Intuitionistic Modal Algebras

IF 0.6 3区 数学 Q2 LOGIC
Sergio A. Celani, Umberto Rivieccio
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引用次数: 0

Abstract

Abstract Recent research on algebraic models of quasi-Nelson logic has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a nucleus . Among these various algebraic structures, for which we employ the umbrella term intuitionistic modal algebras , some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations arise from algebraic terms of the intuitionistic modal language which have not been previously considered. We shall for instance investigate the variety of weak implicative semilattices , whose members are (non-necessarily distributive) meet semilattices endowed with a nucleus and an implication operation which is not a relative pseudo-complement but satisfies the postulates of Celani and Jansana’s strict implication. For each of these new classes of algebras we establish a representation and a topological duality which generalize the known ones for Heyting algebras enriched with a nucleus.
直觉模态代数
最近对拟nelson逻辑代数模型的研究引起了人们对一类代数的关注,这些代数是由Heyting代数的一个特殊的模态算子(在文献中称为核)丰富(子约)而得到的。在这些我们使用总称直觉模态代数的各种代数结构中,有一些至少从20世纪70年代就开始研究了,通常是在拓扑学和层理论的框架内。其他的可能看起来更奇特,因为它们的原始操作来自以前没有考虑过的直觉模态语言的代数项。例如,我们将研究弱隐含半格的多样性,其成员是(非必然分配的)满足半格,其核和蕴涵运算不是相对伪补,但满足Celani和Jansana的严格蕴涵的假设。对于每一类新的代数,我们建立了一个表示和拓扑对偶,推广了已知的富核Heyting代数的表示和拓扑对偶。
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来源期刊
Studia Logica
Studia Logica MATHEMATICS-LOGIC
CiteScore
1.70
自引率
14.30%
发文量
43
审稿时长
6-12 weeks
期刊介绍: The leading idea of Lvov-Warsaw School of Logic, Philosophy and Mathematics was to investigate philosophical problems by means of rigorous methods of mathematics. Evidence of the great success the School experienced is the fact that it has become generally recognized as Polish Style Logic. Today Polish Style Logic is no longer exclusively a Polish speciality. It is represented by numerous logicians, mathematicians and philosophers from research centers all over the world.
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