**Mladen Pavicic ^{1} and
Norman D. Megill^{2}
**

^{1}*
Department of Mathematics, University of Zagreb,
GF, Kaciceva 26, POB-217, HR-10001 Zagreb, Croatia;
mpavicic@faust.irb.hr; http://m3k.grad.hr/pavicic
*

^{2}*
nm@alum.mit.edu
*

** Abstract. **
It is shown that propositional calculuses of both quantum and
classical logics are non-categorical. We find that quantum logic
is in addition to an orthomodular lattice also modeled by a weakly
orthomodular lattice and that classical logic is in addition to a
Boolean algebra also modeled by a weakly distributive lattice. Both
new models turn out to be non-orthomodular. We prove the soundness
and completeness of the calculuses for the models. We also prove
that all the operations in an orthomodular lattice are five-fold
defined. In the end we discuss possible repercussions
of our results to quantum computations and quantum computers.

**PACS numbers: ** 03.65.Bz, 02.10.By, 02.10.Gd

**Keywords: ** quantum logic, orthomodular lattices,
weakly orthomodular lattices, classical logic, Boolean algebra,
weakly distributive lattices, non-categoricity, quantum computation.