Orthomodular Lattices in Occurrence Nets

  • Luca Bernardinello
  • Lucia Pomello
  • Stefania Rombolà
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5606)


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.


Closure Operator Maximal Clique Minkowski Spacetime Orthomodular Lattice Algebraic Lattice 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Luca Bernardinello
    • 1
  • Lucia Pomello
    • 1
  • Stefania Rombolà
    • 1
  1. 1.Dipartimento di informatica, sistemistica e comunicazioneUniversità degli studi di Milano–BicoccaMilanoItaly

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