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Probabilistic logic of quantum observations

Sernadas, A. ; Rasga, J. ; Sernadas, C. ; Alcácer, L. ; Henriques, A. B.

Logic Journal of the IGPL Vol. -, Nº -, pp. - - -, October, 2018.

ISSN (print): 1368-9894
ISSN (online): 1367-0751

Scimago Journal Ranking: 0,35 (in 2018)

Digital Object Identifier: 10.1093/jigpal/jzy051

A probabilistic propositional logic, endowed with a constructor for asserting compatibility of diagonalisable and bounded observables, is presented and illustrated for reasoning about the random results of projective measurements made on a given quantum state. Simultaneous measurements are assumed to imply that the underlying observables are compatible. A sound and weakly complete axiomatisation is provided relying on the decidable first-order theory of real closed ordered fields. The proposed logic is proved to be a conservative extension of classical propositional logic.