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Partially Ordered Sets

Chapter
Part of the EATCS Monographs on Theoretical Computer Science book series (EATCS, volume 13)

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 xX 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, xy means that x has occurred earlier than y in the history given by (X, ≺).

Keywords

Induction Hypothesis World Line Graphical Notation Finite Degree Infinite Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  1. 1.Institut für Methodische GrundlagenGMDSt. Augustin 1Germany

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