Approaches to measuring inconsistency for stratified knowledge bases

A number of proposals have been proposed for measuring inconsistency for knowledge bases. However, it is rarely investigated how to incorporate preference information into inconsistency measures. This paper presents two approaches to measuring inconsistency for stratified knowledge bases. The first approach, termed the multi-section inconsistency measure (MSIM for short), provides a framework for characterizing the inconsistency at each stratum of a stratified knowledge base. Two instances of MSIM are defined: the naive MSIM and the stratum-centric MSIM. The second approach, termed the preference-based approach, aims to articulate the inconsistency in a stratified knowledge base from a global perspective. This approach allows us to define measures by taking into account the number of formulas involved in inconsistencies as well as the preference levels of these formulas. A set of desirable properties are introduced for inconsistency measures of stratified knowledge bases and studied with respect to the inconsistency measures introduced in the paper. Computational complexity results for these measures are presented. In addition, a simple but explanatory example is given to illustrate the application of the proposed approaches to requirements engineering.

[1]  A. Hunter,et al.  Shapley Inconsistency Values , 2006, KR.

[2]  Kevin M. Knight,et al.  Two Information Measures for Inconsistent Sets , 2003, J. Log. Lang. Inf..

[3]  Torsten Schaub,et al.  Introduction to Inconsistency Tolerance , 2005, Inconsistency Tolerance.

[4]  Didier Dubois,et al.  Iterated Revision as Prioritized Merging , 2006, KR.

[5]  John Grant,et al.  Analysing inconsistent first-order knowledgebases , 2008, Artif. Intell..

[6]  Guilin Qi,et al.  Measuring conflict and agreement between two prioritized belief bases , 2005, IJCAI.

[7]  John Grant,et al.  Measuring inconsistency in knowledgebases , 2006, Journal of Intelligent Information Systems.

[8]  Guilin Qi,et al.  Merging Stratified Knowledge Bases under Constraints , 2006, AAAI.

[9]  David Picado Muiòo.  Measuring and repairing inconsistency in probabilistic knowledge bases , 2011 .

[10]  Weiru Liu,et al.  Measuring Inconsistency in a Network Intrusion Detection Rule Set Based on Snort , 2011, Int. J. Semantic Comput..

[11]  Anthony Hunter,et al.  Logical Comparison of Inconsistent Perspectives using Scoring Functions , 2004, Knowledge and Information Systems.

[12]  Weiru Liu,et al.  From inconsistency handling to non-canonical requirements management: A logical perspective , 2013, Int. J. Approx. Reason..

[13]  Didier Dubois,et al.  A Local Approach to Reasoning under Incosistency in Stratified Knowledge Bases , 1995, ECSQARU.

[14]  Weiru Liu,et al.  Measuring the blame of each formula for inconsistent prioritized knowledge bases , 2012, J. Log. Comput..

[15]  John Grant,et al.  Classifications for inconsistent theories , 1978, Notre Dame J. Formal Log..

[16]  Weiru Liu,et al.  A Syntax-based approach to measuring the degree of inconsistency for belief bases , 2011, Int. J. Approx. Reason..

[17]  Jérôme Lang,et al.  Quantifying information and contradiction in propositional logic through test actions , 2003, IJCAI.

[18]  Guohui Xiao,et al.  Inconsistency Measurement based on Variables in Minimal Unsatisfiable Subsets , 2012, ECAI.

[19]  Weiru Liu,et al.  Handling Inconsistency In Distributed Software Requirements Specifications Based On Prioritized Merging , 2009, Fundam. Informaticae.

[20]  Graham Priest,et al.  Minimally inconsistent LP , 1991, Stud Logica.

[21]  Gerhard Brewka,et al.  A rank based description language for qualitative preferences , 2004, NMR.

[22]  Guilin Qi,et al.  Computational Complexity and Anytime Algorithm for Inconsistency Measurement , 2010, Int. J. Softw. Informatics.

[23]  Souhila Kaci,et al.  Weakening conflicting information for iterated revision and knowledge integration , 2001, Artificial Intelligence.

[24]  Weiru Liu,et al.  Under Consideration for Publication in Knowledge and Information Systems a General Framework for Measuring Inconsistency through Minimal Inconsistent Sets , 2022 .

[25]  Guilin Qi,et al.  Computing Inconsistency Measurements under Multi-Valued Semantics by Partial Max-SAT Solvers , 2010, KR.

[26]  Anthony Hunter,et al.  Measuring Inconsistency through Minimal Inconsistent Sets , 2008, KR.

[27]  Weiru Liu,et al.  Measuring Inconsistency in Requirements Specifications , 2005, ECSQARU.

[28]  Gerhard Brewka,et al.  Preferred Subtheories: An Extended Logical Framework for Default Reasoning , 1989, IJCAI.

[29]  Georg Gottlob,et al.  On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals , 1992, Artif. Intell..

[30]  Weiru Liu,et al.  Measuring the significance of inconsistency in the Viewpoints framework , 2013, Sci. Comput. Program..

[31]  Anthony Hunter,et al.  Approaches to Measuring Inconsistent Information , 2005, Inconsistency Tolerance.

[32]  Anthony Hunter,et al.  On the measure of conflicts: Shapley Inconsistency Values , 2010, Artif. Intell..

[33]  Matthias Thimm,et al.  Measuring Inconsistency in Probabilistic Knowledge Bases , 2009, UAI.

[34]  Guilin Qi,et al.  Measuring Inconsistency for Description Logics Based on Paraconsistent Semantics , 2007, Description Logics.