A Comprehensive Framework for Saturation Theorem Proving

Uwe Waldmann; Sophie Tourret; Simon Robillard; Jasmin Blanchette

doi:10.1007/978-3-030-51074-9_18

A Comprehensive Framework for Saturation Theorem Proving

Uwe Waldmann^*, Sophie Tourret, Simon Robillard, Jasmin Blanchette

^*Corresponding author for this work

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

We present a framework for formal refutational completeness proofs of abstract provers that implement saturation calculi, such as ordered resolution or superposition. The framework relies on modular extensions of lifted redundancy criteria. It allows us to extend redundancy criteria so that they cover subsumption, and also to model entire prover architectures in such a way that the static refutational completeness of a calculus immediately implies the dynamic refutational completeness of a prover implementing the calculus, for instance within an Otter orloop. Our framework is mechanized in Isabelle/.

Original language	English
Title of host publication	Automated Reasoning
Subtitle of host publication	10th International Joint Conference, IJCAR 2020, Paris, France, July 1–4, 2020, Proceedings, Part I
Editors	Nicolas Peltier, Viorica Sofronie-Stokkermans
Publisher	Springer
Pages	316-334
Number of pages	19
Volume	1
ISBN (Electronic)	9783030510749
ISBN (Print)	9783030510732
DOIs	https://doi.org/10.1007/978-3-030-51074-9_18
Publication status	Published - 2020
Event	10th International Joint Conference on Automated Reasoning, IJCAR 2020 - Virtual, Online Duration: 1 Jul 2020 → 4 Jul 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12166 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th International Joint Conference on Automated Reasoning, IJCAR 2020
City	Virtual, Online
Period	1/07/20 → 4/07/20

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10.1007/978-3-030-51074-9_18

Waldmann2020_Chapter_AComprehensiveFrameworkForSaturationFinal published version, 445 KBLicence: Article 25fa Dutch Copyright Act

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Waldmann, U., Tourret, S., Robillard, S., & Blanchette, J. (2020). A Comprehensive Framework for Saturation Theorem Proving. In N. Peltier, & V. Sofronie-Stokkermans (Eds.), Automated Reasoning: 10th International Joint Conference, IJCAR 2020, Paris, France, July 1–4, 2020, Proceedings, Part I (Vol. 1, pp. 316-334). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12166 LNAI). Springer. https://doi.org/10.1007/978-3-030-51074-9_18

Waldmann, Uwe ; Tourret, Sophie ; Robillard, Simon et al. / A Comprehensive Framework for Saturation Theorem Proving. Automated Reasoning: 10th International Joint Conference, IJCAR 2020, Paris, France, July 1–4, 2020, Proceedings, Part I. editor / Nicolas Peltier ; Viorica Sofronie-Stokkermans. Vol. 1 Springer, 2020. pp. 316-334 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "A Comprehensive Framework for Saturation Theorem Proving",

abstract = "We present a framework for formal refutational completeness proofs of abstract provers that implement saturation calculi, such as ordered resolution or superposition. The framework relies on modular extensions of lifted redundancy criteria. It allows us to extend redundancy criteria so that they cover subsumption, and also to model entire prover architectures in such a way that the static refutational completeness of a calculus immediately implies the dynamic refutational completeness of a prover implementing the calculus, for instance within an Otter orloop. Our framework is mechanized in Isabelle/.",

author = "Uwe Waldmann and Sophie Tourret and Simon Robillard and Jasmin Blanchette",

year = "2020",

doi = "10.1007/978-3-030-51074-9_18",

language = "English",

isbn = "9783030510732",

volume = "1",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer",

pages = "316--334",

editor = "Nicolas Peltier and Viorica Sofronie-Stokkermans",

booktitle = "Automated Reasoning",

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Waldmann, U, Tourret, S, Robillard, S & Blanchette, J 2020, A Comprehensive Framework for Saturation Theorem Proving. in N Peltier & V Sofronie-Stokkermans (eds), Automated Reasoning: 10th International Joint Conference, IJCAR 2020, Paris, France, July 1–4, 2020, Proceedings, Part I. vol. 1, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12166 LNAI, Springer, pp. 316-334, 10th International Joint Conference on Automated Reasoning, IJCAR 2020, Virtual, Online, 1/07/20. https://doi.org/10.1007/978-3-030-51074-9_18

A Comprehensive Framework for Saturation Theorem Proving. / Waldmann, Uwe; Tourret, Sophie; Robillard, Simon et al.

Automated Reasoning: 10th International Joint Conference, IJCAR 2020, Paris, France, July 1–4, 2020, Proceedings, Part I. ed. / Nicolas Peltier; Viorica Sofronie-Stokkermans. Vol. 1 Springer, 2020. p. 316-334 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12166 LNAI).

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

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Waldmann U, Tourret S, Robillard S, Blanchette J. A Comprehensive Framework for Saturation Theorem Proving. In Peltier N, Sofronie-Stokkermans V, editors, Automated Reasoning: 10th International Joint Conference, IJCAR 2020, Paris, France, July 1–4, 2020, Proceedings, Part I. Vol. 1. Springer. 2020. p. 316-334. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). Epub 2020 Jun 24. doi: 10.1007/978-3-030-51074-9_18

A Comprehensive Framework for Saturation Theorem Proving

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