邻域语义与修正真理论

Neighborhood Semantics and the Revision Theory of Truth

古普塔和赫兹伯格在1982年各自独立地提出了修正真理论,建立了可用于分析真与相关悖论的修正序列。修正真理论根据语句在所有修正序列中的表现,对语句进行分类。然而,修正真理论在某些语句的分类上不能令人满意,如修正真理论把柯瑞悖论的逆命题断定为绝对地真,这与直觉不一致。本文将从两种路径引入邻域语义研究修正真理论。路径一是在基模型上引入邻域基模型,建立邻域基模型修正序列。这类修正序列比经典修正序列更多,增加的修正序列可使包括柯瑞悖论的逆命题在内的一些语句的病态呈现出来。路径二是通过引入邻域语义模型,使得对任意不含模态词的公式φ,模态公式□φ在后继阶段的真值可以反映φ在上一阶段的真值,并且□φ在极限阶段的真值可以反映φ在至这个极限阶前是否稳定真。从而可以通过□φ的真值来限定Tφ的真值,使得满足相应限制的模型类表示了相应的修正序列。本文最后将对两个路径进行整合,构造出能表示邻域基模型修正序列的整体修正序列模型。

Gupta and Herzberg proposed the Revision Theory of Truth in 1982. They con-structed revision sequences which can be used to analyze the concept of truth and re-lated paradoxes. The Revision Theory of Truth classifies sentences according to their behavior in all revision sequences. The Revision Theory of Truth is unsatisfactory in the classification of some sentences. For example, The Revision Theory of Truth clas-sifies the inverse proposition of Curry5s Paradox as categorical truth. This is considered as counterintuitive by some logicians. We will introduce the Neighborhood Semantics from two Paths to study the Revision Theory ofTruth. First, we introduce neighborhood ground models basing on ground models and construct neighborhood ground model revi-sion sequences. The number ofneighborhood ground model revision sequences is larger than that of classical revision sequences. The increased revision sequences can show that some sentence are pathological, such as the inverse proposition of Curry5s Paradox. Second , we introduce neighborhood semantics models such that, for any sentence with-out modality, the truth value of at successor stage can reject the truth value of Ф at the previous stage, and the truth value of 口 Ф at limit stage can reflect stability of Ф before that stage. Hence, we can define different classes ofmodels to represent different kinds of revision sequences, by putting different constraints on the relation between the truth values of and 口Ф We will integratethese two paths in the end ofthispaper. And we will define universe revision sequence models to represent neighborhood ground model revision sequences. These two paths will be integrated in the end of this paper. We define universe revision sequence models to represent neighborhood ground modelrevision sequences.