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This research advances the theoretical foundations of knowledge representation by introducing a quantitative framework to handle inconsistencies in weighted description logic bases. By analyzing complexity bounds across specific logics, it provides essential tools for building more robust AI systems that can reason under uncertainty and conflicting data constraints.
Cost-Based Semantics for Querying Inconsistent Weighted Knowledge Bases
arXiv:2407.20754v3 Announce Type: replace-cross Abstract: 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.
Abstract: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.
This is an extended version of a paper appearing at the 21st International Conference on Principles of Knowledge Representation and Reasoning (KR 2024). 23 pages. This version corrects the proof of Theorem 7 in the appendix
Logic in Computer Science (cs.LO); Artificial Intelligence (cs.AI); Databases (cs.DB)
arXiv:2407.20754 [cs.LO]
(or arXiv:2407.20754v3 [cs.LO] for this version)
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