Logical Inference Based on Incomplete and/or Fuzzy Ontologies

Logical Inference Based on Incomplete and/or Fuzzy Ontologies

Juliusz L. Kulikowski (Polish Academy of Sciences, Poland)
Copyright: © 2009 |Pages: 16
DOI: 10.4018/978-1-59904-576-4.ch001
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In this chapter, a concept of using incomplete or fuzzy ontologies in decision making is presented. A definition of ontology and of ontological models is given, as well as their formal representation by taxonomic trees, bi-partite graphs, multigraphs, relations, super-relations and hyper-relations. The definitions of the corresponding mathematical notions are also given. Then, the concept of ontologies representing incomplete or uncertain domain knowledge is presented. This concept is illustrated by an example of decision making in medicine. The aim of this chapter is to give an outlook on the possibility of ontological models extension in order to use them as an effective and universal form of domain knowledge representation in computer systems supporting decision making in various application areas.
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Ontologies And Ontological Models


In the simplest cases, the idea of ontology can be reduced to a taxonomy of concepts assigned to objects, phenomena or processes appearing in an examined part of abstract or of real world and being analyzed from some fixed points of view. For instance, in sociological investigations a concept of People living in the town can be specified by a structure called a rooted tree, as shown in Figure 1.

Figure 1.

Example of a taxonomic tree based on the attribute “Status”

However, the same concept may be presented in several other ways, like:and so forth. The roots of the trees have been assigned above to the basic concept People living in the town, while the subjected nodes correspond to some subordered concepts. It is also assumed that on each level of any tree the subordered concepts totally cover the corresponding higher-level concept. So-interpreted rooted trees are called taxonomic trees. The fact that even in this simple case the part of real world under examination is represented by an ontology consisting not of a single but of several semantically linked taxonomic trees is worthy of being remarked. In general, formal structures constituting ontologies (in the above-defined, narrow sense) will be called ontological models. This given ontology thus consists of three ontological models having the form of taxonomic trees, linked semantically because their roots have been assigned to the same top-level concept.

And still, the class of problems whose solution might be supported by this ontology is rather poor. It might contain, for example, designing a database of inhabitants of the town, planning some social activities or investments in the town, or it might be used in any deliberations concerning the population of the town. However, more advanced applications of this ontology are limited by its evident deficiencies:

  • 1.

    the taxonomic trees contain no information about the statistical structure of the world as a composition of designates (real entities) represented by a given tree;

  • 2.

    no relationships between the concepts belonging to different taxonomic trees have been described by the ontology; and

  • 3.

    taxonomic tree do not define concepts, but only characterize hierarchical relationships between higher level and lower level concepts.

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