Concrete Quantum Logics

Concrete quantum logics are quantum logics which allow for a set representation.They seem to be of significant conceptual value within quantum axiomatics andthey play an important role in the theory of orthomodular structures asset-representable orthomodular posets or lattices and they also sometimes constitutea “domain” for investigations in “noncommutative.” measure theory. This paperpresents a survey of recent results on this class of logics. Stress is put on thealgebraic and measure-theoretic aspects. Several open questions relevant tothe logicoalgebraic foundation of quantum theories are posed.