知识蕴涵直觉主义逻辑系统

Knowledge implication intuitionism logic

在知识蕴涵命题逻辑的基础上,借助强知识蕴涵,可以构建知识蕴涵直觉主义逻辑系统。结合知识蕴涵逻辑和直觉主义逻辑的形式语义,可以证明知识蕴涵直觉主义逻辑系统具有可靠性和完全性。在该系统中,矛盾律仍然成立,但是排中律、双重否定消去律、司各脱法则都不再成立。在该系统中,弗协调逻辑和直觉主义逻辑的基本特征都被保留了下来,该系统给出了一个处理矛盾问题的既是弗协调的、又是直觉主义的兼容方案。

On the basis of knowledge implication logic, knowledge implication intuitionism logic (ID) is built with strong knowledge implication. The formal semantics concerning knowledge implication logic and intuitionism logic prove the soundness and completeness of ID. In ID, the law of contradiction is valid, but the law of excluded middle and the law of elimination of double negation and Scotus law are not. Both paraconsistent logic and intuitionism logic remain unchanged in their fundamental characteristics in ID. The new system provides a strategy compatible with paraconsistent logic and intuitionism logic for problems about contradictions.