Merging Intuitionistic and De Morgan Logics
| Autor: | Minghui Ma, Juntong Guo |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Mathematics, Vol 12, Iss 1, p 146 (2024) |
| Druh dokumentu: | article |
| ISSN: | 12010146 2227-7390 |
| DOI: | 10.3390/math12010146 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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