A connection between distributivity and locality in compound P-lattices

A P-lattice is a sigma-complete, orthomodular atomic lattice L which is formed by the set of propositions of a physical system. A composition of physical systems is considered, and some concept of locality in a compound physical system is represented in terms of P-lattices. We give a remark toward necessary and sufficient conditions for it to hold, which have been provided implicitly in antecedent studies, and we show that it can be provided under weaker conditions. (C) 2003 American Institute of Physics.