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- W4367693474 abstract "Abstract We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic ( $$textrm{CHL}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mtext>CHL</mml:mtext> </mml:math> ), hereby introduced as an example of a strongly connexive logic with an intuitive semantics. We use the reverse algebraisation paradigm: $$textrm{CHL}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mtext>CHL</mml:mtext> </mml:math> 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 $$textrm{CHL}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mtext>CHL</mml:mtext> </mml:math> ; moreover, we suggest a possible computational interpretation of its connexive conditional, and we revisit Kapsner’s idea of superconnexivity." @default.
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- W4367693474 date "2023-05-02" @default.
- W4367693474 modified "2023-10-06" @default.
- W4367693474 title "Intuitionistic Logic is a Connexive Logic" @default.
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- W4367693474 doi "https://doi.org/10.1007/s11225-023-10044-7" @default.
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