Non-associative and projective linear logics

TL;DR

This paper introduces a non-commutative, non-associative variant of linear logic that incorporates quantum measurement principles, expanding the logical framework for quantum reasoning.

Contribution

It develops a new non-associative, non-commutative linear logic framework integrating quantum measurement concepts, extending Girard's linear logic.

Findings

Defines a new non-associative linear logic system

Integrates quantum measurement assumptions into the logic

Provides a foundation for reasoning about quantum systems

Abstract

A non-commutative, non-associative weakening of Girard's linear logic is developed for multiplicative and additive connectives. Additional assumptions capture the logic of quantic measurements.