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.

Complete Chapter List

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Table of Contents
Dariusz Król, Ngoc Thanh Nguyen
Chapter 1
Juliusz L. Kulikowski
In this chapter, a concept of using incomplete or fuzzy ontologies in decision making is presented. A definition of ontology and of ontological... Sample PDF
Logical Inference Based on Incomplete and/or Fuzzy Ontologies
Chapter 2
Amelia Badica, Costin Badica, Elvira Popescu
The Web is designed as a major information provider for the human consumer. However, information published on the Web is difficult to understand and... Sample PDF
Using Logic Programming and XML Technologies for Data Extraction from Web Pages
Chapter 3
Andreas Jacobsson, Paul Davidsson
This chapter introduces a formal model of virtual enterprises, as well as an analysis of their creation and operation. It is argued that virtual... Sample PDF
A Formal Analysis of Virtual Enterprise Creation and Operation
Chapter 4
Donat Orski
The chapter concerns a class of systems composed of operations performed with the use of resources allocated to them. In such operation systems... Sample PDF
Application of Uncertain Variables to Knowledge-Based Resource Distribution
Chapter 5
Clive Fencott
This chapter undertakes a methodological study of virtual environments (VEs), a specific subset of interactive systems. It takes as a central theme... Sample PDF
A Methodology of Design for Virtual Environments
Chapter 6
Salvador Sanchez-Alonso, Dirk Frosch-Wilke
In current organizations, the models of knowledge creation include specific processes and elements that drive the production of knowledge aimed at... Sample PDF
An Ontological Representation of Competencies as Codified Knowledge
Chapter 7
Marcos De Oliveira, Martin Purvis
In the distributed multi-agent systems discussed in this chapter, heterogeneous autonomous agents interoperate in order to achieve their goals. In... Sample PDF
Aspects of Openness in Multi-Agent Systems: Coordinating the Autonomy in Agent Societies
Chapter 8
Kostas Kolomvatsos, Stathes Hadjiefthymiades
The field of Multi-agent systems (MAS) has been an active area for many years due to the importance that agents have to many disciplines of research... Sample PDF
How Can We Trust Agents in Multi-Agent Environments? Techniques and Challenges
Chapter 9
Mariusz Nowostawski
The concept of autonomy is one of the central concepts in distributed computational systems, and in multi-agent systems in particular. With diverse... Sample PDF
The Concept of Autonomy in Distributed Computation and Multi-Agent Systems
Chapter 10
Maryam Purvis, Toktam Ebadi, Bastin Tony Roy Savarimuthu
The objective of this research is to describe a mechanism to provide an improved library management system using RFID and agent technologies. One of... Sample PDF
An Agent-Based Library Management System Using RFID Technology
Chapter 11
Sharmila Savarimuthu, Martin Purvis, Maryam Purvis, Mariusz Nowostawski
Societies are made of different kinds of agents, some cooperative and uncooperative. Uncooperative agents tend to reduce the overall performance of... Sample PDF
Mechanisms to Restrict Exploitation and Improve Societal Performance in Multi-Agent Systems
Chapter 12
Bastin Tony Roy Savarimuthu, Maryam Purvis, Stephen Cranefield
Norms are shared expectations of behaviours that exist in human societies. Norms help societies by increasing the predictability of individual... Sample PDF
Norm Emergence in Multi-Agent Societies
Chapter 13
Scott A. DeLoach, Madhukar Kumar
This chapter provides an overview of the Multi-agent Systems Engineering (MaSE) methodology for analyzing and designing multi-agent systems. MaSE... Sample PDF
Multi-Agent Systems Engineering: An Overview and Case Study
Chapter 14
František Capkovic
An alternative approach to modeling and analysis of agents’ behaviour is presented in this chapter. The agents and agent systems are understood here... Sample PDF
Modeling, Analysing, and Control of Agents Behaviour
Chapter 15
Martin Tabakov
This chapter presents a methodology for an image enhancement process of computed tomography perfusion images by means of partition generated with... Sample PDF
Using Fuzzy Segmentation for Colour Image Enhancement of Computed Tomography Perfusion Images
Chapter 16
Giovanni Vincenti, Goran Trajkovski
This chapter presents an innovative approach to the field of information fusion. Fuzzy mediation differentiates itself from other algorithms, as... Sample PDF
Fuzzy Mediation in Shared Control and Online Learning
Chapter 17
Adam Jatowt, Yukiko Kawai, Katsumi Tanaka
The Web is a useful data source for knowledge extraction, as it provides diverse content virtually on any possible topic. Hence, a lot of research... Sample PDF
Utilizing Past Web for Knowledge Discovery
Chapter 18
Dariusz Król
In this chapter, we propose a generic framework in C# to distribute and compute tasks defined by users. Unlike the more popular models such as... Sample PDF
Example-Based Framework for Propagation of Tasks in Distributed Environments
Chapter 19
Xia Xie, Jin Huang, Song Wu, Hai Jin, Melvin Koh, Jie Song, Simon See
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Survey on the Application of Economic and Market Theory for Grid Computing
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