Logic and algebra in unfolded Petri nets: on a duality between concurrency and causal dependence

An orthogonality space is a set endowed with a symmetric and irreflexive binary re- lation (an orthogonality relation). In a partially ordered set modelling a concurrent process, two such binary relations can be defined: a causal dependence relation and a concurrency relation, and two distinct orthogonality spaces are consequently obtained. When the condition of N-density holds on both these orthogonality spaces, we study the orthomodular poset formed by closed sets defined according to Dacey. We show that the condition originally imposed by Dacey on the or- thogonality spaces for obtaining an orthomodular poset from his closed sets is in fact equivalent to N-density. The requirement of N-density was as well fundamental in a previous work on or- thogonality spaces with the concurrency relation. Starting from a partially ordered set modelling a concurrent process, we obtain dual results for orthogonality spaces with the causal dependence relation in respect to orthogonality spaces with the concurrency relation.

BERNARDINELLO Luca;  FERIGATO Carlo;  POMELLO Lucia; 

2019-06-17

IOS PRESS

JRC115216

0169-2968 (online),   

https://content.iospress.com/articles/fundamenta-informaticae/fi1800,    https://publications.jrc.ec.europa.eu/repository/handle/JRC115216,   

10.3233/FI-2019-1800 (online),