**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. **
Unified quantum logic which is a propositional
logic underlying quantum formalism is given a new much simplified
axiomatization. A statistical basis for this propositional logical system
is given so as to interpret unified quantum logic as a system of
deduction. The soundness and completeness of algebraic semantics are
proved. Kripkean and probabilistic semantics are discussed.

**PACS numbers: ** 03.65.Bz

**Keywords: ** quantum logic, quantum measurements.