A Weakly Intuitionistic Quantum Logic

TL;DR

This paper explores the development of a weakly intuitionistic quantum logic by modifying traditional quantum logic with a weak Heyting algebra, aiming to better align quantum mechanics with intuitionistic principles.

Contribution

It introduces a novel approach to quantum logic using weak Heyting algebras, extending the framework of traditional quantum logic with intuitionistic features.

Findings

Proposes a weak Heyting algebra for quantum logic

Modifies existing distributive hull schemes for quantum logic

Provides a new logical framework for quantum mechanics

Abstract

In this paper we motivate and study the possibility of an intuitionistic quantum logic. An explicit investigation of the application of the theory of Bruns and Lakser on distributive hulls on traditional quantum logic (as suggested in [Coe]) leads us to a small modification of this scheme. In this way we obtain a weak Heyting algebra (cf. [CJ]) for describing the language of quantum mechanics.