论文标题
基于Kripke上下文的语言的半概念及其模态扩展的非分布逻辑
A non-distributive logic for semiconcepts of a context and its modal extension with semantics based on Kripke contexts
论文作者
论文摘要
对于纯纯的双重布尔代数和纯的双重布尔代数，提出了一个非分配的两排超平衡孔\ textbf {pdbl}及其模态扩展\ textbf {mpdbl}。接下来提出了\ textbf {pdbl}的关系语义，其中任何公式都被解释为上下文的半概念。对于\ textbf {mpdbl}，关系语义基于kripke上下文，公式被解释为基础上下文的半概念。与关系语义相对于关系语义，这些系统被证明是合理的和完整的。将适当的序列添加到\ textbf {mpdbl}中，将基于反身，对称或及时的kripke上下文的语义产生逻辑。这些系统之一是拓扑纯双布尔代数的逻辑。可以证明，使用\ textbf {pdbl}，可以表达概念知识的基本概念和关系，并且可以获得涉及否定的推论。此外，定义了与上下文的半概念的粗糙集理论建立连接的联系。然后表明，使用\ textbf {mpdbl}中涉及模态运算符的公式和序列，可以捕获这些近似运算符及其属性。
A non-distributive two-sorted hypersequent calculus \textbf{PDBL} and its modal extension \textbf{MPDBL} are proposed for the classes of pure double Boolean algebras and pure double Boolean algebras with operators respectively. A relational semantics for \textbf{PDBL} is next proposed, where any formula is interpreted as a semiconcept of a context. For \textbf{MPDBL}, the relational semantics is based on Kripke contexts, and a formula is interpreted as a semiconcept of the underlying context. The systems are shown to be sound and complete with respect to the relational semantics. Adding appropriate sequents to \textbf{MPDBL} results in logics with semantics based on reflexive, symmetric or transitive Kripke contexts. One of these systems is a logic for topological pure double Boolean algebras. It is demonstrated that, using \textbf{PDBL}, the basic notions and relations of conceptual knowledge can be expressed and inferences involving negations can be obtained. Further, drawing a connection with rough set theory, lower and upper approximations of semiconcepts of a context are defined. It is then shown that, using the formulae and sequents involving modal operators in \textbf{MPDBL}, these approximation operators and their properties can be captured.
