An order-theoretic analysis of interpretations among propositional deductive systems

TL;DR

This paper develops a general order-theoretic framework using quantale theory to analyze and characterize interpretations and equivalences among propositional deductive systems, including those with different languages.

Contribution

It introduces a novel order-theoretic approach based on quantale theory to study interpretations among propositional deductive systems, accommodating systems with different languages.

Findings

Provides a unified framework for strong and weak interpretations.

Characterizes interpretability across systems with different languages.

Extends the understanding of propositional deductive systems through order-theoretic methods.

Abstract

In this paper we study interpretations and equivalences of propositional deductive systems by using a quantale-theoretic approach introduced by Galatos and Tsinakis. Our aim is to provide a general order-theoretic framework which is able to describe and characterize both strong and weak forms of interpretations among propositional deductive systems also in the cases where the systems have different underlying languages.