Mladen Pavicic
Atominstitute of the Austrian Universities, Schüttelstraße 115, A-1020 Wien, Austria; pavicic@ati.ac.at
Department of Mathematics, University of Zagreb, GF, Kaciceva 26, POB-217, HR-10001 Zagreb, Croatia; mpavicic@faust.irb.hr; http://m3k.grad.hr/pavicic
Abstract. It is shown that the identity rule - a rule of inference which has the form of modus ponens but with the operation of identity substituted for the operation of implication - turns any ortholattice into either an orthomodular lattice (a model of a quantum theory) or a distributive lattice (a model of classical theory). It is also shown that - as opposed to the implication algebras - one cannot construct an identity algebra although the identity rule contains the operation of identity as the only operation.
PACS numbers: 03.65.Bz, 02.10.By, 02.10.Gd
Keywords: orthomodular lattices, distributive lattices, ortholattices, quantum logic, classical logic.