Categorical abstract algebraic logic: \((\ell,N)\)-algebraic systems (Q816651)

This paper is part of the great programme undertaken by the same author to generalize algebraization of deductive systems / sentential logic (as developed by Blok, Pigozzi, Font, Jansana, etc.) to the level of \(\pi\)-institutions. The latter arose within formal specification theory as a meta-theory for multi-signature deductive systems, independently of the actual details of the logic involved. In this paper, the author introduces \(\mathcal{I}\)-algebraic systems of a \(\pi\)-institution \(\mathcal{I}\), corresponding to \(\mathcal{S}\)-algebras of a sentential logic \(\mathcal{S}\). Then their relationship with full models and with bilogical morphisms is investigated.