1.1 Representation of uncertainty in ontologies
Semantic web ontologies are based on crisp logic and cannot handle uncertainty. Therefore researches are focused on maintaining well defined means for semantic web ontologies to express uncertainty and handle incomplete or partial knowledge in a domain. Overlapping concepts, including the amount of overlap is one of the issues that could be addressed using different methods. Below are two methods to handle uncertainty in semantic web ontologies.
There is a wide range of researches working on developing a framework which augments and supplements the semantic Web Ontology Language OWL for representing and reasoning with uncertainty based on Bayesian Networks (BN) [26] and its application in ontology mapping. This framework, named Bayes OWL, has gone through several iterations since its conception in 2003 [8, 9]. Bayes OWL provides a set of rules and procedures for direct translation of an OWL ontology into a BN Directed Acyclic Graph (DAG). It also provides a method based on Iterative Proportional Fitting Procedure (IPFP) [19, 7, 6, 34, 2, 4] that incorporates available probability constraints when constructing the conditional probability tables (CPTs) of the BN. The translated BN, which preserves the semantics of the original ontology, and is consistent with all the given probability constraints, can support ontology reasoning across the ontologies as Bayesian interfaces [221]. At the present time, Bayes OWL is restricted to translating only OWL-DL concept taxonomies into BNs, an active research group at Department of computer science and electrical engineering at the University of Maryland are working on extending the framework to OWL ontologies with property restrictions.
If ontologies are translated to BNs, then concept mapping between ontologies can be accomplished by evidential reasoning across the translated BNs. This approach to ontology mapping is seen to be advantageous over many existing methods in handling uncertainty in the mapping. Markus Holi and Eero Hyvonen introduce a new probabilistic method to approach the problem of representing uncertainty in semantic web ontologies [222]. In their method, degrees of subsumption, i.e., overlap between concepts can be modeled and computed efficiently using Bayesian networks based on RDF(S) ontologies. Degrees of overlap indicate how well an individual data item matches the query concept, which can be used as a well-defined measure of relevance in information retrieval tasks.
1.2 Fuzziness for semantic web reasoning
Description logics (DL) are languages for knowledge representation to represent the terminological knowledge of an application domain in a structured and formally well-understood way. DL refers to concept descriptions and the logic-based semantics in a domain.The description logic [331] in the web ontology language (OWL-DL) corresponds to SHOIN(D) description logic. In other words OWL-DL is using SHOIN description logic to represent knowledge and reasoning about it. Straccia presented a fuzzy extension of SHOIN(D) showing that its representation and reasoning capabilities go clearly beyond classical SHOIN (D) [332].
1.3 Application of Fuzziness in the architectures proposed for different problems
Giovani and Vincenzo describe a multilayer architecture to design Ambient Intelligent (AmI) [441] systems providing efficient and uniform utilization of control activities [442]. This multiplayer architecture employs markup-based technologies to transform rough information on sensors, actuators and services towards “smart data”. In particular they are using Fuzzy Markup Language (FML) [417, 418] to provide fuzzy web services. FML language is a novel computer language used to model control systems based on fuzzy logic theories. The main feature of FML is the transparency property: the FML programs can be executed on different hardware without additional efforts. This property is fundamental in ubiquitous computing environment where computers are available throughout the physical environment and appear invisible and transparent to the user.Nikravesh introduces a new architecture for semantic web search engines based on Fuzzy Conceptual Model (FCM) [551, 552, 553, 554] handle the ambiguity and imprecision of the “concept” in the Internet. In the FCM approach, the “concept” is defined by a series of keywords with different weights depending on the importance of each keyword. Ambiguity in concepts can be defined by a set of imprecise concepts. Each imprecise concept in fact can be defined by a set of fuzzy concepts. The fuzzy concepts can then be related to a set of imprecise words given the context. Imprecise words can then be translated in to precise words given the ontology and ambiguity resolution through clarification dialog. By constructing the ontology and fine-tuning the strength of links (weights), they could construct a fuzzy set to integrate piecewise the imprecise concepts and precise words to define the ambiguous concept [556].
