A logic of implications in algebra and coalgebra
type: Item
instance of: scholarly article
title: A logic of implications in algebra and coalgebra
zbMATH Open document ID: 1229.18001
author: Jiří Adámek
author: Manuela Sobral
author: Lurdes Sousa
published in: Algebra Universalis
publication date: 2010-01-04T00:00:00Z
full work available at URL: http://hdl.handle.net/10316/11299
review text: This paper rephrases previous work by Rosu that develops a sound and complete calculus for abstract logics in which models are objects in abstract categories, sentences are epimorphisms in the respective categories, and satisfaction is given by (categorical) injectivity. Both Birkhoff calculus for conditional equations in universal algebra and Gumm calculus for coalgebra appear as instances of the abstract calculus developed here. However important potential applications are not discussed, most notably in the area of partial algebra, which may rise doubts about the real value of this work.
reviewed by: Răzvan Diaconescu
Mathematics Subject Classification ID: 18A15
Mathematics Subject Classification ID: 03C05
Mathematics Subject Classification ID: 03B70
zbMATH DE Number: 5652288
zbMATH Keywords: logic of injectivity
zbMATH Keywords: logic of implications
zbMATH Keywords: algebras
zbMATH Keywords: coalgebras
zbMATH Keywords: coalgebraic implications
zbMATH Keywords: Birkhoff calculus
zbMATH Keywords: Gumm calculus
MaRDI profile type: Publication
OpenAlex ID: W2029610160
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DOI: 10.1007/S00012-009-0009-Z
description: scientific article; zbMATH DE number 5652288