Abstract
In this paper, we study partially ordered structures associated to occurrence nets. An occurrence net is endowed with a symmetric, but in general non transitive, concurrency relation. By applying known techniques in lattice theory, from any such relation one can derive a closure operator, and then an orthocomplemented lattice. We prove that, for a general class of occurrence nets, those lattices, formed by closed subsets of net elements, are orthomodular. A similar result was shown starting from a simultaneity relation defined, in the context of special relativity theory, on Minkowski spacetime. We characterize the closed sets, and study several properties of lattices derived from occurrence nets; in particular we focus on properties related to K-density. We briefly discuss some variants of the construction, showing that, if we discard conditions, and only keep the partial order on events, the corresponding lattice is not, in general, orthomodular.
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Bernardinello, L., Pomello, L., Rombolà, S. (2009). Orthomodular Lattices in Occurrence Nets. In: Franceschinis, G., Wolf, K. (eds) Applications and Theory of Petri Nets. PETRI NETS 2009. Lecture Notes in Computer Science, vol 5606. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02424-5_11
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DOI: https://doi.org/10.1007/978-3-642-02424-5_11
Publisher Name: Springer, Berlin, Heidelberg
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