On the Characterization of Inconsistency: A Prime Implicates Based Framework

Abstract

Measuring inconsistency is recognized as an important issue for 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 dominance, rarely satisfied by syntactic measures. Based on prime implicates canonical representation, we first characterize the conflicting variables allowing us to refine an existing inconsistency measure. Secondly, we propose a new measure, to circumscribe the internal conflicts in a knowledge base. This measure is proved to satisfy a new but weaker form of dominance.

Localising iceberg inconsistencies

“…The devising of inconsistency measures has been influenced by a set of rationality postulates proposed by Hunter and Konieczny [25]. Among these basic requirements, the postulates of (Independence) and (Dominance) have been subject to debate [8,27,11]. The postulate of (Independence) is strongly related to minimal inconsistent sets as the primitive conflict characterisation [8,11], and such a link may be undesirable sometimes.…”

“…To answer the second question in a qualitative way, inconsistent knowledge bases were classified by the severity of their inconsistency [17]. Recently, to numerically quantify the extent to which a knowledge base is inconsistent, many inconsistency measures have been proposed [29,24,25,19,28,27,20,42,43]. In contrast, the first question appears quite underdeveloped, and it is the subject of the present work.…”

Knowledge Base Compilation for Inconsistency Measures

“…In (Jabbour et al, 2014c;Jabbour et al, 2014b), the authors introduced the notion of conflicting variable in order to quantify the inconsistency of a knowledge base by circumscribing the sub-parts of the knowledge that create the contradictions. Indeed, conflicting variables are defined to catch the elements of the knowledge base that are really involved in conflicts.…”

“…In this section, we explore the notion of hitting set using deduced MUSes. Indeed, the notion of deduced MUS is introduced in (Jabbour et al, 2014c;Jabbour et al, 2014b) as an original characterization that allows us to summarize the conflict that arise in knowledge bases. More precisely, we show how inconsistency measures based on hitting set of the minimal inconsistent sets (e.g., (Mu, 2015)) can be extended to hitting sets of deduced MUSes.…”

Computing Inconsistency Using Logical Argumentation

“…To tackle this problem, a range of logic-based proposals for analyzing and measuring the amount of inconsistency of knowledge base have been presented in literature, including the maximal n-consistency (Knight, 2002), measures based on variables or via multi-valued models (Grant, 1978;Hunter, 2002;Oller, 2004;Hunter, 2006;Grant and Hunter, 2008;Ma et al, 2010;Xiao et al, 2010;Ma et al, 2011), n-consistency and n-probability (Doder et al, 2010), measures based on minimal inconsistent subsets (Hunter and Konieczny, 2008;Mu et al, 2011a;Mu et al, 2012;Xiao and Ma, 2012), the Shapley inconsistency value (Hunter and Konieczny, 2010), inconsistency measurement based on minimal proofs (Jabbour and Raddaoui, 2013), partitioning based inconsistency measures (Jabbour et al, 2014a), and recently inconsistency characterization using prime implicates (Jabbour et al, 2014c;Jabbour et al, 2014b).…”