限悖论逻辑Lpm的命题演算

限悖论逻辑(有时简称为悖论逻辑)Lpm是一种对悖论中的矛盾进行限制的逻辑。其中L表示逻辑,P表示悖论,而m表示极小化,极小化意味着限制。这里,限制矛盾的基本手法是次协调逻辑。我们说,限悖论逻辑Lpm建立的目的,正是为了消解布尔、弗雷格(BF)的经典逻辑BF中引入矛盾命题后,可以推出任意命题(这称为句法的无意义化或平庸化)这样一个难题,同时又保持BF逻辑中对联词的原有相互定义方式(这种方式受到很多人的欢迎)。Lpm由Priest首先提出语义模型,它对证明论的经典形式曾作为挑战性问题而存在。就限悖论逻辑Lpm而言,其命题逻辑的新证明论最终由林作铨博士及李未教授解决。循此前进,本章给予另一种严格形式的、更普遍的表述,并为统一地解决谓词逻辑的“证明论”提供基础。这是我们对这一问题所做的新工作。

Proposition Calculation of the Logic of Circumscribed Paradox Lpm

The Logic of Circumscribed Paradox Lpm is a kind of logic which is circumscribed to the contradiction in the paradox. L represents logic, "p" represents paradox, "m" represents minimize, minimize means circumscribe. Here the basic method to circumscribe contradiction is paraconsistent logic. The purpose of the establishment of Lpm is, for one thing, to solve a problem of the classical logic, i.e., any proposition could be inferred from the contradict proposition. For another, to keep the original inter-defining way of the conjuctions in the classical logic (this way is very popular among many people). The symatic model of Lpm, which was set forth by Priest firstly, has challeged the classical form of Proof Theory. As fas as the Logic of Circumscribed Paradox Lpm is concerned, its new Proof Theory of the calculation of the proposition is finished by Dr. Lin Zuoquan. This paper provides another mode of statement, which is more strict and general. Hence, it lays the foundation for the Proof Theory of the predicate logic.