Is S5 Paraconsistent?
DOI:
https://doi.org/10.5007/1808-1711.2025.e107472Palabras clave:
Negation, Paraconsistent Logic, Paracomplete Logic, Modal LogicResumen
The aim of this note is to examine the claim of B´eziau that S5 is paraconsistent. In particular, I wish to clarify what exactly is implicitly assumed behind his claim, and how we might be able to assess the claim “S5 is paraconsistent”.
Citas
Avron, A. 2020. The normal and self-extensional extension of Dunn--Belnap logic. Logica Universalis 14(3): 281--96.
Berto, F. 2015. A modality called `negation'. Mind 124(495): 761--793.
Berto, F.; Restall, G. 2019. Negation on the Australian plan. Journal of Philosophical Logic 48(6): 1119--1144.
Béziau, J.-Y. 2002. S5 is a paraconsistent logic and so is first-order classical logic. Logical Studies 9: 301--309.
Button, T. 2016. Knot and tonk: Nasty connectives on many-valued truth-tables for classical sentential logic. Analysis 76(1): 7--19.
Button, T.; Walsh, S. 2018. Philosophy and model theory. Oxford University Press: Oxford.
De, M.; Omori, H. 2015. Classical negation and expansions of Belnap--Dunn logic. Studia Logica 103(4): 825--851.
De, M.; Omori, H. 2018. There is more to negation than modality. Journal of Philosophical Logic 47(2): 281--299.
De, M.; Omori, H.2022. Knot much like tonk. Synthese 200.
Drobyshevich, S.; Odintsov, S.; Wansing, H. 2022. Moisil's modal logic and related systems. In: K. Bimb'o (ed.) Relevance Logics and Other Tools for Reasoning. Essays in Honour of Michael Dunn, pp.150--177. College Publications.
Humberstone, L. 2016. Philosophical Applications of Modal Logic. College Publications.
Kamide, N. 2022. Herbrand and Contraposition-elimination Theorems for Extended First-order Belnap-Dunn Logic. In: K. Bimbó (ed.) Relevance Logics and Other Tools for Reasoning. Essays in Honour of Michael Dunn, pp.237--260. College Publications.
Kamide, N.; Omori, H. 2017. An extended first-order Belnap-Dunn Logic with classical negation. In: International Workshop on Logic, Rationality and Interaction, pp.79--93. Springer.
Karpenko, A. S. 2013. Von Wright's truth-logic and around. Logical Studies 19: 39--50.
Leitgeb, H. 2019. HYPE: A system of hyperintensional logic (with an application to semantic paradoxes). Journal of Philosophical Logic 48(2): 305--405.
Marcos, J. 2005. Nearly every normal modal logics is paranormal. Logique et Analyse 48: 279--300.
Mruczek-Nasieniewska, K.; Nasieniewski, M. 2005. Syntactical and Semantical Characterization of a Class of Paraconsistent Logics. Bulletin of the Section of Logic 34(4): 118--125.
Mruczek-Nasieniewska, K.; Nasieniewski, M. 2008. Paraconsitent Logics Obtained by J. Y. Beziau's Method by Means of some Non-Normal Modal Logics. Bulletin of the Section of Logic 37(3/4): 185--196.
Mruczek-Nasieniewska, K.; Nasieniewski, M. 2009. Beziau's Logics Obtained by Means of Quasi-Regular Logics. Bulletin of the Section of Logic 38(3/4): 189--204.
Niki, S.; Omori, H. 2024. Kamide is in America, Moisil and Leitgeb are in Australia. EPTCS 415: 180--194.
Odintsov, S. P.; Wansing, H. 2020. Routley star and Hyperintensionality. Journal of Philosophical Logic 50: 33--56.
Omori, H.; Skurt, D. 2019. SIXTEEN$_3$ in Light of Routley Stars. In: Proceedings of WoLLIC 2019, pp.516--532. Springer.
Omori, H.; Skurt, D. 2024. On Ivlev's semantics for modality. In: Many-valued semantics and Modal Logics: Essays in Honor of Yuriy Vasilievich Ivlev, volume 485 of Synthese Library, pp.243--275. Springer.
Omori, H.; Wansing, H. 2022. Varieties of negation and contra-classicality in view of Dunn semantics. In: K. Bimbó (ed.) Relevance Logics and Other Tools for Reasoning. Essays in Honour of Michael Dunn, pp.309--337. College Publications.
Segerberg, K. 1986. Modal logics with functional alternative relations. Notre Dame Journal of Formal Logic 27(4): 504--522.
Standefer, S. 2018. Proof theory for functional modal logic. Studia Logica 106(1): 49--84.
Zaitsev, D. 2012. Generalized relevant logic and models of reasoning. Moscow State Lomonosov University doctoral (Doctor of Science) dissertation.
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