On Knowledge Dependence in Weighted Description Logic

We study a family of operators (called ‘Tooth’ operators) that combine Description Logic concepts via weighted sums. These operators are intended to capture the notion of instances satisfying “enough” of the concept descriptions given. We examine two variants of these operators: the “knowledge-independent” one, that evaluates the concepts with respect to the current interpretation, and the “knowledge-dependent” one that instead evaluates them with respect to a specified knowledge base, comparing and contrasting their properties. We furthermore discuss the connections between these operators and linear classification models.