Paraconsistent Foundations for Quantum Probability
This provides a foundational link between logical systems and quantum computing, potentially enabling new programming language types, though it appears incremental as it builds on existing paraconsistent and quantum frameworks.
The paper tackles the problem of connecting paraconsistent logic with quantum probability by showing that a fuzzy 4-truth-valued paraconsistent logic can be approximately mapped to the complex-number algebra of quantum probabilities, with p-bits approximating qubits arbitrarily closely in a formal sense.
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.