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1.
In this paper we show that the prime ideal space of an MV-algebra is the disjoint union of prime ideal spaces of suitable local MV-algebras. Some special classes of algebras are defined and their spaces are investigated. The space of minimal prime ideals is studied as well. Mathematics Subject Classification : 03B50, 06D99. 相似文献
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本文目的是在无逆序对合的分配格上研究余拓扑的Urysohn性质，利用coHeyting代数的pseudo-negation和分子的linked component的概念，在完全分配格上定义了一种新的Urysohn性质，称之为良Urysohn性．文中详细地讨论良Urysohn性的基本性质，并利用文中建立的Urysohn收敛理论给出了良Urysohn性的刻画定理． 相似文献
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本文研究了在一般topos中内蕴Heyting代数对象的性质.利用范畴的态射及伴随的方法,获得了内蕴Heyting代数对象为内蕴分配格结果,推广了集合范畴中的对应结果. 相似文献
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刘春辉 《高校应用数学学报(A辑)》2014,29(4)
运用格理论的原理和方法对格蕴涵代数L的LI-理想概念作进一步研究.首先,在L的全体LI-理想之集ф_(LI)(L)上定义了格运算■和■,蕴涵运算■以及伪补运算■,证明了(ф_(LI)(L),,■,■,■,{O},L)构成一个完备Heyting代数的结论.其次,利用运算固的性质给出了(ф_(LI)(L),,■,■,■,■,{O},L)成为Boolean代数的若干充要条件.最后,借助于L的素LI-理想之特性获得了格(ф_(LI)(L),,■,■,{O},L)中素元的若干等价刻画. 相似文献
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Let (L, ≤, ∨, ∧) be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by ∨ and ∧ respectively, is studied. We obtain: (i) the necessary and suffcient conditions for S(A, b)≠■l; (ii) the necessary conditions for |S(A, b)| = 1. We also obtain the vector ∈ Ln and prove that it is the largest element of S(A, b) if S(A, b)≠■. 相似文献
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The present paper introduces and studies the variety WH of weakly Heyting algebras. It corresponds to the strict implication fragment of the normal modal logic K which is also known as the subintuitionistic local consequence of the class of all Kripke models. The tools developed in the paper can be applied to the study of the subvarieties of WH; among them are the varieties determined by the strict implication fragments of normal modal logics as well as varieties that do not arise in this way as the variety of Basic algebras or the variety of Heyting algebras. Apart from WH itself the paper studies the subvarieties of WH that naturally correspond to subintuitionistic logics, namely the variety of R‐weakly Heyting algebras, the variety of T‐weakly Heyting algebras and the varieties of Basic algebras and subresiduated lattices. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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The decision problem for positively quantified formulae in the theory of linearly ordered Heyting algebras is known, as a special case of work of Kreisel, to be solvable; a simple solution is here presented, inspired by related ideas in Gödel-Dummett logic. 相似文献
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HEYTING代数与FUZZY蕴涵代数 总被引：5，自引：0，他引：5
Heyting代数是作为直觉主义命题逻辑的代数模型而引进的Fuzzy蕴涵代数是 [0 ,1]值逻辑的蕴函联结词的一种代数抽象 .本文给出Heyting代数的若干基本性质 ,并证明了Heyting代数是Fuzzy蕴涵代数 ,也是Heyting型Fuzzy蕴涵代数。 相似文献
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本文证明了格的极小生成元集一定是最小生成元集且只能是非零完全并既约元全体,证明了分配格具有最小生成元集的必要条件是它满足并无限分配律．本文还证明了完全Ｈｅｙｔｉｎｇ代数具有最小生成元集当且仅当它是强代数格,证明了完备格是强代数格当且仅当它和它的对偶格均是具有最小生成元集的分配格． 相似文献
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We study the linear Lindenbaum algebra of Basic Propositional Calculus, called linear basic algebra. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Sergio A. Celani 《Mathematical Logic Quarterly》2006,52(4):404-416
The present paper introduces and studies the variety ????n of n‐linear weakly Heyting algebras. It corresponds to the algebraic semantic of the strict implication fragment of the normal modal logic K with a generalization of the axiom that defines the linear intuitionistic logic or Dummett logic. Special attention is given to the variety ????2 that generalizes the linear Heyting algebras studied in [10] and [12], and the linear Basic algebras introduced in [2]. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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引入一个具有Heyting结构Ockham代数,简称HO-代数．所谓HO-代数,是指具有（2,2,2,1,0,0）类型的代数（L;∧,∨,→,f,0,1）．其中（L;f）是Ockham代数,（L;→）是Heyting代数,且运算f和→由恒等式f（x→y）=f^2（x）∧f（y）与f（x）→y=f^2（x）∨y所连结．主要讨论了HO-代数的同余关系的性质．并刻画了其次直不可约代数的某些性质． 相似文献
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A.M. Pitts 《Fuzzy Sets and Systems》1982,8(1):101-104
The relationship between fuzzy sets and H-valued sets is briefly examined and a claim of Eytan's that the former comprise the objects of a topos is corrected. 相似文献
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Abir Nour 《Mathematical Logic Quarterly》1999,45(4):457-466
In order to modelize the reasoning of an intelligent agent represented by a poset T, H. Rasiowa introduced logic systems called “Approximation Logics”. In these systems a set of constants constitutes a fundamental tool. In this papers, we consider logic systems called L′T without this kind of constants but limited to the case where T is a finite poset. We prove a weak deduction theorem. We introduce also an algebraic semantics using Hey ting algebra with operators. To prove the completeness theorem of the L′T system with respect to the algebraic semantics, we use the method of H. Rasiowa and R. Sikorski for first order logic. In the propositional case, a corollary allows us to assert that it is decidable to know “if a propositional formula is valid”. We study also certain relations between the L′T logic and the intuitionistic and classical logics. 相似文献
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We consider the amalgamation of bounded involution posets over a strictly directed graph as applied to orthomodular lattices, orthomodular posets or orthoalgebras. In the finite setting, we show that the order dimension of the amalgamation does not exceed that of the amalgamated structures by more than one. We also present conditions under which equality obtains. 相似文献
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Yutaka Miyazaki 《Mathematical Logic Quarterly》2001,47(3):341-362
We present here a Kripke‐style semantics for propositional orthomodular logics that is based on the representation theorem for orthomodular lattices by D.J. Foulis ([2]), in which a sort of semigroups is employed. This semantics can characterize the logics above the orthomodular logic by some elementary conditions. 相似文献