Computing Inconsistency Measurements under Multi-Valued Semantics by Partial Max-SAT Solvers

Measuring the inconsistency degree of a knowledge base can help us to deal with inconsistencies. Several inconsistency measures have been given under different multi-valued semantics, including 4-valued semantics, 3-valued semantics, LPm and Quasi Classical semantics. In this paper, we first carefully analyze the relationship between these inconsistency measures by showing that the inconsistency degrees under 4-valued semantics, 3-value semantics, LPm are the same, but different from the one based on Quasi Classical semantics. We then consider the computation of these inconsistency measures and show that computing inconsistency measurement under multi-valued semantics is usually intractable. To tackle this problem, we propose two novel algorithms that respectively encode the problems of computing inconsistency degrees under 4-valued semantics (3-valued semantics, LPm) and under Quasi Classical semantics into the partial MaxSAT problems. We implement these algorithms and do experiments on some benchmark data sets. The preliminary but encouraging experimental results show that our approach is efficient to handle large knowledge bases.