Classical and Empirical Negation in Subintuitionistic Logic

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In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 217-235 (2016)
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Abstract

Subintuitionistic (propositional) logics are those in a standard intuitionistic language that result by weakening the frame conditions of the Kripke semantics for intuitionistic logic. In this paper we consider two negation expansions of subintuitionistic logic, one by classical negation and the other by what has been dubbed “empirical” negation. We provide an axiomatization of each expansion and show them sound and strongly complete. We conclude with some final remarks, including avenues for future research.

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Michael De
Utrecht University

Citations of this work

Metainferential Paraconsistency.Bruno Da Ré, Mariela Rubin & Paula Teijeiro - forthcoming - Logic and Logical Philosophy:1-26.

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References found in this work

Displaying Modal Logic.Heinrich Wansing - 1998 - Dordrecht, Netherland: Springer.
Simplified semantics for relevant logics (and some of their rivals).Greg Restall - 1993 - Journal of Philosophical Logic 22 (5):481 - 511.
Simplified semantics for basic relevant logics.Graham Priest & Richard Sylvan - 1992 - Journal of Philosophical Logic 21 (2):217 - 232.
Displaying Modal Logic.Heinrich Wansing - 2000 - Studia Logica 66 (3):421-426.
A Closer Look at Some Subintuitionistic Logics.Sergio Celani & Ramon Jansana - 2001 - Notre Dame Journal of Formal Logic 42 (4):225-255.

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