Reference
[2] Bock HH (1989) A Conditional Iterative Proportional Fitting (CIPF) Algo-rithm with Applications in the Statistical Analysis of Discrete Spatial Data. Bull. ISI, Contributed papers of 47th Session in Paris, 1:141-142
[4] Cramer E (2000) Probability Measures with Given Marginals and Condition-als: I-projections and Conditional Iterative Proportional Fitting. Statistics and Decisions, 18:311-329
[6] Csiszar I (1975) I-divergence Geometry of Probability Distributions and Mini-mization Problems. The Annuals of Probability, 3(1):146-158
[7] Deming WE, Stephan FF (1940) On a Least Square Adjustment of a Sampled Frequency Table when the Expected Marginal Totals are Known. Ann. Math. Statist. 11:427-444
[8] Ding Z, Peng Y (2004) A Probabilistic Extension to Ontology Language OWL. In Proceedings of the 37th Hawaii International Conference on System Sciences. Big Island, HI
[9] Ding Z, Peng Y, Pan R (2004) A Bayesian Approach to Uncertainty Modeling in OWL Ontology. In Proceedings of 2004 International Conference on Advances in Intelligent Systems - Theory and Applications (AISTA2004). Luxembourg-Kirchberg, Luxembourg
[19] Bayes OWL: Uncertainty Modeling in Semantic Web. Kruithof R (1937) Telefoonverkeersrekening. De Ingenieur 52:E15-E25
[26] Pearl J (1988) Probabilistic Reasoning in Intelligent Systems: Networks of Plau-sible Inference. Morgan Kaufman, San Mateo, CA
[34] Vomlel J (1999) Methods of Probabilistic Knowledge Integration. PhD Thesis, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University
[221] Z. Ding et al. BayesOWL: Uncertainty Modeling in Semantic Web Ontologies. StudFuzz 204, pp 3-29, 2006
[222] M. Holi and E.Hyvonen: Modeling Uncertainty in Semantic Web Taxonomies, StudFuzz 204, pp 31-46, 2006
[331] Franz Baader, Diego Calvanese, Deborah McGuinness, Daniele Nardi, and Peter F. Patel- Schneider, editors. The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, 2003.
[332] U. Straccia. Towards a fuzzy Description Logic for the Semantic Web. pp 167-181, 2005
[417] Acampora G., Loia V., Fuzzy Control Interoperability for Adaptive Domotic Framework. In Proceedings of 2nd IEEE International Conference on Industrial Informatics, (INDIN04), 24-26 June 2004, Berlin, Germany, pp. 184-189.
Semantic web ontologies are based on crisp logic and cannot handle uncertainty. Therefore researches are focused on maintaining well defined means for semantic web ontologies to express uncertainty and handle incomplete or partial knowledge in a domain. Overlapping concepts, including the amount of overlap is one of the issues that could be addressed using different methods. Below are two methods to handle uncertainty in semantic web ontologies.
There is a wide range of researches working on developing a framework which augments and supplements the semantic Web Ontology Language OWL for representing and reasoning with uncertainty based on Bayesian Networks (BN) [26] and its application in ontology mapping. This framework, named Bayes OWL, has gone through several iterations since its conception in 2003 [8, 9]. Bayes OWL provides a set of rules and procedures for direct translation of an OWL ontology into a BN Directed Acyclic Graph (DAG). It also provides a method based on Iterative Proportional Fitting Procedure (IPFP) [19, 7, 6, 34, 2, 4] that incorporates available probability constraints when constructing the conditional probability tables (CPTs) of the BN. The translated BN, which preserves the semantics of the original ontology, and is consistent with all the given probability constraints, can support ontology reasoning across the ontologies as Bayesian interfaces [221]. At the present time, Bayes OWL is restricted to translating only OWL-DL concept taxonomies into BNs, an active research group at Department of computer science and electrical engineering at the University of Maryland are working on extending the framework to OWL ontologies with property restrictions.
If ontologies are translated to BNs, then concept mapping between ontologies can be accomplished by evidential reasoning across the translated BNs. This approach to ontology mapping is seen to be advantageous over many existing methods in handling uncertainty in the mapping. Markus Holi and Eero Hyvonen introduce a new probabilistic method to approach the problem of representing uncertainty in semantic web ontologies [222]. In their method, degrees of subsumption, i.e., overlap between concepts can be modeled and computed efficiently using Bayesian networks based on RDF(S) ontologies. Degrees of overlap indicate how well an individual data item matches the query concept, which can be used as a well-defined measure of relevance in information retrieval tasks.
1.2 Fuzziness for semantic web reasoning
Description logics (DL) are languages for knowledge representation to represent the terminological knowledge of an application domain in a structured and formally well-understood way. DL refers to concept descriptions and the logic-based semantics in a domain.The description logic [331] in the web ontology language (OWL-DL) corresponds to SHOIN(D) description logic. In other words OWL-DL is using SHOIN description logic to represent knowledge and reasoning about it. Straccia presented a fuzzy extension of SHOIN(D) showing that its representation and reasoning capabilities go clearly beyond classical SHOIN (D) [332].
