Pub Date : 2022-01-01Epub Date: 2021-10-13DOI: 10.1007/s10817-021-09609-9
Sarah Sigley, Olaf Beyersdorff
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.
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。
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Pub Date : 2021-11-16DOI: 10.1007/s10817-021-09610-2
Sadegh Dalvandi, Brijesh Dongol, Simon Doherty, H. Wehrheim
{"title":"Integrating Owicki–Gries for C11-Style Memory Models into Isabelle/HOL","authors":"Sadegh Dalvandi, Brijesh Dongol, Simon Doherty, H. Wehrheim","doi":"10.1007/s10817-021-09610-2","DOIUrl":"https://doi.org/10.1007/s10817-021-09610-2","url":null,"abstract":"","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"66 1","pages":"141 - 171"},"PeriodicalIF":1.1,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46190767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-12DOI: 10.1007/s10817-021-09606-y
M. P. Bonacina, Stéphane Graham-Lengrand, N. Shankar
{"title":"Conflict-Driven Satisfiability for Theory Combination: Lemmas, Modules, and Proofs","authors":"M. P. Bonacina, Stéphane Graham-Lengrand, N. Shankar","doi":"10.1007/s10817-021-09606-y","DOIUrl":"https://doi.org/10.1007/s10817-021-09606-y","url":null,"abstract":"","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"66 1","pages":"43 - 91"},"PeriodicalIF":1.1,"publicationDate":"2021-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42181460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-01DOI: 10.1023/B:JARS.0000021187.23857.1b
{"title":"Author Index to Volume 31","authors":"","doi":"10.1023/B:JARS.0000021187.23857.1b","DOIUrl":"https://doi.org/10.1023/B:JARS.0000021187.23857.1b","url":null,"abstract":"","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"31 1","pages":"371"},"PeriodicalIF":1.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1023/B:JARS.0000021187.23857.1b","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49634650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-28DOI: 10.1007/s10817-021-09599-8
A. Popescu, Dmitriy Traytel
{"title":"Distilling the Requirements of Gödel’s Incompleteness Theorems with a Proof Assistant","authors":"A. Popescu, Dmitriy Traytel","doi":"10.1007/s10817-021-09599-8","DOIUrl":"https://doi.org/10.1007/s10817-021-09599-8","url":null,"abstract":"","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"65 1","pages":"1027 - 1070"},"PeriodicalIF":1.1,"publicationDate":"2021-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s10817-021-09599-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44621322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-08DOI: 10.1007/s10817-022-09643-1
Richard Schmoetten, Jake E. Palmer, Jacques D. Fleuriot
{"title":"Towards Formalising Schutz’ Axioms for Minkowski Spacetime in Isabelle/HOL","authors":"Richard Schmoetten, Jake E. Palmer, Jacques D. Fleuriot","doi":"10.1007/s10817-022-09643-1","DOIUrl":"https://doi.org/10.1007/s10817-022-09643-1","url":null,"abstract":"","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"66 1","pages":"953 - 988"},"PeriodicalIF":1.1,"publicationDate":"2021-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41664541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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