Disjunctive Quantum Logic in Dynamic Perspective

In Coecke (2002a) we proposed the intuitionistic or disjunctive representation of quantum logic, i.e., a representation of the property lattice of physical systems as a complete Heyting algebra of logical propositions on these properties, where this complete Heyting algebra goes equipped with an additional operation, the operational resolution, which identifies the properties within the logic of propositions. This representation has an important application “towards dynamic quantum logic”, namely in describing the temporal indeterministic propagation of actual properties of physical systems. This paper can as such by conceived as an addendum to “Quantum Logic in Intuitionistic Perspective” that discusses spin-off and thus provides an additional motivation. We derive a quantaloidal semantics for dynamic disjunctive quantum logic and illustrate it for the particular case of a perfect (quantum) measurement.