Quasi-varieties in abstract algebraic institutions
type: Item
instance of: scholarly article
title: Quasi-varieties in abstract algebraic institutions
zbMATH Open document ID: 0622.68033
DOI: 10.1016/0022-0000(86)90057-7
author: Andrzej Tarlecki
published in: Journal of Computer and System Sciences
publication date: 1986-01-01T00:00:00Z
review text: The author specializes the extremely general notion of institution introduced by \textit{J. A. Goguen} and \textit{R. M. Burstall} [Lect. Notes Comput. Sci. 164, 221-256 (1984; Zbl 0543.68021)] to obtain his own notion of abstract algebraic institution. It is shown that in abstract algebraic institutions quasi-varieties and strict quasi-varieties are characterized respectively as implicational and strict implicational classes. This allows the author to present characterizations of the most general algebraic institution which strongly admit initial semantics [cf. \textit{A. Tarlecki}, Theor. Comput. Sci. 37, 269-304 (1985; Zbl 0608.68014)] in more standard syntactical terms. These general considerations are applied to three familiar classes of total, partial and continuous algebras.
Mathematics Subject Classification ID: 68Q65
Mathematics Subject Classification ID: 68P05
zbMATH DE Number: 4009809
zbMATH Keywords: abstract algebraic institution
zbMATH Keywords: quasi-varieties
zbMATH Keywords: implicational classes
zbMATH Keywords: initial semantics
zbMATH Keywords: continuous algebras
reviewed by: Hirokazu Nishimura
describes a project that uses: ML
MaRDI profile type: Publication
full work available at URL: 0022-0000(86)90057-7
OpenAlex ID: W2017041211
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description: scientific article; zbMATH DE number 4009809