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Preferential Semantics for Plausible Subsumption in Possibility Theory

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Abstract

Handling exceptions in a knowledge-based system is an important issue in many application domains, such as medical domain. Recently, there is an increasing interest in nonmonotonic extension of description logics to handle exceptions in ontologies. In this paper, we propose three preferential semantics for plausible subsumption to deal with exceptions in description logic-based knowledge bases. Our preferential semantics are defined in the framework of possibility theory, which is an uncertainty theory devoted to handling incomplete information. We consider the properties of these semantics and their relationships. We also discuss the relationship between two of our preferential semantics and two existing preferential semantics. We extend a description logic-based knowledge base by adding preferential subsumptions. Entailment of plausible subsumptions relative to an extended knowledge base is defined. Properties of the preferential subsumption relations relative to an extended description logic-based knowledge base are discussed. Finally, we show that our semantics for plausible subsumption can be reduced to standard semantics of an expressive description logic. Thus, the problem of plausible subsumption checking under our semantics can be reduced to the problem of subsumption checking under the classical semantics.

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Notes

  1. This term is borrowed from fuzzy set theory, where the kernel of a fuzzy set is the set of the elements with membership degree 1.

  2. This term is borrowed from fuzzy set theory, where the support of a fuzzy set is the set of the elements with non-zero membership degrees.

  3. This kind of statements was originally proposed in (Britz et al. 2008) to constrain an ordered interpretation.

  4. Remind that we consider qualitative possibility theory in our paper.

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Acknowledgments

We would like to thank three reviewers for their helpful comments, which help to improve the quality of this paper. This work is partially supported by NSFC grants (No. 61003157, No. 61272378 and No. 60803061), Jiangsu Science Foundation (BK2010412 and BK2008293), Excellent Youth Scholars Program of Southeast University, and Doctoral Discipline Foundation for Young Teachers in the Higher Education Institutions of Ministry of Education (No. 20100092120029).

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Authors and Affiliations

  1. Key Laboratory of Computer Network and Information Integration of State Education Ministry, School of Computer Science and Engineering, Southeast University, Nanjing, 211189, P.R. China

    Guilin Qi

  2. State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, P.R. China

    Guilin Qi

  3. School of Computer Science and Engineering, Southeast University, Nanjing, 211189, P.R. China

    Zhizheng Zhang

  4. Provincial Key Laboratory for Computer Information Processing Technology, Suzhou University, Suzhou, P.R. China

    Zhizheng Zhang

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  1. Guilin Qi
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  2. Zhizheng Zhang
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Correspondence to Zhizheng Zhang.

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Qi, G., Zhang, Z. Preferential Semantics for Plausible Subsumption in Possibility Theory. Minds & Machines 23, 47–75 (2013). https://doi.org/10.1007/s11023-012-9300-4

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