind of ordered topological spaces, called Hilbert spaces. We prove that the category
of Hilbert algebras with semi-homomorphisms is dually equivalent to the category of Hilbert spaces with certain relations.
We restrict this result to give a duality for the category of Hilbert algebras with homomorphisms. We apply these results
to prove that the lattice of the deductive systems of a Hilbert algebra and the lattice of open subsets of its dual Hilbert
space, are isomorphic. We explore how this duality is related to the duality given in [6] for finite Hilbert algebras, and
with the topological duality developed in [7] for Tarski algebras.
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格蕴涵代数与BCK代数的关系 总被引:2,自引:1,他引:2
本文给出了有界可换的BCK代数的分配性的一些等价条件,指出了格蕴涵代数与有界可换分配的BCK代数以及格H蕴涵代数与有界关联的BCK代数之间的对偶关系 相似文献
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In this paper, inspired by methods of Bigard, Keimel, and Wolfenstein ([2]), we develop an approach to sheaf representations of MV‐algebras which combines two techniques for the representation of MV‐algebras devised by Filipoiu and Georgescu ([18]) and by Dubuc and Poveda ([16]). Following Davey approach ([12]), we use a subdirect representation of MV‐algebras that is based on local MV‐algebras. This allowed us to obtain: (a) a representation of any MV‐algebras as MV‐algebra of all global sections of a sheaf of local MV‐algebras on the spectruum of its prime ideals; (b) a representation of MV‐algebras, having the space of minimal prime ideals compact, as MV‐algebra of all global sections of a Hausdorff sheaf of MV‐chains on the space of minimal prime ideals, which is a Stone space; (c) an adjunction between the category of all MV‐algebras and the category of MV‐algebraic spaces, where an MV‐algebraic space is a pair (X, F), where X is a compact topological space and F is a sheaf of MV‐algebras with stalks that are local (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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It is shown that the prime and primitive spectra of the multiparameter quantized algebra of odd-dimensional euclidean spaces are homeomorphic to the Poisson prime and Poisson primitive spectra of the multiparameter Poisson algebra of odd-dimensional euclidean spaces in the case when the multiplicative subgroup of a base field generated by the parameters is torsion free. As a corollary, it is shown that the prime and primitive spectra of the multiparameter quantized algebra of odd-dimensional euclidean spaces are topological quotients of the prime and maximal spectra of the corresponding commutative polynomial ring. 相似文献
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In this paper we identify and study several lattice structures in the context of directed topology. The set of d-structures on a topological space is a Heyting algebra. The implication is constructed explicitely. There is a Galois connection between the lattice of subsets of the space and the lattice of d-structures which clarifies the idea of removing a subset of the space which has only constant dipaths. Hence, variation of d-structures and variation of the “forbidden area” may be considered in one structure. Moreover, the lattice of d-structures gives rise to a lattice of directed paths between a fixed pair of points. That lattice permits us to discuss a perspective on generalised persistence. Furthermore, we consider a lattice structure in the hierarchy of structures on the n-cube. 相似文献