Partial Boolean algebras in a broader sense and Boolean embeddings
Partially additive states on orthomodular posets
We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s:P → [0,1] which respect the ordering and the orthocomplementation in P and which are additive on B. We call such functions B-states on P. We first show that every P possesses "enough" two-valued B-states. This improves the main result in [13], where B is the centre of P. Moreover, it allows us to construct a closure-space representation of orthomodular lattices. We do this in the third section. This result may also...
Perspectivity and congruence in partial abelian semigroups
Projection postulate and superposition principle in non-lattice quantum logics