Mathematics – Logic
Scientific paper
2005-12-17
Tatra Mountains Math. Publ. 10 (1997) 199--223
Mathematics
Logic
29 pages. Translated by A. Pulmanova from Mathematical Foundations of the General Systems Theory, MIEM, Moscow, 1987
Scientific paper
We give an axiomatic formulation of quantum structures like semilogics and quasilogics which generalize the boolean semirings of events and fuzzy logics. The notions of distributions, states, representations observables and semiobservables are introduced and their Hilbert space realizations are found. The closed and open structures in semilogics are introduced and the regular distributions on the semilogics are studied.
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