An Anytime Algorithm for Computing Inconsistency Measurement

Abstract

Abstract. Measuring inconsistency degrees of inconsistent knowledge bases is an important problem as it provides context information for facilitating inconsistency handling. Many methods have been proposed to solve this problem and a main class of them is based on some kind of paraconsistent semantics. In this paper, we consider the computational aspects of inconsistency degrees of propositional knowledge bases under 4-valued semantics. We first analyze its computational complexity. As it turns out that computing the exact inconsistency degree is intractable, we then propose an anytime algorithm that provides tractable approximation of the inconsistency degree from above and below. We show that our algorithm satisfies some desirable properties and give experimental results of our implementation of the algorithm.

On the complexity of inconsistency measurement

“…Inconsistency measures, firstly mentioned in (Grant, 1978), can be used to analyse inconsistencies and to provide insights on how to repair them. An inconsistency measure I is a function on knowledge bases, such that the larger the value I(K) the more severe the inconsistency in K. A lot of different approaches of inconsistency measures have been proposed, mostly for classical propositional logic (Hunter and Konieczny, 2004Ma et al, 2010;Mu et al, 2011;Xiao and Ma, 2012;Grant and Hunter, 2011;Ma et al, 2012;Grant and Hunter, 2013;McAreavey et al, 2014;Jabbour et al, 2015Jabbour et al, , 2014bBesnard, 2016;Thimm, 2016b;Ammoura et al, 2015Ammoura et al, , 2017, but also for classical first-order logic (Grant and Hunter, 2008), description logics (Ma et al, 2007;Zhou et al, 2009), default logics (Doder et al, 2010), answer set programming (Ulbricht et al, 2016) probabilistic and other weighted logics (Thimm, 2013;Potyka, 2014;De Bona and Finger, 2015), and relational databases (Decker, 2011), see also (Thimm, 2017b(Thimm, , 2018 for some recent surveys.…”

Towards Large-Scale Inconsistency Measurement

“…The basic idea is that the larger the inconsistency in K the larger the value I(K). However, inconsistency is a concept that is not easily quantified and there have been a couple of proposals for inconsistency measures so far, see e. g. [8,10,1,2,5,13]. There are two main paradigms for assessing inconsistency [5], the first being based on the (number of) formulas needed to produce inconsistencies and the second being based on the proportion of the language that is affected by the inconsistency.…”

Knowledge Base Compilation for Inconsistency Measures

“…A number of logic-based inconsistency measures have been studied and there are different ways to categorize them. One way is by their dependence to the language or formula: the former aims to compute the proportion of the language affected by inconsistency (Grant, 1978;Hunter, 2002;Oller, 2004;Hunter, 2006;Grant and Hunter, 2008;Ma et al, 2010;Xiao et al, 2010a;Ma et al, 2011;Xiao and Ma, 2012;Jabbour and Raddaoui, 2013). Whilst, the latter is concerned with the minimal number of formulas that cause inconsistencies, often through minimal unsatisfiable subsets (Hunter and Konieczny, 2008;Mu et al, 2011a;Mu et al, 2012;Grant and Hunter, 2013;Jabbour et al, 2014a).…”