Abstract
Most of the advanced first-order logic automated theorem proving (ATP) systems adopt binary resolution methods as the core inference mechanism, where only two clauses are involved and a complementary pair of literals are eliminated during each deduction step. Recently, a novel multi-clause inference rule is introduced along with its soundness and completeness, which is called as standard contradiction separation rule (in short, S-CS rule) and allows multiple (two or more) clauses to be involved in each deduction step. This paper introduces and evaluates the application of S-CS rule in first-order logic ATP. Firstly, it analyzes several deduction methods of S-CS rule. It is then focused on how this multi-clause deduction theory can be achieved through forming a specific and effective algorithm, and finally how it can be applied in the top ATP systems in order to improve their performances. Concretely, two novel multi-clause S-CS dynamic deduction algorithms are proposed based on optimized proof search, including related heuristic strategy, then the application method applied in the state of the art ATP system Eprover (the version of Eprover 2.3) is introduced. Eprover with the proposed multi-clause deduction algorithms are evaluated through the FOF division of the CASC-J9 (in 2018) ATP system competition. Experimental results show that Eprover with the proposed multi-clause deduction algorithms outperform the plain Eprover itself to a certain extent.
Highlights
Automated reasoning is an important research branch in the field of artificial intelligence, and it has been successfully applied in many areas [1], e.g., mathematics [2], formal verification [3]
We focus on designing and applying an effective multiclause dynamic deduction algorithm according to S-CS rule
According to theory and practice analysis, two S-CS dynamic deduction algorithms including corresponding heuristic strategies are proposed in this paper, they can preferentially generate S-CS clauses with a small number of literals, and one of them can give full play to the ability of synergized deduction with the same input clause
Summary
Automated reasoning is an important research branch in the field of artificial intelligence, and it has been successfully applied in many areas [1], e.g., mathematics [2], formal verification [3]. The automated theorem proving (ATP) in first-order logic is an important research work in the field of automated reasoning. Saturation is a deduction algorithm for most famous first-order logic ATP systems [19,20,21]. It is represented by given-clause algorithm, that can be divided into discount [4] and otter [5]. The inference rules are applied only in active, the generated new clauses are put into passive. Repeat this operation until an empty clause is generated or timeout.
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More From: International Journal of Computational Intelligence Systems
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