A Framework for Inconsistency-tolerant Reasoning with Sets of Models

We propose a framework for reasoning from inconsistent

knowledge bases using minimal hitting sets, i. e., sets of

interpretations such that each formula of the knowledge

base is satisfied by at least one those interpretations. By

additionally considering preference orders over minimal

hitting sets, we can define a wide variety of non-monotonic

inference relations. We consider concrete preference orders

based on set inclusion, cardinality, the number of

conflicting atoms within the hitting set, and using the

Hamming distance between pairs of interpretations. We

compare the resulting inference relations, characterize

their logical properties, and position them relative to

classical inference from maximal consistent subsets.

Finally, we show that inference based on minimal

conflicting atoms coincides with reasoning in Priest’s

3-valued logic.