模态系统MV及其可靠性与完全性

Proofs of Reliability and Completeness of MV System

模型是研究正规命题模态系统的一个重要工具,系统的可靠性与完全性证明都离不开模型。系统MV的可靠性证明,就是证明它的定理在“所有可能世界要么自身是死点,要么至少可及一个死点的所有模型中”都有效。关于MV的完全性证明,借助了典范模型的方法,典范模型是证明系统完全性的一个十分有效的手段。任何正规系统相对于它的典范模型都是完全的,在MV的典范模型中的所有可能世界要么自身是一个死点,要么至少可及一个死点,由此可得MV相对于所有可能世界要么自身是一个死点,要么至少可及一个死点的模型类是完全的。

Model is an important way to study the normal propositional modal system.The proofs of reliability and completeness of the system can not be proved without model.The proof of reliability of system MV is to prove that it is effective in all models in which all possible worlds are either dead points themselves or at least one dead point can be reached.For the completeness proof of MV,the method of canonical model is used,which is a very favorable means to prove the completeness of the system.Any normal system is complete relative to its canonical model.All possible worlds in the canonical model of MV are either a dead point or at least a dead point.Therefore,MV is complete relative to all possible worlds,either a dead point or at least a dead point.