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Hybridizing concept languages

P. Blackburn and M. Tzakova. Hybridizing concept languages. Annals of Mathematics and Artificial Intelligence, 24:23–49, 1998.

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Abstract:

This paper shows how to increase the expressivity of concept languages using a strategy called hybridization. Building on the well-known correspondences between modal and description logics, we define two hybrid languages. These languages are called `hybrid' because, in addition to the familiar propositional variables and modal operators, they contain variables across individuals and a binder that binds these variables. As we show, combining aspects of modal and first-order logic in this manner allows the expressivity of concept languages to be boosted in a natural way, making it possible to define number restrictions, collections of individuals, irreflexivity of roles, and TBox- and ABox-statements. Subsequent addition of the universal modality allows the notion of subsumption to be internalized, and enables the representation of queries to arbitrary first-order knowledge bases. The paper notes themes shared by the hybrid and concept language literatures, and draws attention to a little-known body of work by the late Arthur Prior.

BibTeX: (download)

@ARTICLE{blackburn98:_hybridizing,
  author = {P. Blackburn and M. Tzakova},
  title = {Hybridizing concept languages},
  journal = {Annals of Mathematics and Artificial Intelligence},
  year = {1998},
  volume = {24},
  pages = {23--49},
  abstract = {
	This paper shows how to increase the expressivity of concept languages
	using a strategy called hybridization. Building on the well-known
	correspondences between modal and description logics, we define two
	hybrid languages. These languages are called `hybrid' because, in
	addition to the familiar propositional variables and modal operators,
	they contain variables across individuals and a binder that binds
	these variables. As we show, combining aspects of modal and first-order
	logic in this manner allows the expressivity of concept languages
	to be boosted in a natural way, making it possible to define number
	restrictions, collections of individuals, irreflexivity of roles,
	and TBox- and ABox-statements. Subsequent addition of the universal
	modality allows the notion of subsumption to be internalized, and
	enables the representation of queries to arbitrary first-order knowledge
	bases. The paper notes themes shared by the hybrid and concept language
	literatures, and draws attention to a little-known body of work by
	the late Arthur Prior. }
}

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