A Note on Gödel-Dummet Logic LC

• Autorzy: Gemma Robles , José M. Méndez

Abstrakty

EN

Let \(A_{0},A_{1},...,A_{n}\) be (possibly) distintict wffs, \(n\) being an odd number equal to or greater than 1. Intuitionistic Propositional Logic IPC plus the axiom \((A_{0}\rightarrow A_{1})\vee ...\vee (A_{n-1}\rightarrow A_{n})\vee (A_{n}\rightarrow A_{0})\) is equivalent to Gödel-Dummett logic LC. However, if \(n\) is an even number equal to or greater than 2, IPC plus the said axiom is a sublogic of LC.

Słowa kluczowe

EN

Intermediate logics; Gödel-Dummet logic LC

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2021
• Tom: 50
• Numer: 3
• Strony: 325-335

Daty

wydano

2021

Twórcy

autor

Gemma Robles

• University of León, Department of Psychology, Sociology and Philosophy

• https://orcid.org/0000000164950388

autor

José M. Méndez

• University of Salamanca

• https://orcid.org/0000000295603327

Bibliografia

• [1] A. R. Anderson, N. D. Belnap Jr., Entailment. The Logic of Relevance and Necessity, vol. I, Princeton University Press, Princeton, NJ (1975).
• [2] M. Dummett, A propositional calculus with denumerable matrix, Journal of Symbolic Logic, vol. 24(2) (1959), pp. 97–106, DOI: https://doi.org/10.2307/2964753
• [3] K. Gödel, Zum intuitionistischen Aussagenkalkül, Anzeiger der Akademie der Wissenschaften in Wien, vol. 69 (1932), pp. 65–66.
• [4] D. D. Jongh, F. S. Maleki, Below Gödel-Dummett, [in:] Booklet of abstracts of Syntax meets Semantics 2019 (SYSMICS 2019), Institute of Logic, Language and Computation, University of Amsterdam (2019), pp. 99–102.
• [5] J. Moschovakis, Intuitionistic Logic, [in:] E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, winter 2018 ed. (2018), URL: https://plato.stanford.edu/archives/win2018/entries/logic-intuitionistic
• [6] G. Robles, J. M. Méndez, A binary Routley semantics for intuitionistic De Morgan minimal logic HM and its extensions, Logic Journal of the IGPL, vol. 23(2) (2014), pp. 174–193, DOI: https://doi.org/10.1093/jigpal/jzu029
• [7] J. K. Slaney, MaGIC, Matrix Generator for Implication Connectives: Version 2.1, Notes and Guide (1995), http://users.cecs.anu.edu.au/jks/magic.html

Identyfikatory

DOI

10.18778/0138-0680.2021.15

nonstd.3pn.id

2033854