论文标题
粗糙双向代数及其在粗糙双元素逻辑上的应用
Rough bi-Heyting algebra and its applications on Rough bi-intuitionistic logic
论文作者
论文摘要
考虑了粗糙的半度性$（t，δ，\ nabla）$来描述一种特殊的分配粗糙半含量，称为粗糙双向代数。双向代数是布尔代数的扩展，它是通过较弱的概念来完成的，即补充$（^{*}）$，双伪符号$（^{+}）$，相对pseocoudecoundocoundoc-pseudocoudectlement $（\ rightarrow）$（\ rightarrow）$（\ rightarrow）$＆diual相对$（$）$（$）$（$）。在本文中，证明了粗糙的半度$（t，δ，\ nabla）$的元素是通过伪组件，相对伪组件以及它们的对偶来完成的。伪组件的定义导致了Brouwerian粗糙的半度性结构$（t，δ，\ nabla，^{*}，rs（\ emptyset），rs（u））$（t，δ，δ，\ nabla）$。另外，它也证明了$（t，δ，\ nabla，\ rightarrow，\ leftarrow，rs（\ emptyset），rs（u））$是一个粗糙的双向代数。这些概念用示例说明了。作为一种应用，这种粗糙的双向代数用于建模粗糙的双关键逻辑。定义了语法，并定义和验证了粗略双关节逻辑的三种类型的语义。
A Rough semiring $(T,Δ,\nabla)$ is considered to describe a special distributive Rough semiring known as a Rough bi-Heyting algebra. A bi-Heyting algebra is an extension of boolean algebra and it is accomplished by weaker notion of complements namely pseudocomplement $(^{*})$, dual pseudocomplement $(^{+})$, relative pseudocomplement $(\rightarrow)$ and dual relative pseudocomplement $(\leftarrow)$. In this paper, it is proved that the elements of the Rough semiring $(T,Δ,\nabla)$ are accomplished with the pseudocomplement, relative pseudocomplement along with their duals. The definition of pseudocomplement leads to the concept of Brouwerian Rough semiring structure $(T,Δ,\nabla,^{*},RS(\emptyset),RS(U))$ on the Rough semiring $(T,Δ,\nabla)$. Also it is proved $(T,Δ,\nabla,\rightarrow,\leftarrow,RS(\emptyset),RS(U))$ is a Rough bi-Heyting algebra. The concepts are illustrated with the examples. As an application, this Rough bi-Heyting algebra is used to model Rough bi-intuitionistic logic. The syntax is defined and three types of semantics for Rough bi-intuitionistic logic are defined and validated.
