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 a… Expand

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 poset… Expand

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

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

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 associative… Expand

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

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 on… Expand

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 algebras… Expand