An extension of the łukasiewicz logic to the modal logic of quantum mechanics

Studia Logica 37 (2):149 - 155 (1978)
An attempt is made to include the axioms of Mackey for probabilities of experiments in quantum mechanics into the calculus x0 of ukasiewicz. The obtained calculusQ contains an additional modal signQ and four modal rules of inference. The propositionQx is read x is confirmed. The most specific rule of inference may be read: for comparable observations implication is equivalent to confirmation of material implication.The semantic truth ofQ is established by the interpretation with the help of physical objects obeying to the rules of quantum mechanics. The embedding of the usual quantum propositional logic inQ is accomplished.
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P. D. Finch (1969). On the Structure of Quantum Logic. Journal of Symbolic Logic 34 (2):275-282.

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