证明模态分辨率的复杂性。

IF 0.9 3区 计算机科学 Q4 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Journal of Automated Reasoning Pub Date : 2022-01-01 Epub Date: 2021-10-13 DOI:10.1007/s10817-021-09609-9
Sarah Sigley, Olaf Beyersdorff
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引用次数: 0

摘要

我们研究了Nalon和Dixon (J Algorithms 62(3-4):117-134, 2007)和Nalon等人(in:使用分析Tableaux和相关方法的自动推理-第24届国际会议,(Tableaux '15),第195 -200页,2015)开发的模态分辨率系统的证明复杂性,这些系统构成了模态定理证明的基础(Nalon等人,in:第26届国际人工智能联合会议论文集(IJCAI'17),第4919-4923页,2017)。我们用一种新的更紧密的变体来补充这些演算,并表明证明可以在所有这些变体之间有效地转换,这意味着从证明复杂性的角度来看,演算是等效的。然后,我们使用proof - delayer游戏开发了模态分辨率的第一个下界技术,该技术可用于建立“真正的”模态下界,以证明类似dg的模态分辨率的大小。我们通过设计一个新的模态鸽子洞原理来说明该技术,我们证明了在模态分辨率中需要指数大小的证明。最后,我们将模态分辨率与hrubesi的模态Frege系统进行比较(Ann Pure apple Log 157(2-3):194- 205,2009),并获得“真正的”模态分离。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Proof Complexity of Modal Resolution.

Proof Complexity of Modal Resolution.

Proof Complexity of Modal Resolution.

Proof Complexity of Modal Resolution.

We investigate the proof complexity of modal resolution systems developed by Nalon and Dixon (J Algorithms 62(3-4):117-134, 2007) and Nalon et al. (in: Automated reasoning with analytic Tableaux and related methods-24th international conference, (TABLEAUX'15), pp 185-200, 2015), which form the basis of modal theorem proving (Nalon et al., in: Proceedings of the twenty-sixth international joint conference on artificial intelligence (IJCAI'17), pp 4919-4923, 2017). We complement these calculi by a new tighter variant and show that proofs can be efficiently translated between all these variants, meaning that the calculi are equivalent from a proof complexity perspective. We then develop the first lower bound technique for modal resolution using Prover-Delayer games, which can be used to establish "genuine" modal lower bounds for size of dag-like modal resolution proofs. We illustrate the technique by devising a new modal pigeonhole principle, which we demonstrate to require exponential-size proofs in modal resolution. Finally, we compare modal resolution to the modal Frege systems of Hrubeš (Ann Pure Appl Log 157(2-3):194-205, 2009) and obtain a "genuinely" modal separation.

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来源期刊
Journal of Automated Reasoning
Journal of Automated Reasoning 工程技术-计算机:人工智能
CiteScore
3.60
自引率
9.10%
发文量
31
审稿时长
>12 weeks
期刊介绍: The Journal of Automated Reasoning is an interdisciplinary journal that maintains a balance between theory, implementation and application. The spectrum of material published ranges from the presentation of a new inference rule with proof of its logical properties to a detailed account of a computer program designed to solve various problems in industry. The main fields covered are automated theorem proving, logic programming, expert systems, program synthesis and validation, artificial intelligence, computational logic, robotics, and various industrial applications. The papers share the common feature of focusing on several aspects of automated reasoning, a field whose objective is the design and implementation of a computer program that serves as an assistant in solving problems and in answering questions that require reasoning. The Journal of Automated Reasoning provides a forum and a means for exchanging information for those interested purely in theory, those interested primarily in implementation, and those interested in specific research and industrial applications.
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