On generating all maximal independent sets
Information Processing Letters
Attributive concept descriptions with complements
Artificial Intelligence
Identifying the Minimal Transversals of a Hypergraph and Related Problems
SIAM Journal on Computing
Generating all maximal models of a Boolean expression
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
An efficient algorithm for the minimal unsatisfiability problem for a subclass of CNF
Annals of Mathematics and Artificial Intelligence
Hybrid Inferences in KL-ONE-Based Knowledge Representation Systems
GWAI '90 Proceedings of the 14th German Workshop on Artificial Intelligence
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
DATE '03 Proceedings of the conference on Design, Automation and Test in Europe - Volume 1
WWW '05 Proceedings of the 14th international conference on World Wide Web
Finding maximally satisfiable terminologies for the description logic ALC
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Non-standard reasoning services for the debugging of description logic terminologies
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
On finding all minimally unsatisfiable subformulas
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
CEL: a polynomial-time reasoner for life science ontologies
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Discovery of minimal unsatisfiable subsets of constraints using hitting set dualization
PADL'05 Proceedings of the 7th international conference on Practical Aspects of Declarative Languages
The Logical Difference Problem for Description Logic Terminologies
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Laconic and Precise Justifications in OWL
ISWC '08 Proceedings of the 7th International Conference on The Semantic Web
A Kernel Revision Operator for Terminologies -- Algorithms and Evaluation
ISWC '08 Proceedings of the 7th International Conference on The Semantic Web
A Modularization-Based Approach to Finding All Justifications for OWL DL Entailments
ASWC '08 Proceedings of the 3rd Asian Semantic Web Conference on The Semantic Web
Usability Issues in Description Logic Knowledge Base Completion
ICFCA '09 Proceedings of the 7th International Conference on Formal Concept Analysis
Some Computational Problems Related to Pseudo-intents
ICFCA '09 Proceedings of the 7th International Conference on Formal Concept Analysis
Axiom Pinpointing in Lightweight Description Logics via Horn-SAT Encoding and Conflict Analysis
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Explaining Inconsistencies in OWL Ontologies
SUM '09 Proceedings of the 3rd International Conference on Scalable Uncertainty Management
ISWC '09 Proceedings of the 8th International Semantic Web Conference
A Conflict-Based Operator for Mapping Revision
ISWC '09 Proceedings of the 8th International Semantic Web Conference
A Relevance-Directed Algorithm for Finding Justifications of DL Entailments
ASWC '09 Proceedings of the 4th Asian Conference on The Semantic Web
Complexity of Axiom Pinpointing in the DL-Lite Family of Description Logics
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Reasoning and explanation in EL and in expressive description logics
ReasoningWeb'10 Proceedings of the 6th international conference on Semantic technologies for software engineering
Root justifications for ontology repair
RR'11 Proceedings of the 5th international conference on Web reasoning and rule systems
The justificatory structure of the NCBO bioportal ontologies
ISWC'11 Proceedings of the 10th international conference on The semantic web - Volume Part I
An algorithm for axiom pinpointing in EL+ and its incremental variant
Proceedings of the 20th ACM international conference on Information and knowledge management
Context-dependent views to axioms and consequences of Semantic Web ontologies
Web Semantics: Science, Services and Agents on the World Wide Web
A generic approach for correcting access restrictions to a consequence
ESWC'10 Proceedings of the 7th international conference on The Semantic Web: research and Applications - Volume Part I
Structural distance between EL+ concepts
MIWAI'11 Proceedings of the 5th international conference on Multi-Disciplinary Trends in Artificial Intelligence
The logical difference for the lightweight description logic EL
Journal of Artificial Intelligence Research
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Axiom pinpointing has been introduced in description logics (DLs) to help the user understand the reasons why consequences hold by computing minimal subsets of the knowledge base that have the consequence in question. Until now, the pinpointing approach has only been applied to the DL $\mathcal {ALC}$ and some of its extensions. This paper considers axiom pinpointing in the less expressive DL $\mathcal {EL}^+$, for which subsumption can be decided in polynomial time. More precisely, we consider an extension of the pinpointing problem where the knowledge base is divided into a staticpart, which is always present, and a refutablepart, of which subsets are taken. We describe an extension of the subsumption algorithm for $\mathcal {EL}^+$ that can be used to compute all minimal subsets of (the refutable part of) a given TBox that imply a certain subsumption relationship. The worst-case complexity of this algorithm turns out to be exponential. This is not surprising since we can show that a given TBox may have exponentially many such minimal subsets. However, we can also show that the problem is not even output polynomial, i.e., unless P=NP, there cannot be an algorithm computing all such minimal sets that is polynomial in the size of its input and output. In addition, we show that finding out whether there is such a minimal subset within a given cardinality bound is an NP-complete problem. In contrast to these negative results, we also show that one such minimal subset can be computed in polynomial time. Finally, we provide some encouraging experimental results regarding the performance of a practical algorithm that computes one (small, but not necessarily minimal) subset that has a given subsumption relation as consequence.