A note on Humberstone's constant Ω

• Autorzy: Niki Satoru , Omori Hitoshi

Identyfikatory

DOI

10.4467/20842589RM.21.006.14376

• Języki publikacji: EN

Abstrakty

EN

We investigate an expansion of positive intuitionistic logic obtained by adding a constant Ω introduced by Lloyd Humberstone. Our main results include a sound and strongly complete axiomatization, some comparisons to other expansions of intuitionistic logic obtained by adding actuality and empirical negation, and an algebraic semantics. We also briefly discuss its connection to classical logic.

Słowa kluczowe

EN

intuitionistic logic; minimal logic; actuality operator; empirical negation; deduction theorem

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2021
• Tom: Vol. 56
• Strony: 75--99
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Niki Satoru

• Department of Philosophy I, Ruhr University, Universit¨atsstraße 150, D-44780 Bochum, Germany

autor

Omori Hitoshi

• Department of Philosophy I, Ruhr University, Universit¨atsstraße 150, D-44780 Bochum, Germany, https://www.ruhr-uni-bochum.de/philosophy/nklogik/

Bibliografia

• [1] A. Colacito, D. de Jongh, and A.L. Vargas, Subminimal negation, Soft Computing 21 (2017), 165–174.
• [2] J.N. Crossley and L. Humberstone, The logic of “actually”, Reports on Mathematical Logic 8 (1977), 11–29.
• [3] M. De, Empirical Negation. Acta Analytica 28 (2013), 49–69.
• [4] M. De and H. Omori, More on empirical negation, In Rajeev Goré, Barteld Kooi, and Agi Kurucz, editors, Advances in modal logic, volume 10, pp. 114–133. College Publications, 2014.
• [5] M. De and H. Omori, Classical negation and expansions of Belnap-Dunn logic, Studia Logica 103 (2015), 825–851.
• [6] M. De and H. Omori, Classical and empirical negation in subintuitionistic logic, in: Lev Beklemishev, St´ephane Demri, and Andr´as M´at´e, editors, Advances in Modal Logic, volume 11, pages 217–235. College Publications, 2016.
• [7] L. Humberstone, Contra-classical logics, Australasian Journal of Philosophy 78:4 (2000), 438–474.
• [8] L. Humberstone, Extensions of intuitionistic logic without the deduction theorem: Some simple examples, Reports on Mathematical Logic 40 (2006), 45–82.
• [9] V.A. Jankov, Conjunctively indecomposable formulas in propositional calculi, Mathematics of the USSR-Izvestiya 3(1):17 (1969).
• [10] I. Johansson, Der minimalkalkül, ein reduzierter intuitionistischer formalismus, Compositio Mathematica 4 (1937), 119–136.
• [11] Y. Komori, On Komori algebras, Bulletin of the Section of Logic 30:2 (2001), 67–70.
• [12] S. Niki, Empirical negation, co-negation and contraposition rule I: Semantical investigations, Bulletin of the Section of Logic 49:3 (2020), 231–253.
• [13] S. Niki and H. Omori, Actuality in intuitionistic logic, in: Nicola Olivetti, Rineke Verbrugge, Sara Negri, and Gabriel Sandu, editors, Advances in Modal Logic, volume 13, pp. 459–479. College Publications, 2020.
• [14] S. Odintsov, Constructive negations and paraconsistency, volume 26 of Trends in Logic, Springer Science & Business Media, 2008.
• [15] H. Ono, Proof Theory and Algebra in Logic, Short Textbooks in Logic, Springer, 2019.
• [16] G. Restall, Subintuitionistic Logics, Notre Dame Journal of Formal Logic 35:1 (1994), 116–126.
• [17] H.P. Sankappanavar and S. Burris, A course in universal algebra, volume 78 of Graduate Texts in Mathematics, Springer, 1981.
• [18] K. Segerberg, Propositional logics related to Heyting’s and Johansson’s, Theoria 34:1 (1968), 26–61.
• [19] Y. Tanaka, An infinitary extension of Jankov’s theorem, Studia Logica 86:1 (2007), 111–131.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).