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Full Axiomatisation of Timed Processes of Interval-Timed Petri Nets

Pelz E.

Fundamenta Informaticae

2018

Vol. 157, nr 4

427--442

In this paper we use partial order semantics to express the truly concurrent behaviour of Interval-Timed Petri nets (ITPNs) in their most general setting, i.e. with autoconcurrency and zero duration, as studied with its standard maximal step semantics in [1]. First we introduce the notion of timed processes for ITPNs inductively. Then we investigate if the equivalence of inductive and axiomatic process semantics - true for classical Petri nets - could hold for ITPNs too. We will see that the notions of independence and immediate firing obligation seem to be antagonistic ones, and that local axioms, adequate to define processes of classical Petri nets, are not sufficient to caracterize timed processes of ITPNs. We propose several original “global” axioms which reveal to be an effective solution. Thus we yield finally a full axiomatic definition of timed processes for ITPNs.

A uniform axiomatic view of lists, multisets, and sets, and the relevant unification algorithms

Dovier A., Policriti A., Rossi G.

Fundamenta Informaticae

1998

Vol. 36, nr 2,3

201-234

The first-order theories of lists, multisets, compact lists (i.e., lists, where the number of contiguous occurrences of each element is immaterial) , and sets are introduced via axioms. Such axiomatizations are shown to be very well-suited for the integration with free functor symbols governed by the classical Clark's axioms in the context of (Constraint) Logic Programming. Adaptations of the extensionally principle to the various theories taken into account is then exploited in the design of unification algorithms for the considered data structures. All the theories presented can be combined providing frameworks to deal with several of the proposed data structures simultaneously. The unification algorithms proposed can be combined (merged) as well, to produce engines for such combination theories.