2022/08/31 by Fazio, Davide, Ledda, Antonio, Paoli, Francesco · 1 citation
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2208.14715
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.