Reasoning and quantification in fuzzy description logics

Authors:
Daniel Sánchez;Andrea G. B. Tettamanzi
Affiliations:
Department of Computer Science and Artificial Intelligence, University of Granada, Granada, Spain;Department of Information Technologies, University of Milan, Crema (CR), Italy
Venue:
WILF'05 Proceedings of the 6th international conference on Fuzzy Logic and Applications
Year:
2005

Citing 3
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Abstract

In this paper we introduce reasoning procedures for $\mathcal{ALCQ}^{+}_{F}$, a fuzzy description logic with extended qualified quantification. The language allows for the definition of fuzzy quantifiers of the absolute and relative kind by means of piecewise linear functions on ℕ and ℚ∩[0,1] respectively. In order to reason about instances, the semantics of quantified expressions is defined based on recently developed measures of the cardinality of fuzzy sets. A procedure is described to calculate the fuzzy satisfiability of a fuzzy assertion, which is a very important reasoning task. The procedure considers several different cases and provides direct solutions for the most frequent types of fuzzy assertions.