Universal models for the positive fragment of intuitionistic logic

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

doi:10.1007/978-3-662-54332-0_13

Universal models for the positive fragment of intuitionistic logic

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

^*Corresponding author for this work

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-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 language	English
Title of host publication	Logic, Language, and Computation - 11th International Tbilisi Symposium, TbiLLC 2015, Revised Selected Papers
Editors	Mehrnoosh Sadrzadeh, Henk Zeevat, Sarah E. Murray, Helle Hvid Hansen
Publisher	Springer Verlag
Pages	229-250
Number of pages	22
ISBN (Print)	9783662543313
DOIs	https://doi.org/10.1007/978-3-662-54332-0_13
Publication status	Published - 1 Jan 2017
Externally published	Yes
Event	11th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2015 - Tbilisi, Georgia Duration: 21 Sept 2015 → 26 Sept 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10148 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	11th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2015
Country/Territory	Georgia
City	Tbilisi
Period	21/09/15 → 26/09/15

Keywords

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

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10.1007/978-3-662-54332-0_13

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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, 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 et al. / 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 et al.
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 proceeding › Conference contribution › Academic › peer-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)). doi: 10.1007/978-3-662-54332-0_13

Universal models for the positive fragment of intuitionistic logic

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