Logical Consistency as a Dynamical Invariant: A Quantum Model of Self-Reference and Paradox

TL;DR

This paper introduces a quantum circuit model that inherently maintains logical consistency during reasoning, effectively handling paradoxes like the Liar Paradox through quantum interference effects.

Contribution

It presents a novel quantum framework that encodes self-referential propositions to naturally enforce logical consistency during computation.

Findings

Quantum model stabilizes paradoxical truth values

Interference effects suppress inconsistent outcomes

Connects quantum logic with belief revision and cognition

Abstract

Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in Tarski's hierarchy or paraconsistent logics. We propose a novel approach: a quantum circuit architecture that intrinsically enforces logical consistency during its unitary evolution. By encoding self-referential or contradictory propositions into a quantum state, the circuit uses interference effects to suppress inconsistent outcomes while preserving coherent ones. We demonstrate this with the Liar Paradox ("This statement is false"), showing that the quantum model naturally stabilizes truth values that would be paradoxical classically. The framework builds on orthomodular quantum logic treating logical propositions as subspace projectors and connects to belief revision and cognitive modeling by providing a physical mechanism for coherence restoration in epistemic states. This work bridges formal logic and quantum computation, suggesting that consistency can be embedded as a structural property of reasoning systems rather than imposed externally.