An information theoretic approach for knowledge representation using Petri nets

Abstract

Abstract-A new hybrid approach for Petri nets (PNs) is proposed in this paper by combining the PNs principles with the foundations of information theory for knowledge representation. The resulting PNs have been named Plausible Petri nets (PPNs) mainly because they can handle the evolution of a discrete event system together with uncertain (plausible) information about the system using states of information. This paper overviews the main concepts of classical PNs and presents a method to allow uncertain information exchange about a state variable within the system dynamics. The resulting methodology is exemplified using an idealized expert system, which illustrates some of the challenges faced in real-world applications of PPNs.

Plausible Petri nets as self‐adaptive expert systems: A tool for infrastructure asset monitoring

“…PPNs (M. Chiachío et al., , ) are a hybrid variant of PNs where the sets of nodes are partitioned into two disjoint subsets, namely, numerical and symbolic , which are denoted using superscripts and , respectively. The symbolic subnet accounts for the discrete behavior of the system using regular tokens, as in classical PNs.…”

“…Equation is used to model the evolution of the symbolic part of the net, as in ordinary PNs. However, the evolution of relies on an ad hoc information flow based on two basic operations (M. Chiachío et al., , ): the conjunction and disjunction of states of information (Rus et al., ; Tarantola & Valette, ). In these operations, the first principles of Boolean logic, in particular the logic operators and (∧) and or (∨), are invoked to allow the information from the numerical subnet to be exchanged within a PPN.…”

“…One of the main challenges in incorporating self‐adaptation in expert systems is the handling of uncertain information during runtime, and the ability to update such information when new evidence becomes available (Bencomo & Belaggoun, ). However, the existing PN formalisms do not provide direct means to efficiently consider uncertain information (M. Chiachío, J. Chiachío, Prescott, & Andrews, ; M. Chiachío, J. Chiachío, Prescott, & Andrews, ). In the literature, a number of PN variants have been introduced to enhance the original PN approach with improved rules of inference and knowledge learning.…”

“…As a key contribution, this article reveals how self‐adaptation can be achieved naturally as a by‐product of the evaluation of a PPN, because an inherent learning mechanism is implemented within the PPN execution semantics. More specifically, an instance of Bayesian model updating is seen to appear as a particular case of the conjunction of states of information (Tarantola & Valette, ), which is a basic operation within the PPN execution rules (Chiachío et al., , ). Consequently, the resulting approach has the advantages of (a) being able to deal with uncertain information in expert systems combining discrete events and continuous state variables, and (b) enabling self‐adaptation by Bayesian learning from external input data.…”

“…In this article, a new methodology is proposed to enable self-adaptation in expert systems using the Plausible Petri nets (PPNs). PPNs are a new class of models within the PN paradigm, originally developed by the authors in M. Chiachío et al (2016Chiachío et al ( , 2018, whereby discrete events (e.g., go/no-go decisions) can be jointly modeled together with continuous processes whose evolution may be uncertain (e.g., deterioration process). In PPNs, the uncertainty is modeled using states of information (Rus, Chiachío, & Chiachío, 2016), which provide a mapping between the possible numerical values of a state variable and their relative plausibility, hence giving greater versatility for representing uncertain knowledge in a more principled approach.…”