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Concepts of measures on ring-like quantum logics. (English) Zbl 0980.81009
Summary: The concepts of \(Q\)-valued measures, observables and states are introduced for ring-like quantum logics providing a unified approach to the basic notions of axiomatic quantum mechanics. Consequences of the existence of certain \(Q\)-valued measures for the underlying ring-like structures are investigated and the dependence of \(Q\)-valued measures on certain algebraic properties of ring-like quantum logics is studied. Moreover, links to the lattice-theoretic model of quantum logics are established.

MSC:
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
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