Petri Nets are efficient and well-formalized tools for modeling the dynamic systems. With some reasonable constraints, they can be readily applied to knowledge representation and engineering, and thus assist in collaborative research. This chapter proposes a way to do this based on the unified grammar of dynamic knowledge. Petri Nets appear interpretable in terms of the said grammar and may be considerably enhanced by the introduction of semantic rules for formulation of expressions in their places. In such form, they are quite apt to be used as a knowledge representation and visualization method in computer-based tools for support of collaborative research, and their quantification potential (i.e., marking of the net and attributing weights to its arcs) may appear very useful for this task, which is usually accomplished by purely qualitative tools.
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Petri nets are a family of mathematical models designed for modeling, analysis and development of dynamic systems, from jurisprudence to biology. The original theory was presented in 1962 by Carl Adam Petri in his Doctoral Dissertation «Communications with Automata», where he described both mathematic and graphic approaches to modeling (Petri, 1962). This approach was developed in his later works (e.g., Petri, 1973; 1977). Classical Petri nets are now also called Low Level Petri Nets; many extended models have been built on top of them, linking this method to various mathematical formalisms and thus widening its modeling capabilities. Three classes of Petri Nets are now in use – discrete nets, continuous time nets and stochastic nets.
Mathematically, Petri nets are directed labeled bipartite multigraphs (Petri, 1962). At the same time, they bear semantic information in the nodes and therefore can be used for representation of qualitative knowledge about the modeled systems. In doing this, they may well cover the alternative change environments (Pshenichny & Kanzheleva, 2011) and therefore should be regarded as a dynamic knowledge representation and engineering method. As such, Petri nets can be applied to use the unified dynamic knowledge grammar suggested by Pshenichny and Mouromtsev (2015, see chapter 16 this book).
The usefulness of Petri nets for organization of knowledge “both inside and outside computer” was emphasized yet by Petri (1977, p. 131). However, in last twenty years, discussing the application of Petri nets to knowledge representation, researchers were inspired mainly by an ability of one particular type of Petri net, the fuzzy one, to represent one particular, however important, type of knowledge – the fuzzy knowledge (Li & Lara-Rosano, 2000; Liu et al., 2013; Xiao-zhong, 2003; Yeung & Tsang, 1994; Wang et al., 2014; Ribarić et al., 2009). Interestingly, most of these authors state that Petri nets are particularly efficient to represent the dynamic knowledge. However, virtually all of them consider knowledge “dynamic”, in the sense that this knowledge is imprecise, incomplete and may change (regardless of whether it describes fixed or changing matters), while the term “dynamic knowledge” sensu Pshenichny and Mouromtsev (2015, see chapter 16 this book) means the knowledge about dynamic environments, or, in other words, the knowledge about changing events. Henceforth the term “dynamic knowledge” will be used in the latter sense. Desirably, such knowledge is precise and complete but includes incompatible statements corresponding to changing events. However, it certainly can be fuzzified and serve as the basis for any fuzzy knowledge. Therefore, consideration of “crisp dynamic knowledge” performed below is relevant to the existing studies of fuzzy knowledge representation by means of Petri nets.
Still, what is essential in this consideration is analysis of subject-predicate structure of dynamic knowledge. This issue has not been addressed by existing studies of knowledge representation by means of Petri nets. The present work intends to start filling this gap, as it is especially relevant in concern of collaborative research and formulation of shared knowledge. An important, though indirect, hint that Petri nets may appear exclusively appropriate in collaborative studies in the least formalized and highly descriptive fields of knowledge is the work of Hussein and El-Sattar (2012) on application of Petri nets to interactive storytelling.
Considering a possible use of Petri nets as a collaborative knowledge representation/engineering tool, this chapter presents a short introduction into Petri net models, brings them into the dynamic knowledge engineering context and suggests the guidelines to apply these models in collaborative studies.