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量化方法。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成本。通过考虑成本不超过给定界限的解释，或仅关注最优成本解释，我们定义了必然答案与可能答案两种概念。我们的主要贡献在于，针对ELbot至ALCO之间的描述逻辑，全面分析了有界成本可满足性及必然与可能答案识别的组合复杂度与数据复杂度。