Open bar – A brouwerian intuitionistic logic with a pinch of excluded middle

Mark Bickford, Liron Cohen, Robert L. Constable, Vincent Rahli

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

1 Scopus citations


One of the differences between Brouwerian intuitionistic logic and classical logic is their treatment of time. In classical logic truth is atemporal, whereas in intuitionistic logic it is time-relative. Thus, in intuitionistic logic it is possible to acquire new knowledge as time progresses, whereas the classical Law of Excluded Middle (LEM) is essentially flattening the notion of time stating that it is possible to decide whether or not some knowledge will ever be acquired. This paper demonstrates that, nonetheless, the two approaches are not necessarily incompatible by introducing an intuitionistic type theory along with a Beth-like model for it that provide some middle ground. On one hand they incorporate a notion of progressing time and include evolving mathematical entities in the form of choice sequences, and on the other hand they are consistent with a variant of the classical LEM. Accordingly, this new type theory provides the basis for a more classically inclined Brouwerian intuitionistic type theory.

Original languageEnglish
Title of host publication29th EACSL Annual Conference on Computer Science Logic, CSL 2021
EditorsChristel Baier, Jean Goubault-Larrecq
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771757
StatePublished - 1 Jan 2021
Event29th EACSL Annual Conference on Computer Science Logic, CSL 2021 - Virtual, Ljubljana, Slovenia
Duration: 25 Jan 202128 Jan 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference29th EACSL Annual Conference on Computer Science Logic, CSL 2021
CityVirtual, Ljubljana


  • Choice sequences
  • Classical logic
  • Constructive type theory
  • Coq
  • Extensional type theory
  • Intuitionism
  • Law of excluded middle
  • Realizability
  • Theorem proving

ASJC Scopus subject areas

  • Software

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