Quasi-varieties in abstract algebraic institutions
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.
scientific article; zbMATH DE number 4009809
scientific article