Abstract
Orthomodular lattices and posets, orthoalgebras, and D-posets are all examples of partial Abelian semigroups. So, too, are the event structures of test spaces. The passage from an algebraic test space to its logic (an orthoalgebra) is an instance of a general construction involving a partial Abelian semigroupL and a distinguished subsetM\( \subseteq \)L such that perspectivity with respect toM is a congruence onL. The quotient ofL by such a congruence is always a cancellative, unital PAS, and every such PAS arises canonically as such a quotient.
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