Reasoning with very expressive fuzzy description logics

Giorgos Stoilos; Giorgos Stamou; Jeff Z. Pan; Vassilis Tzouvaras; Ian Horrocks

doi:10.1613/jair.2279

Reasoning with very expressive fuzzy description logics

Giorgos Stoilos, Giorgos Stamou, Jeff Z. Pan, Vassilis Tzouvaras, Ian Horrocks

Computing Science

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172 Citations (Scopus)

Abstract

It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last decade, mainly due to their decidability and the existence of empirically high performance of reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms (S), inverse roles (I), role hierarchies (H) and number restrictions (N). We illustrate why transitive role axioms are difficult to handle in the presence of fuzzy interpretations and how to handle them properly. Then we extend these results by adding role hierarchies and finally number restrictions. The main contributions of the paper are the decidability proof of the fuzzy DL languages fuzzy-SI and fuzzy-SHIN, as well as decision procedures for the knowledge base satisfiability problem of the fuzzy-SI and fuzzy-SHIN.

Original language	English
Pages (from-to)	273-320
Number of pages	48
Journal	Journal of Artificial Intelligence Research
Volume	30
Issue number	1
DOIs	https://doi.org/10.1613/jair.2279
Publication status	Published - Sept 2007

Keywords

information-retrieval

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abstract = "It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last decade, mainly due to their decidability and the existence of empirically high performance of reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms (S), inverse roles (I), role hierarchies (H) and number restrictions (N). We illustrate why transitive role axioms are difficult to handle in the presence of fuzzy interpretations and how to handle them properly. Then we extend these results by adding role hierarchies and finally number restrictions. The main contributions of the paper are the decidability proof of the fuzzy DL languages fuzzy-SI and fuzzy-SHIN, as well as decision procedures for the knowledge base satisfiability problem of the fuzzy-SI and fuzzy-SHIN.",

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AU - Stoilos, Giorgos

AU - Stamou, Giorgos

AU - Pan, Jeff Z.

AU - Tzouvaras, Vassilis

AU - Horrocks, Ian

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JO - Journal of Artificial Intelligence Research

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Reasoning with very expressive fuzzy description logics

Abstract

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