In this report, we investigate (element-based) inconsistency measures for multisets of business rule bases. Currently, related works allow to assess individual rule bases, however, as companies might encounter thousands of such instances daily, studying not only individual rule bases separately, but rather also their interrelations becomes necessary, especially in regard to determining suitable re-modelling strategies. We therefore present an approach to induce multiset-measures from arbitrary (traditional) inconsistency measures, propose new rationality postulates for a multiset use-case, and investigate the complexity of various aspects regarding multi-rule base inconsistency measurement.

A number of proposals have been made to define inconsistency measures. Each has its rationale. But to date, it is not clear how to delineate the space of options for measures, nor is it clear how we can classify measures systematically. In this paper, we introduce a general framework for comparing syntactic inconsistency measures. It uses the construction of an inconsistency graph for each knowledgebase. We then introduce abstractions of the inconsistency graph and use the hierarchy of the abstractions to classify a range of inconsistency measures.

Inconsistency measures help analyzing contradictory knowledge bases and resolving inconsistencies. In recent years several measures with desirable properties have been proposed, but often these measures correspond to combinatorial or non-convex optimization problems that are hard to solve in practice. In this paper, I study a new family of inconsistency measures for probabilistic knowledge bases. All members satisfy many desirable properties and can be computed by means of convex optimization techniques. For two members, I present linear programs whose computation is barely harder than a probabilistic satisfiability test.

Measuring inconsistency is viewed as an important issue related to handling inconsistencies. Good measures are supposed to satisfy a set of rational properties. However, defining sound properties is sometimes problematic. In this paper, we emphasize one such property, named Decomposability, rarely discussed in the literature due to its modeling difficulties. To this end, we propose an independent decomposition which is more intuitive than existing proposals. To analyze inconsistency in a more fine-grained way, we introduce a graph representation of a knowledge base and various MUSdecompositions. One particular MUS-decomposition, named distributable MUS-decomposition leads to an interesting partition of inconsistencies in a knowledge base such that multiple experts can check inconsistencies in parallel, which is impossible under existing measures. Such particular MUSdecomposition results in an inconsistency measure that satisfies a number of desired properties. Moreover, we give an upper bound complexity of the measure that can be computed using 0/1 linear programming or Min Cost Satisfiability problems, and conduct preliminary experiments to show its feasibility.