An exercise in "anhomomorphic logic"
Abstract
A classical logic exhibits a threefold inner structure comprising an algebra of propositions fraktur U, a space of "truth values" V, and a distinguished family of mappings phi from propositions to truth values. Classically fraktur U is a Boolean algebra, V = Bbb Z_{2}, and the admissible maps phi: fraktur U Bbb Z_{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.
 Publication:

Journal of Physics Conference Series
 Pub Date:
 May 2007
 DOI:
 10.1088/17426596/67/1/012018
 arXiv:
 arXiv:quantph/0703276
 Bibcode:
 2007JPhCS..67a2018S
 Keywords:

 Quantum Physics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 plainTeX, 14 pages, no figures. To appear in a special volume of {\it Journal of Physics}, edited by L. Diosi, HT Elze, and G. Vitiello. Most current version is available at http://www.physics.syr.edu/~sorkin/some.papers/ (or wherever my homepage may be)