Abstract
We introduce the notion of operationalresolution, i.e., an isotone map from a powerset to aposet that meets two additional conditions, whichgeneralizes the description of states as the atoms in aproperty lattice (Piron, 1976; Aerts, 1982) or as theunderlying set of a closure operator (Aerts, 1994;Moore, 1995). We study the structure preservation of therelated state transitions and show how the operational resolution constitutes an epimorphism betweentwo unitary quantales.
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Coecke, B., Stubbe, I. On a Duality of Quantales Emerging from an Operational Resolution. International Journal of Theoretical Physics 38, 3269–3281 (1999). https://doi.org/10.1023/A:1026642501652
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DOI: https://doi.org/10.1023/A:1026642501652