关于正规模态命题逻辑系统的完全性证明

Discussing about the Completeness Proof of Normal Modal Propositional Logic System

模态逻辑的完全性理论至今已经有了很大发展,其证明通常也是逻辑研究中重要且极其困难的一环。从简单的证明命题逻辑有效性的真值表、归谬法的思想出发到反模型的建立;从最早证明模态逻辑系统的Kripke-语义图的出现到Hughes and Gresswell对Kripke-语义图的修正;从L.Henkin极大一致集的提出到从属模型和典范模型的建立;从典范模型的广泛使用到Bull有限模型的建立无不体现了这一点。对正规模态逻辑系统完全性证明的层层刨析,可以更好地把握和使用完全性证明方法。

The complete theory of Model logic has a great development right now, its proof is important and extremely difficult link in the logical research. From the idea of simple prove the proposition logic validity of the truth table and the reduction method to the establishment of anti-model; From the appearance of the Kripke-semantic diagrams which is the earliest proof of modal propositional system to the amendment of Kripke-semantic diagrams which is making by Hughes and Gresswe; From the proposed of maximal consistent sets of wff to the establishment of subordinate models and canonical models; The widespread use of canonical models and the establishment of Bull limited model has all manifested this point. This article in order to better grasp and use of completeness proof through analyzing completeness proof of normal modal propositional logic system.