Revisiting Postulates for Inconsistency Measures

Abstract

Open Archive Toulouse Archive OuverteOATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible Abstract. Postulates for inconsistency measures are examined, the set of postulates due to Hunter and Konieczny being the starting point. Objections are raised against a few individual postulates. More general shortcomings are discussed and a new series of postulates is introduced.

Consistency-Based Reliability Assessment

“…First, inconsistency measures should deserve more attention. Recent work on this topic [7,1] shows promising results such as giving a weight to the inconsistency itself. A second…”

On an MCS-based inconsistency measure

“…However, in a recent article [16], Besnard has provided objections to Free-Formula-Independence and Dominance. Indeed, the author has pointed out in his article undesirable consequences of these properties, such as ignoring certain conflicts, and has provided alternative properties in order to avoid these consequences.…”

“…In particular, in [1] the authors propose axiomatic properties that any inconsistency measure should satisfy. More precisely, an inconsistency measure I is called a basic inconsistency measure if it satisfies the following properties, for all knowledge bases K and K , and for all formulae φ and ψ : It is worth noting that Besnard has provided in [16] objections on Free-Formula-Independence and Dominance. In particular, the objection to Free-Formula-Independence comes from the fact that a free formula may be involved in a conflict if we consider the internal structure of formulae, and in this case it has to increase the amount of inconsistency.…”

“…Moreover, we aim at providing formal reasons explaining why our inconsistency measure does not satisfy certain properties. We show in particular that the properties of additivity introduced in [1] and [20] 1 are incompatible with Dominance [1] and the property of Subsumption Orientation introduced in [16]. We also show that the inconsistency measures that satisfy the properties of Besnard's strong system [16] allow only to distinguish the inconsistent knowledge bases from the consistent ones 2 (the amount of inconsistency is the same in all the inconsistent knowledge bases).…”

Measuring inconsistency in probabilistic knowledge bases

“…Based on the same relation among localising, measuring and repairing inconsistency, we could derive new primitive conflict characterisations from different consolidation methods, yielding suitable versions of (Independence). Besnard (2014) has recently parametrised Hunter and Konieczny's postulates by the primitive conflict characterisation, and taking the consolidation procedure as primitive, the resulting postulates of both approaches could be compared.…”