哲思逻辑——一个形而上学内容的公理体系

Metaphysical logic:an axiomatic system concerning metaphysical content

在经典命题逻辑的系统内,增加一个一元算子*,通过定义引入两个一元算子2和△,可以建立一个经典命题逻辑的扩充系统——哲思逻辑系统。在该扩充系统内,有遵守矛盾律和排中律的经典否定算子,有遵守矛盾律而不遵守排中律的构造性否定算子,有不遵守矛盾律而遵守排中律的弗协调否定算子,还有既不遵守矛盾律又不遵守排中律的辩证否定算子。通过引入关于*的一个形式语义,可以证明哲思逻辑系统具有可靠性和完全性。在哲思逻辑中,A和A之间是矛盾关系,A和2A之间是反对关系,A和△A之间是下反对关系,A和*A之间是差等关系。所以,哲思逻辑又可以称为对当关系逻辑。

Metaphysical logic system (MLS), an extended system of classical propositional logic, can be obtained from the classical propositional logic system by adding an unary operator and introducing two unary operators ▽and △ by definition. In the MLS, there are four kinds of negation operators: the classical negation operator which obeys both law of contradiction and law of excluded middle, the constructive negation operator which obeys law of contradiction but not law of excluded middle, the paraconsistent negation operator which obeys law of excluded middle but not law of contradiction, and the dialectical negation operator which obeys neither law of contradiction nor law of excluded middle. By introducing a formal semantics about , the soundness and completeness of MLS can be proved. In the MLS, there is a contradictory opposition between A and A, a contrary opposition between A and ▽A , a subcontrary opposition between A and △A, and a subaltern opposition between A and A. Therefore, metaphysical logic can be also termed oppositional logic.