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 satisfy- ing "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.