**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.