Kochen-Specker theorem and non-deterministic semantics

In this work we provide a connection between the Kochen-Specker theorem in quantum mechanics and the failure of the principle truth functionality in logic. By exploiting this connection, 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 to infinite non-deterministic truth tables. This allows us to introduce a natural interpretation of quantum states in terms of a non-deterministic semantic. We also provide a similar construction for arbitrary probabilistic theories based in orthomodular lattices, allowing to study pots-quantum models using logical techniques.