Remarks on Propositional Logics and the categorial relationship between Institutions and {\Pi}-Institutions

TL;DR

This paper investigates the relationship between institutions and { Pi}-institutions in propositional logics, establishing a categorical adjunction through functors between their categories.

Contribution

It introduces a formal categorical framework linking institutions and { Pi}-institutions, providing a precise adjunction in propositional logic settings.

Findings

Established a pair of functors forming an adjunction between Inst and { Pi}-Inst categories.

Clarified the categorical relationship and applications in propositional logics.

Enhanced understanding of the structural connections in logical frameworks.

Abstract

In this work we explore some applications of the notions of Institution and {\Pi}-Institution in the setting of propositional logics and establish a precise categorial relation between these notions, i.e., we provide a pair of functors that establishes an adjunction between the categories Inst and {\Pi}-Inst.