Grading Adjoint Logic

TL;DR

This paper introduces Graded Adjoint Logic, a highly expressive logical system that integrates Adjoint Logic with graded modalities, providing advanced control over structural rules through formal calculus frameworks.

Contribution

It presents the first formal system combining Adjoint Logic with graded necessity modalities, including sequent calculus, natural deduction, and term assignment.

Findings

Formal sequent calculus for Graded Adjoint Logic

Natural deduction and term assignment frameworks provided

Enhanced control over structural rules demonstrated

Abstract

We introduce a new logic that combines Adjoint Logic with Graded Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. We give a sequent calculus, natural deduction, and term assignment for Graded Adjoint Logic.