The Fuzzy Description Logic ALC_FH with Hedge Algebras as Concept Modifiers

Abstract

In this paper we present the fuzzy description logic ALCFH introduced, where primitive concepts are modified by means of hedges taken from hedge algebras. ALCFH is strictly more expressive than Fuzzy-ALC defined in [11]. We show that given a linearly ordered set of hedges primitive concepts can be modified to any desired degree by prefixing them with appropriate chains of hedges. Furthermore, we define a decision procedure for the unsatisfiability problem in ALCFH, and discuss knowledge base expansion when using terminologies, truth bounds, expressivity as well as complexity issues. We extend [8] by allowing modifiers on non-primitive concepts and extending the satisfiability procedure to handle concept definitions.

Semantic Web Uncertainty Management

“…All existing proposals for fuzzy DL extend the semantics of the description language by fuzzifying their interpretation using fuzzy logic (Hölldobler, Khang, & Störr, 2002;Sánchez & Tettamanzi, 2004;Straccia, 2001Straccia, , 2004aStraccia, , 2004b, 2005a, 2005bTresp & Molitor, 1998). In general, a fuzzy interpretation  is a pair  = (∆  , ·  ), where ∆  is the domain and ·  is an interpretation function that maps language elements to some membership degree in [0,1].…”

“…The manipulators/modifiers (Hölldobler et al, 2002;Straccia, 2005aStraccia, , 2005bTresp & Molitor, 1998) are unary operators that can modify the membership functions of the concepts they are applied to (e.g., "mostly," "very"), whereas fuzzy quantifiers (Sánchez & Tettamanzi, 2004) allow expressing vague quantities (e.g., "about 2") and quantity intervals (e.g., "roughly between 1 and 3"). Hollunder (1994) proposed a possibilistic extension to the description language.…”

The Role of Vague Categories in Semantic and Adaptive Web Interfaces

“…From here on, we'll follow the assumption that both research areas will converge in the future, and therefore, DLs, perhaps extended or combined with other paradigms, will form the basis of Adaptive-Semantic Web sites. In addition, we take the ALC F H fuzzy description logic described in [12] (which in turn is an extension of the Fuzzy-ALC defined in [25]) as a point of departure for the discussion of practical aspects of vague semantics in user interface descriptions. In ALC F H , concepts are expressions that describe, by means of roles, the properties of a set of individuals.…”

“…The concept of personalized fuzzy links [21] are a different formulation for that concept of imprecise adaptiveness. Previous research have addressed the integration of vague concepts into crisp description logics [25,26,12], resulting in what can be called fuzzy description logics (fDL). Retrieval of multimedia objects [24] and electronic commerce [12] have been mentioned as application areas for fDLs.…”

“…Previous research have addressed the integration of vague concepts into crisp description logics [25,26,12], resulting in what can be called fuzzy description logics (fDL). Retrieval of multimedia objects [24] and electronic commerce [12] have been mentioned as application areas for fDLs. In this paper, we describe vagueness in UI descriptions as a component of a Semantic Web application, with the objective of providing a framework for adaptation.…”