论文标题
准N4时间逻辑的代数性
Algebraizability of the Logic of Quasi-N4-Lattices
论文作者
论文摘要
The class of quasi-N4-lattices (QN4-lattices) was introduced as a common generalization of quasi-Nelson algebras and N4-lattices, in such a way that N4-lattices are precisely the QN4-lattices satisfying the double negation law (~~x = x) and quasi-Nelson algebras are the QN4-lattices satisfying the explosive law (x ^ ~x) -> y = （（x ^ 〜x） - > y） - >（（x ^ 〜x） - > y）。在本文中，我们通过希尔伯特风格的演示文稿介绍了逻辑（l_qn4），其代数语义是一类代数，我们表明，该代数与qn4-lattices相等。通过证明美国引入的演算是可以从Blok和Pigozzi的意义上获得代数的，并且其等效的代数语义与QN4-时间类别等于术语。作为未来研究的前景，我们考虑了一个问题，即如何将L_QN4放置在相关逻辑家族中。
The class of quasi-N4-lattices (QN4-lattices) was introduced as a common generalization of quasi-Nelson algebras and N4-lattices, in such a way that N4-lattices are precisely the QN4-lattices satisfying the double negation law (~~x = x) and quasi-Nelson algebras are the QN4-lattices satisfying the explosive law (x ^ ~x) -> y = ((x ^ ~x) -> y) -> ((x ^ ~x) -> y). In this paper we introduce, via a Hilbert-style presentation, a logic (L_QN4) whose algebraic semantics is a class of algebras that we show to be term-equivalent to QN4-lattices. The result is obtained by showing that the calculus introduced by us is algebraizable in the sense of Blok and Pigozzi, and its equivalent algebraic semantics is term-equivalent to the class of QN4-lattices. As a prospect for future investigation, we consider the question of how one could place L_QN4 within the family of relevance logics.
