一阶逻辑中的扩展子句消去原则

对于一阶逻辑定理证明器，子句集化简一直是必不可少的步骤，这将有助于提高后续一阶逻辑定理证明器的证明效率. 针对子句冗余性的判断，提出了一种评估子句冗余性的原则:集合蕴涵模归结原则. 并且证明了该原则在不带等词一阶逻辑上的可靠性，根据该原则删除子句，不会影响原始子句集的不可满足性或者可满足性. 此外，依据该原则提出了两种新型的一阶逻辑预处理方法:集合归结包含消去（set resolution subsumption, SRSE）方法和集合归结不对称恒真消去（set resolution asymmetric tautology elimination, SRATE）方法，并证明了这两种子句消去方法在不带等词一阶逻辑子句集上的可靠性. 最后在理论上比较了SRSE方法和归结包含消去（sesolution subsumption elimination, RSE）方法以及SRATE方法和归结不对称恒真（sesolution asymmetric tautology elimination, RATE）方法之间的有效性，结果表明SRSE方法和SRATE方法分别比RSE方法和RATE方法更为有效. 

Extended Unifying Principle of Clause Elimination in First-Order Logic

Simplifications are indispensable steps of first-order theorem proving, which can enhance the proving efficiency of first-order theorem provers. Set implication modulo resolution, a principle of identifying the redundancy property of clauses, is proposed. The soundness of this principle in first-order logic without equality is proved, which means that eliminating clauses according to the principle has not effect on the unsatisfiability or satisfiability of original formulas. In addition, two novel preprocessing methods in first-order theorem proving are developed given the principle of set implication modulo resolution, i.e., set resolution subsumption elimination (SRSE) and set resolution asymmetric tautology elimination (SRATE). The soundness of the two clause elimination methods is also demonstrated. Finally, the effectiveness is theoretically compared between SRSE and resolution subsumption elimination (RSE) and between SRATE and resolution asymmetric tautology elimination (RATE), which shows SRSE and SRATE are more effective than RSE and RATE, respectively.