An exercise in "anhomomorphic logic"

Details An exercise in "anhomomorphic logic" An exercise in "anhomomorphic logic"

2007-03-30

arxiv.org/abs/quant-ph/0703276v2

J.Phys.Conf.Ser.67:012018,2007

Physics

Quantum Physics

plainTeX, 14 pages, no figures. To appear in a special volume of {\it Journal of Physics}, edited by L. Diosi, H-T Elze, and G

Scientific paper

10.1088/1742-6596/67/1/012018

A classical logic exhibits a threefold inner structure comprising an algebra of propositions `A', a space of ``truth values'' `V', and a distinguished family of mappings `phi' from propositions to truth values. Classically A is a Boolean algebra, V=Z_2, and the admissible maps phi:A-->Z_2 are {\it 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.

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