Notre Dame Journal of Formal Logic

Dual Gaggle Semantics for Entailment

Katalin Bimbó

Abstract

A sequent calculus for the positive fragment of entailment together with the Church constants is introduced here. The single cut rule is admissible in this consecution calculus. A topological dual gaggle semantics is developed for the logic. The category of the topological structures for the logic with frame morphisms is proven to be the dual category of the variety, that is defined by the equations of the algebra of the logic, with homomorphisms. The duality results are extended to the logic of entailment that includes a De Morgan negation.

Article information

Source
Notre Dame J. Formal Logic, Volume 50, Number 1 (2009), 23-41.

Dates
First available in Project Euclid: 19 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1232375160

Digital Object Identifier
doi:10.1215/00294527-2008-025

Mathematical Reviews number (MathSciNet)
MR2536698

Zentralblatt MATH identifier
1190.03024

Subjects
Primary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}
Secondary: 03F05: Cut-elimination and normal-form theorems 18C50: Categorical semantics of formal languages [See also 68Q55, 68Q65]

Keywords
entailment relevance logics gaggle theory topological duality theory sequent calculus cut-free proofs

Citation

Bimbó, Katalin. Dual Gaggle Semantics for Entailment. Notre Dame J. Formal Logic 50 (2009), no. 1, 23--41. doi:10.1215/00294527-2008-025. https://projecteuclid.org/euclid.ndjfl/1232375160


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