一阶逻辑中基于稳定度的项评估方法

Stability-based Term Evaluation Method in First-order Logic

针对一阶逻辑中项结构比较复杂、语法与语义特征难以抽取的问题,基于项在文字替换过程中的Herbrand语义特征,分析其制约因素和度量规则,给出项稳定度的定义并提出一种基于稳定度的项评估方法。将所提方法作为文字选择的启发式策略,应用于自动定理证明器中子句集的归入冗余判定中,结果表明,该方法能较好地刻画一阶逻辑中的项特征,与基于项序的文字选择方法相比,其检测次数平均减少50.8%,运行时间平均缩短53.3%。

To address the complex term structure and difficult extraction of grammatical and semantic features in first-order logic,this paper analyzes the constraints and measurement rules of Herbrand semantic features of a term in text replacement.On this basis,the paper gives a definition of the stability of a term,and proposes a stability-based term evaluation method.As a heuristic strategy for text selection,this method is applied to the redundancy judgement of the clause set in Automated Theorem Prover(ATP).Results show that this method can better characterize the features of a term in first-order logic.Compared with the word selection method based on term order,its detection times are reduced by 50.8%on average,and its running time is shortened by 53.3%on average.