First-Order Quasi-canonical Proof Systems

Yotam Dvir; Arnon Avron

doi:10.1007/978-3-030-29026-9_5

First-Order Quasi-canonical Proof Systems

Yotam Dvir^*, Arnon Avron

^*Corresponding author for this work

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

Abstract

Quasi-canonical Gentzen-type systems with dual-arity quantifiers is a wide class of proof systems. Using four-valued non-deterministic semantics, we show that every system from this class admits strong cut-elimination iff it satisfies a certain syntactic criterion of coherence. As a specific application, this result is applied to the framework of Existential Information Processing (EIP), in order to extend it from its current propositional level to the first-order one—a step which is crucial for its usefulness for handling information that comes from different sources (that might provide contradictory or incomplete information).

Original language	English
Title of host publication	Automated Reasoning with Analytic Tableaux and Related Methods - 28th International Conference, TABLEAUX 2019, Proceedings
Editors	Serenella Cerrito, Andrei Popescu
Publisher	Springer
Pages	77-93
Number of pages	17
ISBN (Print)	9783030290252
DOIs	https://doi.org/10.1007/978-3-030-29026-9_5
State	Published - 2019
Event	28th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2019 - London, United Kingdom Duration: 3 Sep 2019 → 5 Sep 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11714 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	28th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2019
Country/Territory	United Kingdom
City	London
Period	3/09/19 → 5/09/19

Funding

Funders	Funder number
Israel Science Foundation	817-15

Keywords

Coherence
Cut-elimination
Gentzen-type proof systems
Information processing
Knowledge bases
Non-deterministic matrices

Access to Document

10.1007/978-3-030-29026-9_5

Cite this

Dvir, Y., & Avron, A. (2019). First-Order Quasi-canonical Proof Systems. In S. Cerrito, & A. Popescu (Eds.), Automated Reasoning with Analytic Tableaux and Related Methods - 28th International Conference, TABLEAUX 2019, Proceedings (pp. 77-93). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11714 LNAI). Springer. https://doi.org/10.1007/978-3-030-29026-9_5

Dvir, Yotam ; Avron, Arnon. / First-Order Quasi-canonical Proof Systems. Automated Reasoning with Analytic Tableaux and Related Methods - 28th International Conference, TABLEAUX 2019, Proceedings. editor / Serenella Cerrito ; Andrei Popescu. Springer, 2019. pp. 77-93 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Dvir, Y & Avron, A 2019, First-Order Quasi-canonical Proof Systems. in S Cerrito & A Popescu (eds), Automated Reasoning with Analytic Tableaux and Related Methods - 28th International Conference, TABLEAUX 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11714 LNAI, Springer, pp. 77-93, 28th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2019, London, United Kingdom, 3/09/19. https://doi.org/10.1007/978-3-030-29026-9_5

First-Order Quasi-canonical Proof Systems. / Dvir, Yotam; Avron, Arnon.
Automated Reasoning with Analytic Tableaux and Related Methods - 28th International Conference, TABLEAUX 2019, Proceedings. ed. / Serenella Cerrito; Andrei Popescu. Springer, 2019. p. 77-93 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11714 LNAI).

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

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Dvir Y, Avron A. First-Order Quasi-canonical Proof Systems. In Cerrito S, Popescu A, editors, Automated Reasoning with Analytic Tableaux and Related Methods - 28th International Conference, TABLEAUX 2019, Proceedings. Springer. 2019. p. 77-93. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-29026-9_5

First-Order Quasi-canonical Proof Systems

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Keywords

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