Between quantum logic and concurrency

We start from two closure operators defined on the elements of a special kind of partially ordered sets, called causal nets. Causal nets are used to model histories of concurrent processes, recording occurrences of local states and of events. If every maximal chain (line) of such a partially ordered set meets every maximal antichain (cut), then the two closure operators coincide, and generate a complete orthomodular lattice. In this paper we recall that, for any closed set in this lattice, every line meets either it or its orthocomplement in the lattice, and show that to any line, a two-valued state on the lattice can be associated. Starting from this result, we delineate a logical language whose formulas are interpreted over closed sets of a causal net, where every line induces an assignment of truth values to formulas. The resulting logic is non-classical; we show that maximal antichains in a causal net are associated to Boolean (hence "classical") substructures of the overall quantum logic.Comment: In Proceedings QPL 2012, arXiv:1407.842

Orthomodular Lattices Induced by the Concurrency Relation

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Application and Theory of Petri Nets33rd International Conference, PETRI NETS 2012, Hamburg, Germany, June 25-29, 2012. Proceedings /

XI, 419p.online resource

Non-Interference Notions Based on Reveals and Excludes Relations for Petri Nets

Abstract. In distributed systems, it is often important that a user is not able to infer if a given action has been performed by another component, while still being able to interact with that component. This kind of problems has been studied with the help of a notion of "interference" in formal models of concurrent systems (e.g. CCS, Petri nets). Here, we propose several new notions of interference for ordinary Petri nets, study some of their properties, and compare them with notions already proposed in the literature. Our new notions rely on the unfolding of Petri nets, and on an adaptation of the "reveals" relation for ordinary Petri nets, previously defined on occurrence nets, and on a new relation, called "excludes", here introduced for detecting negative information flow

Logic and algebra in unfolded Petri nets: on a duality between concurrency and causal dependence

An orthogonality space is a set endowed with a symmetric and irreflexive binary re- lation (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 or- thogonality 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 or- thogonality 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.JRC.E.2-Technology Innovation in Securit