Existence and nonexistence of complete refinement operators
ECML-94 Proceedings of the European conference on machine learning on Machine Learning
A Polynomial Approach to the Constructive Induction of Structural Knowledge
Machine Learning - Special issue on evaluating and changing representation
On the relative expressiveness of description logics and predicate logics
Artificial Intelligence
The complexity of concept languages
Information and Computation
An epistemic operator for description logics
Artificial Intelligence
{\cal A}{\cal L}-log: Integrating Datalog and Description Logics
Journal of Intelligent Information Systems
Foundations of Inductive Logic Programming
Foundations of Inductive Logic Programming
Some Lower Bounds for the Computational Complexity of Inductive Logic Programming
ECML '93 Proceedings of the European Conference on Machine Learning
Refinement Operators Can Be (Weakly) Perfect
ILP '99 Proceedings of the 9th International Workshop on Inductive Logic Programming
Generalizing Refinement Operators to Learn Prenex Conjunctive Normal Forms
ILP '99 Proceedings of the 9th International Workshop on Inductive Logic Programming
Decidable reasoning in terminological knowledge representation systems
Journal of Artificial Intelligence Research
Computing least common subsumers in description logics with existential restrictions
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
The limits on combining recursive horn rules with description logics
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Inductive Logic Programming
Hybrid Learning of Ontology Classes
MLDM '07 Proceedings of the 5th international conference on Machine Learning and Data Mining in Pattern Recognition
ECML '07 Proceedings of the 18th European conference on Machine Learning
Logic programming languages for databases and the web
A 25-year perspective on logic programming
Induction of concepts in web ontologies through terminological decision trees
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part I
Ideal downward refinement in the EL description logic
ILP'09 Proceedings of the 19th international conference on Inductive logic programming
ORE - a tool for repairing and enriching knowledge bases
ISWC'10 Proceedings of the 9th international semantic web conference on The semantic web - Volume Part II
Class expression learning for ontology engineering
Web Semantics: Science, Services and Agents on the World Wide Web
Creating knowledge out of interlinked data: making the web a data washing machine
Proceedings of the International Conference on Web Intelligence, Mining and Semantics
Introduction to linked data and its lifecycle on the web
RW'11 Proceedings of the 7th international conference on Reasoning web: semantic technologies for the web of data
A counterfactual-based learning algorithm for ALC description logic
AI*IA'05 Proceedings of the 9th conference on Advances in Artificial Intelligence
Towards an inductive methodology for ontology alignment through instance negotiation
ODBASE'06/OTM'06 Proceedings of the 2006 Confederated international conference on On the Move to Meaningful Internet Systems: CoopIS, DOA, GADA, and ODBASE - Volume Part I
Measuring similarity in description logics using refinement operators
ICCBR'11 Proceedings of the 19th international conference on Case-Based Reasoning Research and Development
A bisimulation-based method of concept learning for knowledge bases in description logics
Proceedings of the Third Symposium on Information and Communication Technology
Universal OWL axiom enrichment for large knowledge bases
EKAW'12 Proceedings of the 18th international conference on Knowledge Engineering and Knowledge Management
On c-learnability in description logics
ICCCI'12 Proceedings of the 4th international conference on Computational Collective Intelligence: technologies and applications - Volume Part I
Concept Induction in Description Logics Using Information-Theoretic Heuristics
International Journal on Semantic Web & Information Systems
Introduction to linked data and its lifecycle on the web
RW'13 Proceedings of the 9th international conference on Reasoning Web: semantic technologies for intelligent data access
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While the problem of learning logic programs has been extensively studied in ILP, the problem of learning in description logics (DLs) has been tackled mostly by empirical means. Learning in DLs is however worthwhile, since both Horn logic and description logics are widely used knowledge representation formalisms, their expressive powers being incomparable (neither includes the other as a fragment). Unlike most approaches to learning in description logics, which provide bottom-up (and typically overly specific) least generalizations of the examples, this paper addresses learning in DLs using downward (and upward) refinement operators. Technically, we construct a complete and proper refinement operator for the ALER description logic (to avoid overfitting, we disallow disjunctions from the target DL). Although no minimal refinement operators exist for ALER, we show that we can achieve minimality of all refinement steps, except the ones that introduce the ⊥ concept. We additionally prove that complete refinement operators for ALER cannot be locally finite and suggest how this problem can be overcome by an MDL search heuristic. We also discuss the influence of the Open World Assumption (typically made in DLs) on example coverage.