The logic of the future in quantum theory

TL;DR

This paper explores a novel logical framework for future statements in quantum mechanics, proposing that their truth values correspond to the probability of events occurring, thus integrating logic and quantum probability.

Contribution

It introduces a lattice of future-tense propositions with truth values in [0,1], linking quantum probabilities to a many-valued logic for future statements.

Findings

Truth values of future statements are identified with event probabilities.

Constructs a lattice of future-tense propositions with quantum-mechanical probability assignments.

Provides a logical structure consistent with quantum probability formulas.

Abstract

According to quantum mechanics, statements about the future made by sentient beings like us are, in general, neither true nor false; they must satisfy a many-valued logic. I propose that the truth value of such a statement should be identified with the probability that the event it describes will occur. After reviewing the history of related ideas in logic, I argue that it gives an understanding of probability which is particularly satisfactory for use in quantum mechanics. I construct a lattice of future-tense propositions, with truth values in the interval $[0,1]$, and derive logical properties of these truth values given by the usual quantum-mechanical formula for the probability of a history.