Postulate satisfaction for inconsistency measures in monotonic logics and databases

Inconsistency measures for propositional logic have been investigated in great detail for the past 20 years. Many such measures have been proposed. Rationality postulates, conditions about inconsistency measures, were defined to distinguish the measures that satisfy intuitively desirable properties. The satisfaction or violation of various postulates is known for many inconsistency measures. But propositional logic has many limitations and in many applications more complex logics are appropriate. We consider monotonic extensions of propositional logic such as modal, temporal, description, and first-order logic. We focus on a class of inconsistency measures whose computation depends only on the structure of the minimal inconsistent subsets. The definition of these inconsistency measures is the same for these logics as for propositional logic. The situation is similar for the rationality postulates. This paper studies the connection between the satisfaction or violation of the postulates for propositional logic and monotonic extensions of propositional logic. We show that the results are the same for the most prominent postulates. Additionally, we consider the same question for databases. We show that although the setting is substantially different from these logics, in general the results are the same.