中文摘要：

文献[1]中给出了模态描述逻辑的语法与语义,同时给出了两个模型之间的互模拟关系。目前对各种模态描述逻辑系统的研究主要是它们的语法与语义,对其代数性质做研究很少见,然而研究各种模态描述逻辑系统的模型构造,模型之间互模拟、同构等代数性质有重要的理论与现实意义。文中在文献[1]的基础上,定义了模态描述逻辑的可能世界的理论和两个可能世界的等价,继续研究描述逻辑系统的代数性质,得到了的合式公式在模型间互模拟下的不变性。

英文摘要：

The syntax and semantics of MALC have been defined in reference[1],and the bisimulation between one and another model has been defined as well.Current research mainly concerns about the syntax and semantics of various modal logic systems,their algebraic properties are neglected.But the algebraic properties such as modal logic modeling,bisimulation between models,isomorphism between models of variety of modal logic system has important theoretical and practical significance.Define the theory of possible worlds and the equivalent of two possible worlds of modal logic system based on reference[ 1 ], continue to study the algebraic properties of modal logic systern,and get the invariant property of formulas under bisimulation between its models.