论文标题
在次命的晶格和逻辑的亚还原上
On subreducts of subresiduated lattices and logic
论文作者
论文摘要
爱泼斯坦和霍恩（Horn）在1970年的十年中引入了次命的晶格，作为某些逻辑的代数对应物，刘易（Lewy）和黑客（Hacking）先前研究了强烈的含义。这些逻辑是次观论逻辑的示例，即以直觉逻辑语言的逻辑来通过使用Kripke模型来定义其语义的语言，就像定义了直觉逻辑一样，但不需要模型在直觉主义情况下所需的某些属性。同样，与次言逻辑的研究有关，Celani和Jansana将这些代数视为弱蜂巢代数的亚元素的元素。 在这里，我们研究了次命晶格的隐含性和含义最小的亚还原。此外，我们提出了一个微积分，其代数语义是由这些代数类别给出的。还将这种划线的几个扩展研究与它们的一些有趣属性一起研究。
Subresiduated lattices were introduced during the decade of 1970 by Epstein and Horn as an algebraic counterpart of some logics with strong implication previously studied by Lewy and Hacking. These logics are examples of subuintuitionistic logics, i.e., logics in the language of intuitionistic logic that are defined semantically by using Kripke models, in the same way as intuitionistic logic is defined, but without requiring of the models some of the properties required in the intuitionistic case. Also in relation with the study of subintuitionistic logics, Celani and Jansana get these algebras as the elements of a subvariety of that of weak Heyting algebras. Here, we study both the implicative and the implicative-infimum subreducts of subresiduated lattices. Besides, we propose a calculus whose algebraic semantics is given by these classes of algebras. Several expansions of this calculi are also studied together to some interesting properties of them.
