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): 1367-0751
ISSN (online): 1368-9894
Scimago Journal Ranking: 0,35 (in 2018)
Digital Object Identifier: 10.1093/jigpal/jzy051
Abstract
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.
