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

Abstract

An attempt is made to include the axioms of Mackey for probabilities of experiments in quantum mechanics into the calculusŁ x0 of Łukasiewicz. The obtained calculusŁQ 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.