关于余代数逻辑的研究

余代数为各种各样的模态逻辑提供一致的语义框架.Lutz Schr？der证明了任意自函子的余代数类都有一个rank-1的公理化.反过来,每一个rank-1的模态逻辑都有一个可靠的、强完备的余代数语义.另一方面,Clemens Kupke等提出模态逻辑可以描述成布尔代数上的自函子,并基于对偶理论研究余代数逻辑的可靠完备性.通过对偶理论重新证明了rank-1的模态逻辑都是余代数的,并且证明通过对偶理论构造出来的函子和Schr？der所构造的函子是等价的.

Research on Coalgebraic Logics

Coalgebras provide a unifying semantic framework for a wide variety of modal logics. It has previously been shown by Lutz Schroder that the class of coalgebras for an endofunctor can always be axiomatized in rank 1. And conversely, every rank-1 modal logic has a sound and strongly complete coalgebraic semantics. On the other hand, Clemens Kupke has shown that modal logics can be naturally described as functors on Boolean algebras and studied soundness and completeness of coalgebraic logics from the perspective of duality theory. This paper reproves that rank-I modal logics are coalgebraic using duality theory and proves that the functor we construct is equivalent to that of Lutz Schroder.