1.3 Application of Fuzziness in the architectures proposed for different problems
Giovani and Vincenzo describe a multilayer architecture to design Ambient Intelligent (AmI) [441] systems providing efficient and uniform utilization of control activities [442]. This multiplayer architecture employs markup-based technologies to transform rough information on sensors, actuators and services towards “smart data”. In particular they are using Fuzzy Markup Language (FML) [417, 418] to provide fuzzy web services. FML language is a novel computer language used to model control systems based on fuzzy logic theories. The main feature of FML is the transparency property: the FML programs can be executed on different hardware without additional efforts. This property is fundamental in ubiquitous computing environment where computers are available throughout the physical environment and appear invisible and transparent to the user.Nikravesh introduces a new architecture for semantic web search engines based on Fuzzy Conceptual Model (FCM) [551, 552, 553, 554] handle the ambiguity and imprecision of the “concept” in the Internet. In the FCM approach, the “concept” is defined by a series of keywords with different weights depending on the importance of each keyword. Ambiguity in concepts can be defined by a set of imprecise concepts. Each imprecise concept in fact can be defined by a set of fuzzy concepts. The fuzzy concepts can then be related to a set of imprecise words given the context. Imprecise words can then be translated in to precise words given the ontology and ambiguity resolution through clarification dialog. By constructing the ontology and fine-tuning the strength of links (weights), they could construct a fuzzy set to integrate piecewise the imprecise concepts and precise words to define the ambiguous concept [556].
Reference
[2] Bock HH (1989) A Conditional Iterative Proportional Fitting (CIPF) Algo-rithm with Applications in the Statistical Analysis of Discrete Spatial Data. Bull. ISI, Contributed papers of 47th Session in Paris, 1:141-142
[4] Cramer E (2000) Probability Measures with Given Marginals and Condition-als: I-projections and Conditional Iterative Proportional Fitting. Statistics and Decisions, 18:311-329
[6] Csiszar I (1975) I-divergence Geometry of Probability Distributions and Mini-mization Problems. The Annuals of Probability, 3(1):146-158
[7] Deming WE, Stephan FF (1940) On a Least Square Adjustment of a Sampled Frequency Table when the Expected Marginal Totals are Known. Ann. Math. Statist. 11:427-444
[8] Ding Z, Peng Y (2004) A Probabilistic Extension to Ontology Language OWL. In Proceedings of the 37th Hawaii International Conference on System Sciences. Big Island, HI
[9] Ding Z, Peng Y, Pan R (2004) A Bayesian Approach to Uncertainty Modeling in OWL Ontology. In Proceedings of 2004 International Conference on Advances in Intelligent Systems - Theory and Applications (AISTA2004). Luxembourg-Kirchberg, Luxembourg
[19] Bayes OWL: Uncertainty Modeling in Semantic Web. Kruithof R (1937) Telefoonverkeersrekening. De Ingenieur 52:E15-E25
[26] Pearl J (1988) Probabilistic Reasoning in Intelligent Systems: Networks of Plau-sible Inference. Morgan Kaufman, San Mateo, CA
[34] Vomlel J (1999) Methods of Probabilistic Knowledge Integration. PhD Thesis, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University
[221] Z. Ding et al. BayesOWL: Uncertainty Modeling in Semantic Web Ontologies. StudFuzz 204, pp 3-29, 2006
[222] M. Holi and E.Hyvonen: Modeling Uncertainty in Semantic Web Taxonomies, StudFuzz 204, pp 31-46, 2006
[331] Franz Baader, Diego Calvanese, Deborah McGuinness, Daniele Nardi, and Peter F. Patel- Schneider, editors. The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, 2003.
[332] U. Straccia. Towards a fuzzy Description Logic for the Semantic Web. pp 167-181, 2005
[417] Acampora G., Loia V., Fuzzy Control Interoperability for Adaptive Domotic Framework. In Proceedings of 2nd IEEE International Conference on Industrial Informatics, (INDIN04), 24-26 June 2004, Berlin, Germany, pp. 184-189.
[418] Acampora G., Loia V., Fuzzy Control Interoperability and Scalability for Adaptive Domotic Framework. In IEEE Transactions on Industrial Informatics, vol.1, issue 2, pages 97-111
[441] Basten, T., Geilen, M., de Groot, H. Ambient Intelligence: Impact on Embedded System Design. Kluwer Academic Publishers, Boston, 2003
[442] Acampora, G.; Loia, V. Enhancing the FML vision for the design of open ambient intelligence environment. In proceedings of Systems, Man and Cybernetics, 2005 IEEE International Conference on Volume 3, 10-12 Oct. 2005 Page(s):2578 - 2583 Vol. 3
[556] M. Nikravesh. Beyond the Semantic Web: Fuzzy Logic-Based Web Intelligence, StudFuzz 204, pp 149-242, 2006
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