中介逻辑的模型论性质

中介逻辑是朱梧槚与肖奚安合作创立的一个新的逻辑系统,该系统的创立有着很强的哲学背景,因此在创立后得到了很大的发展。但对于该系统语义的研究还不够广泛和深入。本文系统地研究了中介逻辑的模型论性质。第一部分系统地定义了中介逻辑模型论的一些概念:如语言、结构、解释、满足等,第二部分证明了对任一和谐理论,都可在其见证集的等价类上建立其模型。利用此定理,笔者证明了广义完全性定理,并由此证明了中介逻辑的可靠性与完备性。本文最后一部分讨论了中介模型论的其他重要性质。利用中介逻辑的完备性,本文证明了紧致性定理,即一理论有模型当且仅当其任一有穷子集有模型。文中还证明了中介逻辑的Lowenheim-Skolem-Tarski定理。

Model Theoretic Properties of Medium Logic

Medium Logic is a new logic system created by Zhu Wujia and Xiao Xi'an. The creation of this system has a strong philosophic background,so it is greatly developed. But the study of its semantics is not wide and deep enough. In this paper,the model theoretic properties of Medium Logic are studied systematically. In the first part of this paper,some model concepts for Medium Logic are defined strictly,such as language,structure,interpretation and satisfaction. In the second part, it is proved that for any consistent theory, its model on the equivalent classes of its witness set can be constructed, and the soundness and completeness of Medium Logic is proved. In the last part of this paper,other important properties of Medium Logic model theory are discussed. The compact theorem is proved, which states that theory T has model if and only if any finite subset of T has model. The Lowenheim-skolem-Tarski theorem of Medium Logic is also proved.