Intuitionistic logic as a connexive logic

Fazio D.;Ledda A.;Paoli F.

2023-01-01

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Abstract

We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic (CHL), hereby introduced as an example of a strongly connexive logic with an intuitive semantics. We use the reverse algebraisation paradigm: CHL is presented as the assertional logic of a point regular variety (whose structure theory is examined in detail) that turns out to be term equivalent to the variety of Heyting algebras. We provide Hilbert-style and Gentzen-style proof systems for CHL ; moreover, we suggest a possible computational interpretation of its connexive conditional, and we revisit Kapsner’s idea of superconnexivity.