An exercise in "anhomomorphic logic"

A classical logic exhibits a threefold inner structure comprising an algebra of propositions , a space of "truth values" V, and a distinguished family of mappings from propositions to truth values. Classically is a Boolean algebra, V = 2, and the admissible maps : 2 are homomorphisms. If one admits a larger set of maps, one obtains an anhomomorphic logic that seems better suited to quantal reality (and the needs of quantum gravity). I explain these ideas and illustrate them with three simple examples.