Abstract.
We consider relational structures \((X,R_1,R_2)\) such that \(X\) is a set and \(R_1,R_2\) are two binary relations on \(X\). For a number of different classes of structures we show that any structure can be represented as the intersection of its maximal extensions. Such a property – called extension completeness – can be seen as a generalisation of Szpilrajn's theorem which states that each partial order is the intersection of its total order extensions. When \(R_1\) can be interpreted as causality and \(R_2\) as ‘weak’ causality we obtain a model of concurrent histories generalising that based on causal partial orders.
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Received 1 February 1994 / 6 May 1996
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Janicki, R., Koutny, M. Fundamentals of modelling concurrency using discrete relational structures . Acta Informatica 34, 367–388 (1997). https://doi.org/10.1007/s002360050090
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DOI: https://doi.org/10.1007/s002360050090