On the Complexity of Axiom Pinpointing in the ELFamily of Description Logics

We investigate the computational complexity of axiom pinpointing, which is the task of finding minimal subsets of a Description Logic knowledge base that have a given consequence. We consider the problems of enumerating such subsets with and without order, and show hardness results that already hold for the propositional Horn fragment, or for the Description Logic EL. We show complexity results for several other related decision and enumeration problems for these fragments that extend to more expressive logics. In particular we show that hardness of these problems depends not only on expressivity of the fragment but also on the shape of the axioms used.

[1]  G. Danielson,et al.  On finding the simple paths and circuits in a graph , 1968 .

[2]  Roberto Sebastiani,et al.  Axiom Pinpointing in Lightweight Description Logics via Horn-SAT Encoding and Conflict Analysis , 2009, CADE.

[3]  Rafael Peñaloza,et al.  Automata-Based Axiom Pinpointing , 2010, Journal of Automated Reasoning.

[4]  Georg Gottlob,et al.  Identifying the Minimal Transversals of a Hypergraph and Related Problems , 1995, SIAM J. Comput..

[5]  Ian Horrocks,et al.  From SHIQ and RDF to OWL: the making of a Web Ontology Language , 2003, J. Web Semant..

[6]  J. Y. Yen.  Finding the K Shortest Loopless Paths in a Network , 1971 .

[7]  Gert Smolka,et al.  Attributive Concept Descriptions with Complements , 1991, Artif. Intell..

[8]  Diego Calvanese,et al.  The Description Logic Handbook: Theory, Implementation, and Applications , 2003, Description Logic Handbook.

[9]  Matthew Horridge,et al.  Supporting Early Adoption of OWL 1.1 with Protege-OWL and FaCT++ , 2006, OWLED.

[10]  Mihalis Yannakakis,et al.  On Generating All Maximal Independent Sets , 1988, Inf. Process. Lett..

[11]  Rafael Peñaloza,et al.  Pinpointing in the Description Logic EL , 2007, Description Logics.

[12]  Jean H. Gallier,et al.  Linear-Time Algorithms for Testing the Satisfiability of Propositional Horn Formulae , 1984, J. Log. Program..

[13]  Leonid Khachiyan,et al.  On the Complexity of Dualization of Monotone Disjunctive Normal Forms , 1996, J. Algorithms.

[14]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[15]  Sebastian Brandt,et al.  Polynomial Time Reasoning in a Description Logic with Existential Restrictions, GCI Axioms, and - What Else? , 2004, ECAI.

[16]  Holger Knublauch,et al.  The Protégé OWL Plugin: An Open Development Environment for Semantic Web Applications , 2004, SEMWEB.

[17]  James A. Hendler,et al.  Swoop: A Web Ontology Editing Browser , 2006, J. Web Semant..

[18]  Franz Baader,et al.  How Pervasive Is the Myerson-Satterthwaite Impossibility? , 2009, IJCAI.

[19]  Guilin Qi,et al.  A Modularization-Based Approach to Finding All Justifications for OWL DL Entailments , 2008, ASWC.

[20]  Bijan Parsia,et al.  Debugging OWL ontologies , 2005, WWW '05.

[21]  Bijan Parsia,et al.  Finding All Justifications of OWL DL Entailments , 2007, ISWC/ASWC.

[22]  Rafael Peñaloza,et al.  Axiom Pinpointing in General Tableaux , 2007, TABLEAUX.

[23]  Bijan Parsia,et al.  Explaining Inconsistencies in OWL Ontologies , 2009, SUM.

[24]  Rafael Peñaloza,et al.  Axiom Pinpointing is Hard , 2009, Description Logics.

[25]  Stefan Schlobach,et al.  Non-Standard Reasoning Services for the Debugging of Description Logic Terminologies , 2003, IJCAI.

[26]  Daniele Pretolani,et al.  Finding the K shortest hyperpaths using reoptimization , 2006, Oper. Res. Lett..

[27]  Bijan Parsia,et al.  Laconic and Precise Justifications in OWL , 2008, SEMWEB.

[28]  Jeff Z. Pan,et al.  Finding Maximally Satisfiable Terminologies for the Description Logic ALC , 2006, AAAI.

[29]  Raymond Reiter,et al.  A Theory of Diagnosis from First Principles , 1986, Artif. Intell..