摘要
一阶逻辑自动定理证明是知识表示与自动推理领域重要的研究内容,如何有效选取子句参与演绎是提升自动推理能力和效率的研究热点。基于多元动态演绎良好的演绎特性,通过分析子句的变元项性质和函数项结构,提出了一种子句活跃度和复杂度的度量与计算方法,能很好地对不同项结构的子句进行有效评估;基于该子句评估方法,提出了一种子句充分协同演绎的多元动态演绎算法,能有效优化多元演绎搜索路径。将该多元动态演绎算法应用于国际顶尖证明器Eprover 2.6中,以2021年国际自动推理FOF组竞赛例为测试对象,在标准的300 s测试时间内,加入了多元动态演绎算法的Eprover 2.6相比原始Eprover 2.6多证明定理4个,在证明定理总数相同的条件下,平均证明时间减少了1.12 s;能证明Eprover 2.6未证明定理16个,占未证明定理总数的15.1%。实验结果表明,该多元动态演绎算法是一种有效的推理方法,能在一定程度上提升自动定理的证明能力和时间效率。
First-order logic automated theorem proving is an important research content in the fields of knowledge representation and automated reasoning.How to effectively select clauses to participate in deduction is a research hotspot to improve the capability and efficiency of automated reasoning.Based on the good de-duction characteristics of multi-clause dynamic deduction,this paper proposes a measure and calculation method of clause activity and complexity by analyzing the properties of the variable terms and the structure of function terms of clauses,which can effectively evaluate clauses with different term structures.Based on the clause evaluation method,a multi-clause dynamic deduction algorithm with fully synergized deduction of clauses is proposed,which can effectively optimize the multi-clause deduction search path.The multi-clause dynamic deduction algorithm is applied to the international top prover Eprover 2.6,and the 2021 international automated reasoning competition problems(FOF group)is used as the test object.Within the standard 300 seconds,Eprover 2.6 with the proposed multi-clause dynamic deduction algorithm proven four more theorems than the original Eprover 2.6,and the average proof time is decreases by 1.12 seconds under the condition of proving the same number of theorems as Eprover 2.6.In addition,it can prove 16 unproven theorems of Eprover 2.6,accounting for 15.1%of the total unproven theorems.The experimental results show that the proposed multi-clause dynamic deduction algorithm is an effective inference method,which can improve the capability and time efficiency of automated reasoning to a certain extent.
作者
林玲瑜
曹锋
易见兵
方旺盛
李俊
吴贯锋
LIN Ling-yu;CAO Feng;YI Jian-bing;FANG Wang-sheng;LI Jun;WU Guan-feng(School of Information Engineering,Jiangxi University of Science and Technology,Ganzhou 341000;School of Mathematics,Southwest Jiaotong University,Chengdu 610031,China)
出处
《计算机工程与科学》
CSCD
北大核心
2023年第12期2256-2264,共9页
Computer Engineering & Science
基金
国家自然科学基金(62066018,62106206)
江西省科技厅项目(20212ACB202003)
江西省教育厅项目(GJJ200818,GJJ180482)
江西理工大学博士启动基金(205200100060)。
关键词
一阶逻辑
定理证明
自动推理
多元动态演绎
子句评估
first-order logic
theorem proving
automated reasoning
multi-clause dynamic deduction
clause evaluation
作者简介
林玲瑜(1999),女,广东汕头人,硕士生,研究方向为智能信息处理、自动推理和一阶逻辑自动定理证明。E-mail:812774058@qq.com;通信作者:曹锋(1984),男,江西上饶人,博士,讲师,研究方向为智能信息处理、自动推理和一阶逻辑自动定理证。E-mail:caofeng19840301@163.com;易见兵(1980),男,江西宜春人,博士,副教授,研究方向为人工智能。E-mail:yijianbing8@163.com。
