1 Search Results for "Bickford, Mark"

Document
DOI: 10.4230/LIPIcs.CSL.2021.11
Open Bar - a Brouwerian Intuitionistic Logic with a Pinch of Excluded Middle

Authors: Mark Bickford, Liron Cohen, Robert L. Constable, and Vincent Rahli

Published in: LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)

Abstract
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.
Cite as

Mark Bickford, Liron Cohen, Robert L. Constable, and Vincent Rahli. Open Bar - a Brouwerian Intuitionistic Logic with a Pinch of Excluded Middle. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 11:1-11:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{bickford_et_al:LIPIcs.CSL.2021.11,
  author =	{Bickford, Mark and Cohen, Liron and Constable, Robert L. and Rahli, Vincent},
  title =	{{Open Bar - a Brouwerian Intuitionistic Logic with a Pinch of Excluded Middle}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{11:1--11:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Baier, Christel and Goubault-Larrecq, Jean},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.11},
  URN =		{urn:nbn:de:0030-drops-134455},
  doi =		{10.4230/LIPIcs.CSL.2021.11},
  annote =	{Keywords: Intuitionism, Extensional type theory, Constructive Type Theory, Realizability, Choice sequences, Classical Logic, Law of Excluded Middle, Theorem proving, Coq}
}
  • Refine by Author
  • 1 Bickford, Mark
  • 1 Cohen, Liron
  • 1 Constable, Robert L.
  • 1 Rahli, Vincent

  • Refine by Classification
  • 1 Theory of computation → Constructive mathematics
  • 1 Theory of computation → Type theory

  • Refine by Keyword
  • 1 Choice sequences
  • 1 Classical Logic
  • 1 Constructive Type Theory
  • 1 Coq
  • 1 Extensional type theory
  • Show More...

  • Refine by Type
  • 1 document

  • Refine by Publication Year
  • 1 2021

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact