Bilateral Inversion Principles

TL;DR

This paper introduces a bilateral harmony framework for logic, defining processes of inversion and conversion to relate different types of logical rules, offering an alternative to Francez's approach.

Contribution

It presents a novel bilateral account of harmony with inversion and conversion processes, expanding on prior unilateral and bilateral logic theories.

Findings

Defines inversion process linking introduction and elimination rules.

Introduces conversion process relating assertive and rejective rules.

Provides a distinct framework from Francez's vertical and horizontal harmony.

Abstract

This paper formulates a bilateral account of harmony that is an alternative to one proposed by Francez. It builds on an account of harmony for unilateral logic proposed by K\"urbis and the observation that reading the rules for the connectives of bilateral logic bottom up gives the grounds and consequences of formulas with the opposite speech act. I formulate a process I call 'inversion' which allows the determination of assertive elimination rules from assertive introduction rules, and rejective elimination rules from rejective introduction rules, and conversely. It corresponds to Francez's notion of vertical harmony. I also formulate a process I call 'conversion', which allows the determination of rejective introduction rules from assertive elimination rules and conversely, and the determination of assertive introduction rules from rejective elimination rules and conversely. It corresponds to Francez's notion of horizontal harmony. The account has a number of features that distinguishes it from Francez's.