Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory

Yannick Forster; Dominik Kirst; Dominik Wehr

doi:10.1007/978-3-030-36755-8_4

Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory

Yannick Forster, Dominik Kirst, Dominik Wehr

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

7 Scopus citations

Abstract

We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic natural deduction and sequent calculi with respect to model-theoretic, algebraic, and game semantics. As completeness with respect to standard model-theoretic semantics is not readily constructive, we analyse the assumptions necessary for particular syntax fragments and discuss non-standard semantics admitting assumption-free completeness. We contribute a reusable Coq library for first-order logic containing all results covered in this paper.

Original language	English
Title of host publication	Logical Foundations of Computer Science - International Symposium, LFCS 2020, Proceedings
Editors	Sergei Artemov, Anil Nerode
Publisher	Springer
Pages	47-74
Number of pages	28
ISBN (Print)	9783030367541
DOIs	https://doi.org/10.1007/978-3-030-36755-8_4
State	Published - 1 Jan 2020
Externally published	Yes
Event	International Symposium on Logical Foundations of Computer Science, LFCS 2020 - Deerfield Beach, United States Duration: 4 Jan 2020 → 7 Jan 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11972 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	International Symposium on Logical Foundations of Computer Science, LFCS 2020
Country/Territory	United States
City	Deerfield Beach
Period	4/01/20 → 7/01/20

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/978-3-030-36755-8_4

Cite this

Forster, Y., Kirst, D., & Wehr, D. (2020). Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory. In S. Artemov, & A. Nerode (Eds.), Logical Foundations of Computer Science - International Symposium, LFCS 2020, Proceedings (pp. 47-74). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11972 LNCS). Springer. https://doi.org/10.1007/978-3-030-36755-8_4

Forster, Yannick ; Kirst, Dominik ; Wehr, Dominik. / Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory. Logical Foundations of Computer Science - International Symposium, LFCS 2020, Proceedings. editor / Sergei Artemov ; Anil Nerode. Springer, 2020. pp. 47-74 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Forster, Y, Kirst, D & Wehr, D 2020, Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory. in S Artemov & A Nerode (eds), Logical Foundations of Computer Science - International Symposium, LFCS 2020, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11972 LNCS, Springer, pp. 47-74, International Symposium on Logical Foundations of Computer Science, LFCS 2020, Deerfield Beach, United States, 4/01/20. https://doi.org/10.1007/978-3-030-36755-8_4

Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory. / Forster, Yannick; Kirst, Dominik; Wehr, Dominik.
Logical Foundations of Computer Science - International Symposium, LFCS 2020, Proceedings. ed. / Sergei Artemov; Anil Nerode. Springer, 2020. p. 47-74 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11972 LNCS).

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

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AB - We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic natural deduction and sequent calculi with respect to model-theoretic, algebraic, and game semantics. As completeness with respect to standard model-theoretic semantics is not readily constructive, we analyse the assumptions necessary for particular syntax fragments and discuss non-standard semantics admitting assumption-free completeness. We contribute a reusable Coq library for first-order logic containing all results covered in this paper.

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Forster Y, Kirst D, Wehr D. Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory. In Artemov S, Nerode A, editors, Logical Foundations of Computer Science - International Symposium, LFCS 2020, Proceedings. Springer. 2020. p. 47-74. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-36755-8_4

Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory

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