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Quantum logic as partial infinite-valued Łukasiewicz logic. (English) Zbl 0839.03041

Summary: It is shown that an old and neglected Łukasiewicz (1913) paper contains a construction of a many-valued logic which can be in an almost straightforward way used to describe physical experiments. The logic is infinite-valued and its truth values are interpreted as probabilities of experimental confirmation of propositions about results of future experiments. In the case of experiments on quantum objects the logic is partial, i.e. the existence of conjunctions and disjunctions cannot be guaranteed for all pairs of propositions. An outline of previous attempts of using many-valued logics in the description of quantum phenomena is given.

MSC:

03G12 Quantum logic
03B50 Many-valued logic
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References:

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