Incollection,
Merging ordered sets
Formal Concept Analysis, Springer, (2011)
Abstract
While extending partial orders towards linear orders is a very well-
researched topic, the combination of two ordered sets has not yet
attracted too much attention. In the underlying article, however, we
describe the possibilities to merge two given quasiordered sets in the
sense that the restriction of the combined order towards the given
ordered sets returns the initial orders again. It turns out that these
mergings form a complete lattice. We elaborate these lattices of
mergings and present its contextual representation. While the
motivating example was discovered in role-oriented software modeling,
we give a further possible application in the field of scheduling. 1
Introduction In order theory, a well-studied problem is the question
of finding linear extensions of a given partial order. In this paper
we will investigate the somehow related problem of merging two given
orders (P, <=P ) and (Q, <=Q ). Thereby, we understand a merging as an
order on P ∪ Q, such that the restrictions onto P and Q return the
initial posets again. Such a construction can for example be observed,
when considering the roleplay relation in role-oriented software
modeling. We refer to Ste00 for a detailed
