IDENTITY RULE FOR CLASSICAL AND QUANTUM THEORIES

It is shown that the identity rule-a rule of inference which has the f orm of modus ponens but with the operation of identity substituted for the operation of implication-turns any ortholattice into either an or thomodular lattice (a model of a quantum theory) or a distributive lat tice (a model of a 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 o nly operation.