We present algorithms based on satisfiability problem (SAT) solving, as well as answer set programming (ASP), for solving the problem of determining inconsistency degrees in propositional knowledge bases. We consider six different inconsistency measures whose respective decision problems lie on the first level of the polynomial hierarchy. Namely, these are the contension inconsistency measure, the forgetting-based inconsistency measure, the hitting set inconsistency measure, the max-distance inconsistency measure, the sum-distance inconsistency measure, and the hit-distance inconsistency measure. In an extensive experimental analysis, we compare the SAT-based and ASP-based approaches with each other, as well as with a set of naive baseline algorithms. Our results demonstrate that overall, both the SAT-based and the ASP-based approaches clearly outperform the naive baseline methods in terms of runtime. The results further show that the proposed ASP-based approaches perform superior to the SAT-based ones with regard to all six inconsistency measures considered in this work. Moreover, we conduct additional experiments to explain the aforementioned results in greater detail.

翻译：我们提出了基于可满足性问题(SAT)求解和回答集编程(ASP)的算法，用于解决命题知识库中不一致性程度的确定问题。我们考虑了六种不同的不一致性度量，它们各自的判定问题位于多项式层级的第一层。具体而言，这些度量包括：涵容不一致性度量、基于遗忘的不一致性度量、命中集不一致性度量、最大距离不一致性度量、总和距离不一致性度量以及命中距离不一致性度量。通过大量实验分析，我们将基于SAT和ASP的方法相互比较，并与一组朴素基线算法进行对比。结果表明，总体而言，基于SAT和基于ASP的方法在运行时间上明显优于朴素基线方法。结果进一步显示，针对本工作中考虑的所有六种不一致性度量，所提出的基于ASP的方法性能优于基于SAT的方法。此外，我们还进行了额外实验以更详细地解释上述结果。