*International Journal
of Theoretical Physics,*
**32**, 1481-1505 (1993)

#
NON-ORDERED QUANTUM LOGIC AND ITS YES-NO REPRESENTATION

**Mladen Pavicic
**

*
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 orthomodular lattice is an ortholattice
in which a * unique * operation of bi-implication
corresponds to equality relation and that the ordering relation
in the binary formulation of quantum logic as well as the
operation of implication (conditional) in quantum logic are
completely irrelevant for their axiomatization. The soundness and
completeness theorems for the corresponding algebraic unified quantum
logic are proved. A proper semantics, i.e., a representation
of quantum logic is given by means of a new YES-NO relation
which enables a proof of the finite model property and decidability
of quantum logic. A statistical YES-NO physical interpretation of
the quantum logical propositions is provided.

**PACS numbers: ** 03.65.Bz

**Keywords: ** quantum logic, quantum measurements,
orthomodular lattices, implication operation.