## 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

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

#### 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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