Logic and Algebra in Unfolded Petri Nets: on a Duality Between Concurrency and Causal Dependence

Issue title: Interdisciplinary Nature of Information Processing Special Issue Dedicated to Giancarlo Mauri on the Occasion of His 70th Birthday

Guest editors: Alberto Dennunzio, Gheorghe Păun, Grzegorz Rozenberg and Claudio Zandron

Article type: Research Article

Authors: Bernardinello, Luca^{a; *} | Ferigato, Carlo^b | Pomello, Lucia^c

Affiliations: [a] DISCo, Università degli studi di Milano - Bicocca, Milano, Italy. luca.bernardinello@unimib.it | [b] European Commission, Joint Research Centre (JRC), Ispra (VA), Italy. carlo.ferigato@ec.europa.eu | [c] DISCo, Università degli studi di Milano - Bicocca, Milano, Italy. lucia.pomello@unimib.it

Correspondence: [*] Address for correspondence: DISCo, Università degli studi di Milano - Bicocca, viale Sarca 336-U14, Milano, Italy

Abstract: An orthogonality space is a set endowed with a symmetric and irreflexive binary relation (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 orthogonality 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 orthogonality 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.

DOI: 10.3233/FI-2020-1871

Journal: Fundamenta Informaticae, vol. 171, no. 1-4, pp. 39-56, 2020