Abstract
The present chapter gives some mathematical theory of partially ordered sets. Referring to the appendix on terminology, we recall that a partially ordered set is a pair (X, ≺) where ≺ is an irreflexive and transitive relation on X. We shall not immediately give the interpretation of the elements of X. For the purpose of this chapter, it suffices to think of a poset (X, ≺) as describing a history or a process (of a concurrent system) and of an element x ∊ X as representing a basic occurrence, i.e., an item which has occurred once, and only once, in the history given by (X, ≺). The relation ≺ means ‘before’; that is, x ≺ y means that x has occurred earlier than y in the history given by (X, ≺).
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© 1988 Springer-Verlag Berlin Heidelberg
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Best, E., Fernández, C.C. (1988). Partially Ordered Sets. In: Nonsequential Processes. EATCS Monographs on Theoretical Computer Science, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73483-0_2
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DOI: https://doi.org/10.1007/978-3-642-73483-0_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-73485-4
Online ISBN: 978-3-642-73483-0
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