A Python toolkit for dealing with Petri nets over ontological graphs

TL;DR

This work introduces Petri nets over ontological graphs to fuse the formal dynamics of Petri nets with semantic knowledge encoded in OWL ontologies, enabling semantics-driven reasoning and control. It formalizes two models, CMPNOG and IMPNOG, with input/output arc formulas and marking schemes that operate on concepts or instances drawn from ontologies. A concrete instantiation demonstrates enabling via semantic relations such as $INSTANCE{-}OF$ and shows token flow across ontological graphs, complemented by a Python toolkit example using $owlready2$ for ontology processing. The approach broadens the applicability of Petri nets to knowledge-rich domains and outlines a path toward tools and invariants analysis, with potential impact on business, reasoning, and process control tasks.

Abstract

We present theoretical rudiments of Petri nets over ontological graphs as well as the designed and implemented Python toolkit for dealing with such nets. In Petri nets over ontological graphs, the domain knowledge is enclosed in a form of ontologies. In this way, some valuable knowledge (especially in terms of semantic relations) can be added to model reasoning and control processes by means of Petri nets. In the implemented approach, ontological graphs are obtained from ontologies built in accordance with the OWL 2 Web Ontology Language. The implemented tool enables the users to define the structure and dynamics of Petri nets over ontological graphs.

Figures (5)

• Figure 1: The ontological graph $og_1$ assigned to place $pl_1$.
• Figure 2: The ontological graph $og_2$ assigned to places $pl_2$ and $pl_3$.
• Figure 3: A simple example of an instancely marked Petri net (the initial marking).
• Figure 4: A simple example of an instancely marked Petri net (the marking after firing transitions $tr_2$ and $tr_3$).
• Figure 5: A simple example of an instancely marked Petri net (the marking after firing transition $tr_5$).