模型论逻辑与理论计算机科学

近年来，逻辑中语义的思想与方法在理论计算机科学的许多分支中的渗透与应用，已愈来愈受重视．作为语义方法的逻辑基础，（一阶）模型论是研究（一阶）逻辑的语法构造与语义属性之间联系的一门数理逻辑的分支；而模型论逻辑（又称广义模型论）则是在抽象逻辑的框架中，用模型论的方法研究各种扩充逻辑系统的异、同及相互关系．本文从抽象逻辑的观点出发．介绍模型论中与计算机科学（ＣＳ）密切相关的若干概念及其应用．特别是广义的有限模型论，它在ＣＳ的刺激下于８０年代形成并急速发展起来，已在数据库、计算复杂性以及形式语言与自动机等理论中取得突出成果或重大的应用．

Model Theoretic Logic and Theoretical Computer Science

In recent years semantic ideas and methods have been emphasized in many branches of theoretical computer science. As the logical foundation of sematics, it is Known that the model theory treats the relationships between syntactic constructs and semantical features thereof, and that the model theoretic logic (abstract model theory) cares, under the frame of abstract logic, for the similarity, distinctness and interrelationships among various extended logics. This paper concerns mainly around notions and apparatus in model theories aligned with computer science. Particularly the generalized finite model theory, which was established and developed swiftly during 1980's, in responce to the challenges from computer science, is introduced to gather with its achievement in the technical realms such as database, computational complexity, formal languages and automata theory etc.