Superlogic Manifolds and Geometric approach to Quantum Logic

TL;DR

This paper introduces superlogic, a geometric framework for quantum logic that captures non-commutative and nilpotent features, offering a novel perspective on the connection between quantum mechanics and logic.

Contribution

It proposes a new superlogic approach that geometrizes quantum logic, emphasizing non-distributivity and non-commutativity to better model quantum phenomena.

Findings

Superlogic incorporates nilpotent elements.

It reflects non-commutative spaces.

Provides a geometric interpretation of quantum logic.

Abstract

The main purpose of this paper is to present a new approach to logic or what we will call superlogic. This approach constitutes a new way of looking at the connection between quantum mechanics and logic. It is a {\it geometrisation} of the quantum logic. Note that this superlogic is not distributive reflecting a good propriety to describe quantum mechanics, non commutative spaces and contains a nilpotent element.