部分动态De Morgan代数的集合表示

I. Chajda, Jan Paseka
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引用次数: 4

摘要

所谓德摩尔根代数,是指具有反调对合的有界偏序集。这样的代数可以看作是满足双重否定律的命题逻辑的代数公理化。我们的目的是在每一个De Morgan代数中引入所谓的时态算子,以得到否定满足双重否定律的时态逻辑的代数对应物,而不必是布尔型的。根据一个坐标系的张力算子G和H的标准构造,我们解决了以下问题:如果给定一个动态De Morgan代数,如何找到一个坐标系,使得它的张力算子G和H可以通过这个构造得到。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Set Representation of Partial Dynamic De Morgan Algebras
By a De Morgan algebra is meant a bounded poset equipped with an antitone involution considered as negation. Such an algebra can be considered as an algebraic axiomatization of a propositional logic satisfying the double negation law. Our aim is to introduce the so-called tense operators in every De Morgan algebra for to get an algebraic counterpart of a tense logic with negation satisfying the double negation law which need not be Boolean. Following the standard construction of tense operators G and H by a frame we solve the following question: if a dynamic De Morgan algebra is given, how to find a frame such that its tense operators G and H can be reached by this construction.
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