Incorporating Generalized Quantifiers Into Description Logic For Representing Data Source Contents

Systems for helping users to select data sources in an environment, such as the Internet, must be expressive enough to allow a variety of data sources to be formally represented. We build upon and extend the concept language, description logic (DL), to propose a novel representation system to achieve that goal. We point out that there are technical barriers within description logic limiting the types of data sources that can be represented. Specifically, we show that (1) DL is awkward in representing sufficient conditions, and (2) DL can describe properties of a concept itself only in the case of existential quantification. To be concrete, whereas it is easy in DL to say 'There are some objects in a concept C such that each of them holds the property P', it is awkward, if not impossible, to say 'All (Most, More-than-n, More-than-1/2) of those that hold the property P are in the concept C' or 'Most (More-than-n, More-than-1/2) of those that are in the concept C hold the property P'. These barriers cause us to extend DL with the notion of generalized quantifiers. We improve the previous results of generalized quantifiers to make them inter-operable with traditional logic. The proposed formalism integrates the nice features of generalized quantifiers into description logic, and hence achieves more expressive power than various representation systems based purely on description logic. It is also shown that our proposed language preserves those mathematical properties that traditional logic-based formalisms are known to hold.