States on symmetric logics: extensions (Q2822855)

The authors investigate the set-representable quantum logics that are closed under the formation of symmetric difference. They study states on these logics and ask when the states are automatically subadditive with respect to the symmetric difference. They show that for finite logics this is never the case. In the second result, they construct a quantum logic (over an uncountable set) for which each state is subadditive on the symmetric difference. The paper is an interesting contribution to the logico-algebraic foundation of quantum mechanics.