Summing of Boolean Algebras and Logics

Some nearly Boolean orthomodular posets

“…This immediately follows from the description of the states on P (see e.g. [10]) and from compatibility properties of a Boolean power (see e.g. [9] and [2]).…”

Boolean Methods and Pták's Sum

“…In this section, for notation and concepts on Quantum Logics see, [12] and for Ptak's sum see [11,7]. The main result of this section is to establish for the first time, a formal connection between Ptak's sum and bounded Boolean powers.…”

“…In [11] Pták has introduced a way of combining a Boolean algebra and a logic. This, so called Pták's sum, have been investigated by many researches, see e.g.…”

“…[7,8]. Also in [11] an open question was posed : "Let Κ, M be logics of two independent experiments and let we consider these two experiments as a single one. Assume that L is the logic of the latter combined experiment.…”

The Homomorphism on the Ptak's Sum

“…Summing of a Boolean algebra and quantum logic has been defined by P. Ptak [2] and studied in Janis and Riecanova [4] and Janis [3]. First we introduce the definition.…”