Analysing inconsistent first-order knowledgebases

It is well-known that knowledgebases may contain inconsistencies. We provide a framework of measures, based on a first-order four-valued logic, to quantify the inconsistency of a knowledgebase. This allows for the comparison of the inconsistency of diverse knowledgebases that have been represented as sets of first-order logic formulae. We motivate the approach by considering some examples of knowledgebases for representing and reasoning with ontological knowledge and with temporal knowledge. Analysing ontological knowledge (including the statements about which concepts are subconcepts of other concepts, and which concepts are disjoint) can be problematical when there is a lack of knowledge about the instances that may populate the concepts, and analysing temporal knowledge (such as temporal integrity constraints) can be problematical when considering infinite linear time lines isomorphic to the natural numbers or the real numbers or more complex structures such as branching time lines. We address these difficulties by providing algebraic measures of inconsistency in first-order knowledgebases.

[1]  Eliezer L. Lozinskii,et al.  Information and evidence in logic systems , 1994, J. Exp. Theor. Artif. Intell..

[2]  J. M. Dunn,et al.  Modern Uses of Multiple-Valued Logic , 1977 .

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

[4]  Didier Dubois,et al.  Encoding Information Fusion in Possibilistic Logic: A General Framework for Rational Syntactic Merging , 2000, ECAI.

[5]  V. S. Subrahmanian,et al.  Applications Of Paraconsistency In Data And Knowledge Bases , 2004, Synthese.

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

[7]  Raymond Reiter,et al.  Equality and Domain Closure in First-Order Databases , 1980, JACM.

[8]  Gunter Saake,et al.  Logics for Emerging Applications of Databases , 2003, Springer Berlin Heidelberg.

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

[10]  Nuel D. Belnap,et al.  A Useful Four-Valued Logic , 1977 .

[11]  Philippe Besnard,et al.  Paraconsistent Reasoning as an Analytic Tool , 2001, Log. J. IGPL.

[12]  Walter Alexandre Carnielli,et al.  A Logical Framework for Integrating Inconsistent Information in Multiple Databases , 2002, FoIKS.

[13]  Newton C. A. da Costa,et al.  On the theory of inconsistent formal systems , 1974, Notre Dame J. Formal Log..

[14]  Bashar Nuseibeh,et al.  Managing inconsistent specifications: reasoning, analysis, and action , 1998, TSEM.

[15]  Jan Chomicki,et al.  Query Answering in Inconsistent Databases , 2003, Logics for Emerging Applications of Databases.

[16]  Graham Priest,et al.  Reasoning About Truth , 1989, Artif. Intell..

[17]  Chengqi Zhang,et al.  A Verification Model for Electronic Transaction Protocols , 2004, APWeb.

[18]  D. Gabbay,et al.  Inconsistency Handling in Multiperspective Specifications , 1994 .

[19]  W. Carnielli,et al.  A Taxonomy of C-systems , 2001 .

[20]  V. S. Subrahmanian,et al.  How Dirty Is Your Relational Database? An Axiomatic Approach , 2007, ECSQARU.

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

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

[23]  Anthony Hunter.  How to act on inconsistent news: Ignore, resolve, or reject , 2006, Data Knowl. Eng..

[24]  Itala M. Loffredo D'Ottaviano,et al.  Paraconsistency: The Logical Way to the Inconsistent , 2002 .

[25]  Dov M. Gabbay,et al.  Inconsistency Handling in Multperspective Specifications , 1994, IEEE Trans. Software Eng..

[26]  Alberto O. Mendelzon,et al.  Merging Databases Under Constraints , 1998, Int. J. Cooperative Inf. Syst..

[27]  Arnon Avron,et al.  The Value of the Four Values , 1998, Artif. Intell..

[28]  Sébastien Konieczny,et al.  On the Logic of Merging , 1998, KR.

[29]  Anthony Hunter,et al.  Evaluating Significance of Inconsistencies , 2003, IJCAI.

[30]  Michael Kifer,et al.  Applications of Annotated Predicate Calculus to Querying Inconsistent Databases , 2000, Computational Logic.

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

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

[33]  Alan Smaill,et al.  Proceedings of the 14th European Conference on Artificial Intelligence (ECAI 2000) , 2000 .

[34]  Dov M. Gabbay,et al.  Inconsistency Handling in Multi-Perspective Specifications , 1993, ESEC.

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

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

[37]  Weiru Liu,et al.  Measuring inconsistency in requirements engineering , 2005 .

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

[39]  Anthony Hunter,et al.  Measuring inconsistency in knowledge via quasi-classical models , 2002, AAAI/IAAI.

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

[41]  Kevin Knight,et al.  Measuring Inconsistency , 2002, J. Philos. Log..