Reflections and coreflections in generalized orthomodular lattices
Regular elements in complete uniquely complemented lattices
Relative Complements in the Weak Congruence Lattice
Relative conditional expectations on a logic
In this paper, the authors introduce the notion of conditional expectation of an observable on a logic with respect to a sublogic, in a state , relative to an element of the logic. This conditional expectation is an analogue of the expectation of an integrable function on a probability space.
Relative Pseudo-Complements, Join-Extensions, and Meet-Retractions.
Relatively additive states on quantum logics
In this paper we carry on the investigation of partially additive states on quantum logics (see [2], [5], [7], [8], [11], [12], [15], [18], etc.). We study a variant of weak states — the states which are additive with respect to a given Boolean subalgebra. In the first result we show that there are many quantum logics which do not possess any 2-additive central states (any logic possesses an abundance of 1-additive central state — see [12]). In the second result we construct a finite 3-homogeneous...
Relatively complemented ordered sets
We investigate conditions for the existence of relative complements in ordered sets. For relatively complemented ordered sets with 0 we show that each element b ≠ 0 is the least one of the set of all upper bounds of all atoms contained in b.
Remarks about measures on orthomodular posets
Remarque sur les treillis complets pseudo complémentes
Residuation Theory (Book Review by R. McFadden.
Ring-like structures corresponding to generalized orthomodular lattices
Ring-like structures derived from -lattices with antitone involutions
Using the concept of the -lattice introduced recently by V. Snášel we define -lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.
Ring-like structures with unique symmetric difference related to quantum logic
Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.