General systems, classical systems, quantum systems and fuzzy systems: an introductory survey

The January 2011 issue of International Journal of General Systems discusses general systems, classical systems, quantum systems and fuzzy systems. In the first contribution to this issue, Jarosław Pykacz interprets the 'truth values' of predictions about properties of quantum mechanical systems (objects) as degrees that are associated with the results of future experiments. In the second contribution, Thomas Vetterlein discusses the Boolean atlas structure as a 'partial Boolean algebra', a structure that was endowed to the set of closed subspaces of a Hilbert space in 1965 by Kochen and Specker. In his contribution, 'Partial quantum logics revisited', Vetterlein considers the set of effects, self-adjoint Hilbert space operators representing generalised yes-no experiments. In their article, 'Representations of pseudo Vitali spaces and Loomis-Sikorski Theorem', they introduce a non-commutative version of Vitali spaces, that is distributive lattices with partially defined compatible sums.