A Framework for Decision Support Systems Adapted to Uncertain Knowledge

Abstract

ly the OntoBayes model is designed with two parts: a knowledge part and a decision model part. The former is an integration of certain and uncertain knowledge based on ontologies and BNs respectively, while the latter can describe different decision models based on IDs. In order to facilitate the use of OntoBayes in DSSs, particularly to facilitate the share and reuse of knowledge and decision models for decision makers, a formal language for representing the knowledge part and the decision model part is necessary and important. We make use of OWL as the underlying KR language for OntoBayes. Therefore the design of OntoBayes must be implemented based on OWL. For that, we need extend OWL with the features of BNs and IDs. In the following sections we will describe these extensions in details. 4.2. THE EXTENSION OF BNS 59 4.2 The Extension of BNs The first step for building the OntoBayes model is to extend BNs in OWL. According to Definition 2.9, the extension of BNs follows two perspectives: the qualitative and quantitative perspective. But before investigating the extension according to these perspectives, it is significant to extract the essentials of BNs at a high and general level with an upper ontology. The upper ontology will be considered as the underlying abstract specification for the Bayesian extension. 4.2.1 An Upper Ontology In Section 2.1.2 it was pointed out that ontologies can be categorized into different levels with regard to their generality. At the highest and most abstract level it is upper ontologies which are used to refer to top-level ontologies in this work. In Figure 4.1 a simplified view of an upper ontology is illustrated to capture the essentials of a BN. The graphical notions used here are based on the RDF-Triples as shown in Figure 2.2. Ellipses with solid line represent ontological concepts, whereas ellipse with dashed line represent predefined XML schema datatypes. Each arrow with a label indicates the relationship between two concepts. The numbers on the label are the cardinality constraints. This figure introduces the very general and commonsense concepts and their properties in the Bayesian world. As mentioned above there are two perspectives in the Bayesian world: the qualitative and quantitative perspective. In the figure we make use of two boxes with dashed blue edges and green edges to frame the qualitative and quantitative information in the upper ontology, respectively. From the qualitative perspective a BN consists of a number of chance nodes1 As depicted in the figure there is a red arrow with a label dependsOn associated with chance nodes. It indicates the only relationship between different chance nodes — the (statistical) dependency. Every chance node in a BN is either conditional or unconditional depending on whether it depends on other chance nodes or not. A chance node is a discrete variable2 which has a domain of finite and mutually exclusive states. In this work the domain is simplified as the datatype string. A chance node is an evidence node when it is instantiated with an observed state. From the quantitative perspective each chance node of a BN is assigned with at least one corresponding joint probability distribution, but only one distribution is set as active. This active distribution will be used as a default distribution when 1In place of using the more common term “nodes”, here we makes use of the term “chance nodes”, because it can facilitate to extend BNs to IDs which classify nodes into three types: chance nodes, value nodes and decision nodes. 2As mentioned in Chapter 2 we consider that all nodes of a BN in the context of our work have only discrete domain of values, in order to facilitate the Bayesian extension in OWL. 60 CHAPTER 4. THE ONTOBAYES MODEL