PARTIAL ABELIAN SEMIGROUPS

Orthomodular lattices and posers, orthoalgebras, and D-posets are all examples of partial Abelian semigroups. So, too, are the event structures of rest spaces. The passage from an algebraic test space to its logic (an orthoalgebra) is an instance of a general construction involving a partial Abelian semigroup L. and a distinguished subset M subset of or equal to L such that perspectivity with respect to M is a congruence on L. The quotient oft by such a congruence is always a cancellative, unital PAS, and every such PAS arises canonically as such a quotient.