Dummett Logic, Irreflexive Modality and Novikov Completeness

In Sergei Odintsov (ed.), Larisa Maksimova on Implication, Interpolation, and Definability. Springer Verlag (2018)
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Abstract

We study an extension of superintuitionistic logic LC in the language containing an additional unary logical connective. This connective is interpreted on every finite chain by the so called irreflexive modality. We show that the resulting logic is conservative over LC, determines a new logical connective in LC w.r.t. P. Novikov’s approach to the notion of a new logical connective. Moreover, we show that is an explicit example of Novikov complete extension of LC, i.e. every proper extension of it is not conservative over LC.

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