Paraconsistent Foundations for Quantum Probability

TL;DR

This paper proposes a fuzzy paraconsistent logic framework that can approximately map to quantum probabilities, enabling p-bits to serve as near-approximations of qubits with arbitrarily small errors.

Contribution

It introduces a novel logical approach linking paraconsistent logic to quantum probability, providing a formal method to approximate qubits using p-bits.

Findings

Fuzzy 4-truth-valued paraconsistent logic can be approximately mapped into quantum probability algebra.

The approximation error is related to the observer's evidential uncertainty.

Programmatic mappings between probabilistic and quantum types are feasible.

Abstract

It is argued that a fuzzy version of 4-truth-valued paraconsistent logic (with truth values corresponding to True, False, Both and Neither) can be approximately isomorphically mapped into the complex-number algebra of quantum probabilities. I.e., p-bits (paraconsistent bits) can be transformed into close approximations of qubits. The approximation error can be made arbitrarily small, at least in a formal sense, and can be related to the degree of irreducible "evidential error" assumed to plague an observer's observations. This logical correspondence manifests itself in program space via an approximate mapping between probabilistic and quantum types in programming languages.