Regular Orthomodular Posets

What is it about?

Rozenberg and Ehrenfeucht has shown a duality between 2-structures (a.k.a. transition systems) and (elementary) Petri nets. Bernardinello et al. has observed that the regions of a 2-structure form an regular orthomodular poset and there is a similar relation between 2-structures and orthomodular posets. We study the problem of closing a given orthomodular poset to a regular one. Also, as in a seminal work of Rozenberg and Ehrenfeucht, one can be interested in a concrete representation, i.e. as a family of sets. We show here an appropriate construction for orthomodular posets too.

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