Intuitionistic Logic is a Connexive Logic

Davide Fazio; Antonio Ledda; Francesco Paoli

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arXiv · 2208.14715

Intuitionistic Logic is a Connexive Logic

Davide Fazio·Antonio Ledda·Francesco Paoli

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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 strong connexive logic with 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.

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BibTeX RIS

Davide Fazio, Antonio Ledda, Francesco Paoli. 2022-08-31. Intuitionistic Logic is a Connexive Logic. https://arxiv.org/abs/2208.14715

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