A Fuzzy Description Logic with Product T-norm

Abstract

<i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Fuzzy Description Logics (fuzzy DLs)</i> have been proposed as a language to describe structured knowledge with vague concepts. It is well known that the choice of the fuzzy operators may determine some logical properties. However, up to date the study of fuzzy DLs has been restricted to the Łukasiewicz logic and the "Zadeh semantics". In this work, we propose a novel semantics combining the common product t-norm with the standard negation. We show some interesting properties of the logic and propose a reasoning algorithm based on a mixture of tableaux rules and the reduction to mixed Integer Quadratically Constrained Programming.