A theory of diagnosis from first principles
Artificial Intelligence
On generating all maximal independent sets
Information Processing Letters
The complexity of logic-based abduction
Journal of the ACM (JACM)
Identifying the Minimal Transversals of a Hypergraph and Related Problems
SIAM Journal on Computing
WWW '05 Proceedings of the 14th international conference on World Wide Web
Finding the K shortest hyperpaths
Computers and Operations Research
Computational aspects of monotone dualization: A brief survey
Discrete Applied Mathematics
Pinpointing in the Description Logic $\mathcal {EL}^+$
KI '07 Proceedings of the 30th annual German conference on Advances in Artificial Intelligence
Laconic and Precise Justifications in OWL
ISWC '08 Proceedings of the 7th International Conference on The Semantic Web
Explanation in the DL-Lite Family of Description Logics
OTM '08 Proceedings of the OTM 2008 Confederated International Conferences, CoopIS, DOA, GADA, IS, and ODBASE 2008. Part II on On the Move to Meaningful Internet Systems
Finding maximally satisfiable terminologies for the description logic ALC
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
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
DL-Lite: tractable description logics for ontologies
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Non-standard reasoning services for the debugging of description logic terminologies
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
The DL-lite family and relations
Journal of Artificial Intelligence Research
Axiom Pinpointing in General Tableaux
Journal of Logic and Computation
Finding all justifications of OWL DL entailments
ISWC'07/ASWC'07 Proceedings of the 6th international The semantic web and 2nd Asian conference on Asian semantic web conference
Automata-Based Axiom Pinpointing
Journal of Automated Reasoning
Reasoning about explanations for negative query answers in DL-lite
Journal of Artificial Intelligence Research
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We investigate the complexity of axiom pinpointing for different members of the DL-Lite family of Description Logics. More precisely, we consider the problem of enumerating all minimal subsets of a given DL-Lite knowledge base that have a given consequence. We show that for the DL-LiteHcore, DL-LiteHkrom and DL-LiteHNhorn fragments such minimal subsets are efficiently enumerable with polynomial delay, but for the DL-Litebool fragment they cannot be enumerated in output polynomial time unless P = NP. We also show that interestingly, for the DL-LiteHNhorn fragment such minimal sets can be enumerated in reverse lexicographic order with polynomial delay, but it is not possible in the forward lexicographic order since computing the first one is already coNP-hard.