同构、P-态射、互模拟与模态等价性

Isomorphism,Pseudo-epimorphism,Bisimulation and Modal Equivalence

结构的模态等价性是指这些结构上有效性的模态公式恰好相同。本文比较了模型之间的三类关系:同构、P-态射、互模拟,从而得出互模拟关系概括了最大范围的模态等价性,因为模型之间的互模拟关系包含它们之间的同构关系和P-态射关系。同时,对框架等价性也给予了一定的研究,得出结论是:同构的框架一定是模态等价的,但具有另外两种关系的框架不一定是模态等价的。

Structural modal equivalence refers to state that they have the same modal theory by the modal equivalence of two structures. We compare three kinds of relations： isomorphism, pseudo-epimorphism, bisimulation, and conclude that bisimulation characterizes the widest modal equivalence because bisimulation includes isomorphism and pseudo-epimorphism between models. Furthermore, through the research of the frame equivalence the author finds isomorphic frames should be of modal equivalence, but pseudo-epimorphic or bisimilar frames maybe not of modal equivalence.