基于中介逻辑的多模态逻辑系统

多模态逻辑作为模态逻辑的扩充，是模态逻辑进行时态和动态扩充的基础。中介逻辑是一个新的逻辑系统，自创立后得到了很大发展，并在数理逻辑及计算机科学领域中得到广泛应用。为将中介逻辑进行时态和动态扩充，本文构造了一种基于中介逻辑的多模态逻辑系统ＭＭＫ，讨论了它的推理规则和语义解释，并证明了ＭＭＫ的可靠性和完备性，在此基础上给出了一种基于中介逻辑的时态逻辑系统ＭＴ，对它的可靠性和完备性进行了讨论。最后，分析了相应的经典多模态逻辑系统与ＭＭＫ系统及经典时态逻辑系统和ＭＴ系统之间的关系。

A System of Multi-Modal Logic Based on Medium Logic

The multi-modal logic,as an extension to the modal logic,is the base on which themodal logic is able to extend to the tense logic and dynamic logic. The medium logic is a newlogic system and has been developed rapidly since it was set up. Some systems have been developed such as the medium modal logic in the areas of the mathematical logic and computer science. As the modal logic may be extended to the tense logic and dynamic logic based on themedium logic,in this paper,a normal system of multi--modal logic based on the medium logic(named MMK) has been put forward. The formalizations and semantics of MMK have beendiscussed; its soundness and completeness were proved. Furthermore, a system of tense logicbased on the medium logic(named MT),of which the soundness and completeness were alsodiscussed, was presented.Finally, the relations between MMK and the classical multi-modallogic,and MT and classical tense logic were analysed.