An exercise in "anhomomorphic logic"
Rafael D. Sorkin · Journal of Physics Conference Series · 2007
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 ϕ from propositions to truth values. Classically is a Boolean algebra, V = 2 , and the admissible maps ϕ: 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.