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.