Isomorphic Formulae in Classical Propositional Logic

TL;DR

This paper explores the concept of isomorphism between propositional logic formulae, providing characterizations and decision procedures for identifying when two formulae are structurally equivalent within classical and linear logic frameworks.

Contribution

It introduces a formal notion of isomorphism for propositional formulae and offers decision procedures to determine such equivalences, advancing understanding of logical deduction equality.

Findings

Characterizations of isomorphic formulae

Decision procedures for isomorphism

Application to classical and linear logic

Abstract

Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This equality is motivated by generality of deductions. Characterizations are given for pairs of isomorphic formulae, which lead to decision procedures for this isomorphism.