Notes on quantum logics and involutive bounded posets (Q1701729)

The authors concentrate on numerous conditions expressing orthomodularity in ortholattices. They give a detailed overview of exclusion systems of subalgebras distinguishing lattices, modular lattices, distributive lattices, ortholattices, orthomodular lattices, modular ortholattices, and Boolean algebras. They point an elementary ``widely cited error'' from a previous work, cited as [\textit{M.-L. Dalla Chiara} and \textit{R. Giuntini}, ``Quantum logics'', in: D. M. Gabbay (ed.) and F. Guenthner (ed.), Handbook of philosophical logic. Vol. 6. 2nd ed. Dordrecht: Kluwer Academic Publishers. 129--228 (2002; \url{doi:10.1007/978-94-017-0460-1_2})]. (The detailed reference in the paper is incorrect.)