How to Make a New Logic

TL;DR

This paper introduces a method called Stahlization for creating new logical systems by reversing the direction of inference arrows in existing Gentzen-style logics, exploring its implications.

Contribution

It proposes a novel operation, Stahlization, for systematically constructing new logics from existing Gentzen systems by inverting inference directions.

Findings

Stahlization produces consistent new logical systems.

The operation offers a systematic way to explore logic transformations.

Applications to specific logics demonstrate its utility.

Abstract

We discuss about how to make a new logic with considering a slogan: \it take the inversion of what you know. \rm Suppose that we have a Gentzen-style logical system $S$. The operation to make a new logic from $S$ is the following: \it for all the axioms and rules of $S$, change the direction of all the arrows occurred in the sequents of the axiom or the rule to the opposite side. \rm We call this operation \it Stahlization. \rm We consider certain logics in this respect.