Topological systems as a framework for institutions

TL;DR

This paper explores how generalized topological systems can serve as an effective framework for lattice-valued institutions, extending existing concepts in algebraic logic and category theory.

Contribution

It introduces a generalized topological system framework that effectively models lattice-valued institutions, bridging concepts from lattice theory and topology.

Findings

Provides a new categorical framework for lattice-valued institutions

Shows the equivalence between generalized topological systems and lattice-valued institutions

Enhances understanding of the relationship between topology and algebraic logic

Abstract

Recently, J.~T.~Denniston, A.~Melton, and S.~E.~Rodabaugh introduced a lattice-valued analogue of the concept of institution of J.~A.~Goguen and R.~M.~Burstall, comparing it, moreover, with the (lattice-valued version of the) notion of topological system of S.~Vickers. In this paper, we show that a suitable generalization of topological systems provides a convenient framework for doing certain kinds of (lattice-valued) institutions.