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Merging Intuitionistic and De Morgan Logics

Author

Listed:
  • Minghui Ma

    (Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou 510275, China
    Authors contributed equally to this work.)

  • Juntong Guo

    (Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou 510275, China
    Authors contributed equally to this work.)

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.

Suggested Citation

  • Minghui Ma & Juntong Guo, 2024. "Merging Intuitionistic and De Morgan Logics," Mathematics, MDPI, vol. 12(1), pages 1-25, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:1:p:146-:d:1312025
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