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New trends in quantum structures
Preface. Introduction. 1. D-posets and Effect Algebras. 2. MV-algebras and QMV-algebras. 3. Quotients of Partial Abelian Monoids. 4. Tensor Product of D-Posets and Effect Algebras. 5. BCK-algebras.Expand
Quotients of partial abelian monoids
The basic algebraic structure that is studied in this chapter is a partial Abelian monoid (PAM in short) (cf. [Wil 1], [Wil 2], [Pul 4], [GuPu]). A PAM is a structure (P; 0, ⊕), where e is aExpand
Generalized difference posets and orthoalgebras.
A diierence on a poset (P;) is a partial binary operation on P such that b a is deened if and only if a b subject to conditions a b =) b (b a) = a and a b c =) (c a) (c b) = b a. A diierence posetExpand
Ideals and quotients in lattice ordered effect algebras
A generalization of the commutators in OMLs is defined in the frame of lattice ordered effect algebras, such that the quotient with respect to a Riesz ideal I is an MV-algebra if and only if I contains all generalized commutator. Expand
Some Ideal Lattices in Partial Abelian Monoids and Effect Algebras
It is shown that the so-called R1-ideals in cancellative PAMs (CPAM) form a complete Brouwerian sublattice of the lattice of all ideals, and they are standard elements of it. Expand
Congruences in partial abelian semigroups
Abstract. A partial abelian semigroup (PAS) is a structure $ (L, \perp, \oplus) $, where $ \oplus $ is a partial binary operation on L with domain $ \perp $, which is commutative and associativeExpand
A note on observables on MV-algebras
It is shown that every at most countable subset of any MV-algebra is contained in the range of an observable, and a much stronger result holds for any bold fuzzy algebra [0,1]S, which is whole contained inThe range of a (σ-additive) observable. Expand
Difference posets and the histories approach to quantum theories
Direct limits and tensor products of difference posets are studied. In the spirit of a recent paper by Isham, a potential model for an “unsharp histories” approach to quantum theory based onExpand
Hidden Variables and Bell Inequalities on Quantum Logics
In the quantum logic approach, Bell inequalities in the sense of Pitowski are related with quasi hidden variables in the sense of Deliyannis. Some properties of hidden variables on effect algebrasExpand