Canonicity of Proofs in Constructive Modal Logic

Matteo Acclavio*, Davide Catta, Federico Olimpieri

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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Abstract

In this paper we investigate the Curry-Howard correspondence for constructive modal logic in light of the gap between the proof equivalences enforced by the lambda calculi from the literature and by the recently defined winning strategies for this logic. We define a new lambda-calculus for a minimal constructive modal logic by enriching the calculus from the literature with additional reduction rules and we prove normalization and confluence for our calculus. We then provide a typing system in the style of focused proof systems allowing us to provide a unique proof for each term in normal form, and we use this result to show a one-to-one correspondence between terms in normal form and winning innocent strategies.

Original languageEnglish
Title of host publicationAutomated Reasoning with Analytic Tableaux and Related Methods - 32nd International Conference, TABLEAUX 2023, Proceedings : 32nd International Conference
EditorsRevantha Ramanayake, Josef Urban
PublisherSpringer Science+Business Media
Publication date2023
Pages342-363
ISBN (Print)9783031435126
DOIs
Publication statusPublished - 2023
Event32nd International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2023 - Prague, Czech Republic
Duration: 18. Sept 202321. Sept 2023

Conference

Conference32nd International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2023
Country/TerritoryCzech Republic
CityPrague
Period18/09/202321/09/2023
SeriesLecture Notes in Computer Science
Volume14278 LNAI
ISSN0302-9743

Keywords

  • Constructive Modal Logic
  • Game Semantics
  • Lambda Calculus

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