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Published on: May 30, 2014
Non-Deterministic Semantics for Quantum States
Juan Pablo Jorge1, Federico Holik2
1Physics Department, University of Buenos Aires, Buenos Aires 1428, Argentina.
Abstract:
In this work, we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particular valuations associated with infinite non-deterministic truth tables. This allows us to introduce a natural interpretation of quantum states in terms of a non-deterministic semantics. We also provide a similar construction for arbitrary probabilistic theories based in orthomodular lattices, allowing to study post-quantum models using logical techniques.
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