Reasoning within Fuzzy Description Logics

TLDR

Description Logics are well‑known logics for managing structured knowledge, enabling reasoning about individuals and concepts, and their use in multimedia information retrieval has highlighted the need to handle imprecision in object content representation. This paper introduces a fuzzy extension of ALC that integrates Zadeh's fuzzy logic with classical Description Logic. The extension makes concepts fuzzy, defines its syntax and semantics, establishes key properties, and presents a constraint‑propagation calculus for reasoning about imprecise concepts.

Abstract

Description Logics (DLs) are suitable, well-known, logics for managing structured knowledge. They allow reasoning about individuals and well defined concepts, i.e., set of individuals with common properties. The experience in using DLs in applications has shown that in many cases we would like to extend their capabilities. In particular, their use in the context of Multimedia Information Retrieval (MIR) leads to the convincement that such DLs should allow the treatment of the inherent imprecision in multimedia object content representation and retrieval. In this paper we will present a fuzzy extension of ALC, combining Zadeh's fuzzy logic with a classical DL. In particular, concepts becomes fuzzy and, thus, reasoning about imprecise concepts is supported. We will define its syntax, its semantics, describe its properties and present a constraint propagation calculus for reasoning in it.