A Characteristic Function Approach to Inconsistency Measures for Knowledge Bases.

Knowledge is an important component in many intelligent systems.
Since items of knowledge in a knowledge base can be conflicting, especially if
there are multiple sources contributing to the knowledge in this base, significant
research efforts have been made on developing inconsistency measures for
knowledge bases and on developing merging approaches. Most of these efforts
start with flat knowledge bases. However, in many real-world applications, items
of knowledge are not perceived with equal importance, rather, weights (which
can be used to indicate the importance or priority) are associated with items of
knowledge. Therefore, measuring the inconsistency of a knowledge base with
weighted formulae as well as their merging is an important but difficult task. In
this paper, we derive a numerical characteristic function from each knowledge
base with weighted formulae, based on the Dempster-Shafer theory of evidence.
Using these functions, we are able to measure the inconsistency of the knowledge
base in a convenient and rational way, and are able to merge multiple knowledge
bases with weighted formulae, even if knowledge in these bases may be
inconsistent. Furthermore, by examining whether multiple knowledge bases are
dependent or independent, they can be combined in different ways using their
characteristic functions, which cannot be handled (or at least have never been
considered) in classic knowledge based merging approaches in the literature.