A Mechanised and Constructive Reverse Analysis of Soundness and Completeness of Bi-intuitionistic Logic

Ian Shillito, Dominik Kirst

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Using the Coq proof assistant, we investigate the minimal non-constructive principles needed to show soundness and completeness of propositional bi-intuitionistic logic. Before being revisited and corrected by Goré and Shillito, the completeness of bi-intuitionistic logic, an extension of intuitionistic logic with a dual operation to implication, had a rather erratic history, making it an ideal case for computer mechanisation. Moreover, contributing a constructive perspective, we observe that the completeness of bi-intuitionistic logic explicates the same characteristics already observed in an ongoing effort to analyse completeness theorems in general.

Original languageEnglish
Title of host publicationCPP 2024 - Proceedings of the 13th ACM SIGPLAN International Conference on Certified Programs and Proofs, Co-located with
Subtitle of host publicationPOPL 2024
EditorsAmin Timany, Dmitriy Traytel, Brigitte Pientka, Sandrine Blazy
PublisherAssociation for Computing Machinery, Inc
Pages218-229
Number of pages12
ISBN (Electronic)9798400704888
DOIs
StatePublished - 9 Jan 2024
Event13th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2024, in affiliation with the annual Symposium on Principles of Programming, Languages, ,POPL 2024 - London, United Kingdom
Duration: 15 Jan 202416 Jan 2024

Publication series

NameCPP 2024 - Proceedings of the 13th ACM SIGPLAN International Conference on Certified Programs and Proofs, Co-located with: POPL 2024

Conference

Conference13th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2024, in affiliation with the annual Symposium on Principles of Programming, Languages, ,POPL 2024
Country/TerritoryUnited Kingdom
CityLondon
Period15/01/2416/01/24

Keywords

  • bi-intuitionistic logic
  • completeness
  • constructive reverse mathematics
  • Coq

ASJC Scopus subject areas

  • Computer Science Applications
  • Software

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