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Proof Automation in the Theory of Finite Sets and Finite Set Relation Algebra
The Computer Journal ( IF 1.077 ) Pub Date : 2021-05-03 , DOI: 10.1093/comjnl/bxab030
Maximiliano Cristiá, Ricardo D Katz, Gianfranco Rossi

|$\{log\}$| (‘setlog’) is a satisfiability solver for formulas of the theory of finite sets and finite set relation algebra (FS&RA). As such, it can be used as an automated theorem prover for this theory. |$\{log\}$| is able to automatically prove a number of FS&RA theorems, but not all of them. Nevertheless, we have observed that many theorems that |$\{log\}$| cannot automatically prove can be divided into a few subgoals automatically dischargeable by |$\{log\}$|⁠. The purpose of this work is to present a prototype interactive theorem prover (ITP), called |$\{log\}$|-ITP, providing evidence that a proper integration of |$\{log\}$| into world-class ITP’s can deliver a great deal of proof automation concerning FS&RA. An empirical evaluation based on 210 theorems from the TPTP and Coq’s SSReflect libraries shows a noticeable reduction in the size and complexity of the proofs with respect to Coq.

中文翻译:

有限集和有限集关系代数理论中的证明自动化

| $ \ {log \} $ | ('setlog')是有限集和有限集关系代数(FS&RA)理论公式的可满足性求解器。这样,它可以用作该理论的自动定理证明者。| $ \ {log \} $ | 能够自动证明许多FS&RA定理,但不是全部。但是,我们已经观察到许多定理,即| $ \ {log \} $ | 不能自动证明的| ||可| $ \ {log \} $ |⁠划分为几个子目标。这项工作的目的是介绍一个称为| $ \ {log \} $ |的原型交互式定理证明器(ITP)-ITP,提供证明| $ \ {log \} $ |正确整合的证据进入世界一流的ITP可以提供有关FS&RA的大量证明自动化。根据TPTP和Coq的SSReflect库中的210个定理进行的经验评估表明,与Coq相比,证明的大小和复杂性显着降低。
更新日期:2021-05-04
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