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The lattice of all 4-valued implicative expansions of Belnap–Dunn logic containing Routley and Meyer's basic logic Bd.
- Source :
- Logic Journal of the IGPL; Jun2024, Vol. 32 Issue 3, p493-516, 24p
- Publication Year :
- 2024
-
Abstract
- The well-known logic first degree entailment logic (FDE), introduced by Belnap and Dunn, is defined with |$\wedge $| , |$\vee $| and |$\sim $| as the sole primitive connectives. The aim of this paper is to establish the lattice formed by the class of all 4-valued C-extending implicative expansions of FDE verifying the axioms and rules of Routley and Meyer's basic logic B and its useful disjunctive extension B |$^{\textrm {d}}$|. It is to be noted that Boolean negation (so, classical propositional logic) is definable in the strongest element in the said class. [ABSTRACT FROM AUTHOR]
- Subjects :
- PROPOSITION (Logic)
LOGIC
BANACH lattices
Subjects
Details
- Language :
- English
- ISSN :
- 13670751
- Volume :
- 32
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Logic Journal of the IGPL
- Publication Type :
- Academic Journal
- Accession number :
- 177681411
- Full Text :
- https://doi.org/10.1093/jigpal/jzad005