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.

Bernardinello, L., Ferigato, C., Pomello, L. (2020). Logic and Algebra in Unfolded Petri Nets: On a Duality between Concurrency and Causal Dependence. FUNDAMENTA INFORMATICAE, 171(1-4), 39-56 [10.3233/FI-2020-1871].

### Logic and Algebra in Unfolded Petri Nets: On a Duality between Concurrency and Causal Dependence

#### 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.
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Articolo in rivista - Articolo scientifico
Concurrency, Orthogonality relations, Causal Dependence relation, Petri nets
English
2020
39
56
18
Bernardinello, L., Ferigato, C., Pomello, L. (2020). Logic and Algebra in Unfolded Petri Nets: On a Duality between Concurrency and Causal Dependence. FUNDAMENTA INFORMATICAE, 171(1-4), 39-56 [10.3233/FI-2020-1871].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/260673`