Over time, there have been refinements in the way that probability distributions are used for representing beliefs. Models which rely on single probability distnlnrti ons depict a complete ordering among the propositions of interest, yet human beliefs are sometimes not completely ordered. Non-singleton sets of probability distributions can represent partially ordered beliefs. Convex sets are pa...

In this paper we study the partially ordered set of endomorphism monoids of Rosenberg relations, which are used to characterize maximal clones on a finite set. The problem naturally splits into 49 cases of interrelationships of endomorphism monoids of Rosenberg relations. In order to make the paper self-contained, in addition to new results, we survey some previously published partial results p...

The results' in this paper were motivated by a search for the answers to the following questions : When can a given partially ordered algebra be embedded in a complete partially ordered algebra in such a fashion that the original algebra is dense and that the operations acquire or maintain continuity properties? What type of identities are preserved under such embeddings? Properties of extensio...

To take into account that expert’s degrees of certainty are not always comparable, researchers have used partially ordered set of degrees instead of the more traditional linearly (totally) ordered interval [0, 1]. In most cases, it is assumed that this partially ordered set is a lattice, i.e., every two elements have the greatest lower bound and the least upper bound. In this paper, we prove a ...

Let P be a partially ordered set and let Pp denote the set of all order-preserving mappings of P to P ordered by/ < g in Pp iif(p) < g(p) for all p £ P. We prove that if P and Q are finite, connected partially ordered sets and Pp = Q<¡ then Psg. Is a partially ordered set determined by its order-preserving mappings? L. M. Gluskin [4] has shown that the set of order-preserving mappings of a part...

A Jbre F of a partially ordered set P is a subset which intersects each nontrivial maximal antichain of P. Let I be the smallest constant such that each finite partially ordered set P contains a fibre of size at most I ‘1 PI. We show that 1, < 3 by finding a good 3-coloring of the nontrivial antichains of P. Some decision problems involving iibres are also considered. For instance, it is shown ...