Abstract
In this paper we introduce non-normal modal extensions of the sub-classical logics CLoN, CluN and CLaN, in the same way that S0.5 0 extends classical logic. The first modal system is both paraconsistent and paracomplete, while the second one is paraconsistent and the third is paracomplete. Despite being non-normal, these systems are sound and complete for a suitable Kripke semantics. We also show that these systems are appropriate for interpreting □ as “is provable in classical logic”. This allows us to recover the theorems of propositional classical logic within three sub-classical modal systems.
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Coniglio, M.E., Peron, N.M. Modal Extensions of Sub-classical Logics for Recovering Classical Logic. Log. Univers. 7, 71–86 (2013). https://doi.org/10.1007/s11787-012-0076-3
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DOI: https://doi.org/10.1007/s11787-012-0076-3