Effects in quantum logic of observables.

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V.L. Vasyukov

Abstract

In the paper a modal and bimodal extension o f quantum logic o f observables QLO is proposed. The former allows to obtain the syntactic counterpart o f D.Mundici’s result on embedding o f C*-algebra into an MValgebra while the latter has as its algebraic counterpart quantum MV-algebra o f R.Giumtini. The soundness and completeness o f both extensions is proved in respect to the set-theoretical semantics developed early for QLO.

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References

Emch G.G. Algebraic Methods in Statistical Mechanics and Quantum Field Theory. N .-Y., 1972.

Giuntini R. Quantum MV Algebras // Studia Logica. Vol. 56. 1996. P.393-417.

Mangcmi P. Su certe algebra connesse con logiche a pi_ valore // Bollettino dell’Unione Matematica Italiana. Vol. 8. 1973. P.68-78.

Mundici D. Interpretation o f AF C*-Algebras in Lukasiewicz Sentential Calculus // Journal of Functional Analysis. Vol. 65. 1986. P.15-63.

Vasyukov V.L . Quantum Logic of Observables // V.A.Smirnov (ed.). Syntactic and Semantic Studies o f Non-Extensional Logics. Moscow, 1989. P.120-169 (in Russian).

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