  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.
