In this paper, we explore a quantitative approach to querying inconsistent description logic knowledge bases. We consider weighted knowledge bases in which both axioms and assertions have (possibly infinite) weights, which are used to assign a cost to each interpretation based upon the axioms and assertions it violates. Two notions of certain and possible answer are defined by either considering interpretations whose cost does not exceed a given bound or restricting attention to optimal-cost interpretations. Our main contribution is a comprehensive analysis of the combined and data complexity of bounded cost satisfiability and certain and possible answer recognition, for description logics between ELbot and ALCO.

翻译：本文探讨了一种查询不一致描述逻辑知识库的定量方法。我们考虑加权知识库，其中公理和断言均具有（可能无限的）权重，这些权重用于根据解释所违反的公理和断言为其分配代价。通过考虑代价不超过给定界限的解释，或仅关注最优代价解释，我们定义了必然答案与可能答案两种概念。我们的主要贡献是对ELbot至ALCO之间的描述逻辑，在有界代价可满足性以及必然与可能答案识别问题上，进行了组合复杂性与数据复杂性的综合分析。