Quantum logics and bivariable functions

To model noncompatible events, a quantum logic was chosen among various algebraic structures as the suitable one. This paper deals with a characterization of a center in various types of quantum logics by means of special bivariable functions defined on them. Any quantum logic can be described as a union of blocks (a block in a given quantum logic L is the maximal Boolean subalgebra of L) [16]. Center C(L) of a quantum logic L is its Boolean subalgebra of elements compatible with all other elements of L. Each quantum logic L has a center that can be taken as a common part of its blocks. In this paper three types of quantum logics are studied: