ATMS的模型论基础

ON MODEL-THEORETIC FOUNDATIONS OF THE ATMS

本文将每个ＡＴＭＳＫ转化为一阶语言Ｌｘ的模型ＭＫ，模型ＭＫ是语言ＬＫ的一阶理论ＴＫ的模型．应用非单调推理理论中的谓词限定的技巧，可以构造出ＬＫ的理论ＴＫＰＣ，使得ＭＫ是ＴＫＰＣ的唯一模型．同时，语言ＬＫ还包含关系符号ξ，使得对每个ｎ，｛Ｅ｜ＭＫ｜＝ｎξＥ｝是ｎ相对于ＡＴＭＳＫ的标号．

In this paper, every ATMS K is associated with a model MK of a firstorder language LK, which is a model of an LK-theory TK. MK is also the unique model of the LK-theory TKPC, which is constructed by means of circumscription in nonmonotonic reasoning. The above mentioned language LK contains a relation symbol ξ, whose interpretation in MK has the property that {E|MK|=nξE} is the label of n for every node n of the ATMS K.