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Transition operators assigned to physical systems. (English) Zbl 1386.81010

Summary: By a physical system we recognize a set of propositions about a given system with their truth values depending on the states of the system. Since every physical system can go from one state to another one, there exists a binary relation on the set of states describing this transition. Our aim is to assign to every such system an operator on the set of propositions which is fully determined by the mentioned relation. We establish conditions under which the given relation can be recovered by means of this transition operator.

MSC:

81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
03G10 Logical aspects of lattices and related structures
03G12 Quantum logic
03G05 Logical aspects of Boolean algebras
06B23 Complete lattices, completions
06A15 Galois correspondences, closure operators (in relation to ordered sets)
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References:

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