Merging Intuitionistic and De Morgan Logics

Minghui Ma () and Juntong Guo
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Minghui Ma: Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou 510275, China
Juntong Guo: Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou 510275, China

Mathematics, 2024, vol. 12, issue 1, 1-25

Abstract: We introduce De Morgan Heyting logic for Heyting algebras with De Morgan negation (DH-algebras). The variety DH of all DH-algebras is congruence distributive. The lattice of all subvarieties of DH is distributive. We show the discrete dualities between De Morgan frames and DH-algebras. The Kripke completeness and finite approximability of some DH-logics are proven. Some conservativity of DH expansion of a Kripke complete superintuitionistic logic is shown by the construction of frame expansion. Finally, a cut-free terminating Gentzen sequent calculus for the DH-logic of De Morgan Boolean algebras is developed.

Keywords: Heyting algebra; De Morgan algebra; intuitionistic logic (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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