Chair for Automata Theory LTCS – Report Making Quantification Relevant Again

Defeasible Description Logics (DDLs) extend Description Logics with defeasible concept inclusions. Reasoning in DDLs often employs rational or relevant closure according to the (propositional) KLM postulates. If in DDLs with quantification a defeasible subsumption relationship holds between concepts, this relationship might also hold if these concepts appear in existential restrictions. Such nested defeasible subsumption relationships were not detected by earlier reasoning algorithms—neither for rational nor relevant closure. In this report, we present a new approach for EL⊥ that alleviates this problem for relevant closure (the strongest form of preferential reasoning currently investigated) by the use of typicality models that extend classical canonical models by domain elements that individually satisfy any amount of consistent defeasible knowledge. We also show that a certain restriction on the domain of the typicality models in this approach yields inference results that correspond to the (weaker) more commonly known rational closure.