Classical and Empirical Negation in Subintuitionistic Logic

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

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Subintuitionistic Logics.Greg Restall - 1994 - Notre Dame Journal of Formal Logic 35 (1):116-129.

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