Universal models for the positive fragment of intuitionistic logic

Nick Bezhanishvili, Dick de Jongh, Apostolos Tzimoulis, Zhiguang Zhao

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

Abstract

We describe the n-universal model U(n) of the positive fragment of the intuitionistic propositional calculus IPC. We show that U(n) is isomorphic to a generated submodel of U(n) - the n-universal model of IPC. Using U(n), we give an alternative proof of Jankov’s theorem stating that the intermediate logic KC, the logic of the weak law of excluded middle, is the greatest intermediate logic extending IPC that proves exactly the same positive formulas as IPC.

Original languageEnglish
Title of host publicationLogic, Language, and Computation - 11th International Tbilisi Symposium, TbiLLC 2015, Revised Selected Papers
EditorsMehrnoosh Sadrzadeh, Henk Zeevat, Sarah E. Murray, Helle Hvid Hansen
PublisherSpringer Verlag
Pages229-250
Number of pages22
ISBN (Print)9783662543313
DOIs
Publication statusPublished - 1 Jan 2017
Externally publishedYes
Event11th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2015 - Tbilisi, Georgia
Duration: 21 Sep 201526 Sep 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10148 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2015
CountryGeorgia
CityTbilisi
Period21/09/1526/09/15

Fingerprint

Intermediate Logics
Intuitionistic Logic
Fragment
Excluded third
Calculus
Isomorphic
Logic
Alternatives
Theorem
Model

Keywords

  • Fragment of intuitionistic logic
  • Jankov’s theorem
  • Positive morphism
  • Universal models

Cite this

Bezhanishvili, N., de Jongh, D., Tzimoulis, A., & Zhao, Z. (2017). Universal models for the positive fragment of intuitionistic logic. In M. Sadrzadeh, H. Zeevat, S. E. Murray, & H. H. Hansen (Eds.), Logic, Language, and Computation - 11th International Tbilisi Symposium, TbiLLC 2015, Revised Selected Papers (pp. 229-250). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10148 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-662-54332-0_13
Bezhanishvili, Nick ; de Jongh, Dick ; Tzimoulis, Apostolos ; Zhao, Zhiguang. / Universal models for the positive fragment of intuitionistic logic. Logic, Language, and Computation - 11th International Tbilisi Symposium, TbiLLC 2015, Revised Selected Papers. editor / Mehrnoosh Sadrzadeh ; Henk Zeevat ; Sarah E. Murray ; Helle Hvid Hansen. Springer Verlag, 2017. pp. 229-250 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Bezhanishvili, N, de Jongh, D, Tzimoulis, A & Zhao, Z 2017, Universal models for the positive fragment of intuitionistic logic. in M Sadrzadeh, H Zeevat, SE Murray & HH Hansen (eds), Logic, Language, and Computation - 11th International Tbilisi Symposium, TbiLLC 2015, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10148 LNCS, Springer Verlag, pp. 229-250, 11th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2015, Tbilisi, Georgia, 21/09/15. https://doi.org/10.1007/978-3-662-54332-0_13

Universal models for the positive fragment of intuitionistic logic. / Bezhanishvili, Nick; de Jongh, Dick; Tzimoulis, Apostolos; Zhao, Zhiguang.

Logic, Language, and Computation - 11th International Tbilisi Symposium, TbiLLC 2015, Revised Selected Papers. ed. / Mehrnoosh Sadrzadeh; Henk Zeevat; Sarah E. Murray; Helle Hvid Hansen. Springer Verlag, 2017. p. 229-250 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10148 LNCS).

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

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Bezhanishvili N, de Jongh D, Tzimoulis A, Zhao Z. Universal models for the positive fragment of intuitionistic logic. In Sadrzadeh M, Zeevat H, Murray SE, Hansen HH, editors, Logic, Language, and Computation - 11th International Tbilisi Symposium, TbiLLC 2015, Revised Selected Papers. Springer Verlag. 2017. p. 229-250. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-662-54332-0_13