A Generalisation of a Relational Structures Model of Concurrency

We show how complex concurrent behaviours can be modelled by relational structures ($$X, \diamondsuit, \sqsubset$$), where X is a set (of event occurrences), $$\diamondsuit$$ (interpreted as commutativity), $$\sqsubset$$ (interpreted as weak causality) are binary relations on X. The paper is a continuation of the approach initiated in [6,18,1,9] substantially developed in [10,12], and recently partially generalized in [7]. For the first time an axiomatic model for the most general case is given. The results can be interpreted as a generalisation of Szpilrajn Theorem [25].