A First-Order Logic Clause Set Preprocessing Method Based on Clause Deduction Distance

Abstract

Currently, many preprocessing methods in first-order automated theorem provers use symbol-based method, which is used to measure the relation of symbols in goal clauses (negated conjectures) and symbols in other clauses, and simplify clause set by setting threshold of the correlation metric. From the perspective of deduction between literals to measure the relation of different clauses, a novel method defining the relation between goal clauses with other clauses in clause set, and its application for clause set preprocessing by setting threshold are proposed in this paper, including literal deduction distance, clause deduction distance and their relationship. In the algorithm implementation, literals in the clause set are classified with a tree construction by the literal deduction distance, which intuitively describe the deduction relationship of literals in clause set. Importantly, the time complexity of the algorithm is polynomial. Apply the proposed method as a preprocessing method to the top theorem prover-Vampire 4.1, and take the CASC-26 (in 2017) competition theorems (FOF division) as the test object, experimental results show that the proposed preprocessing method has a good capability to simplify clause set and indeed enhances the capability of plain Vampire 4.1 and Vampire 4.1 with unrestricted threshold to a certain extent.