Existence and nonexistence of complete refinement operators
ECML-94 Proceedings of the European conference on machine learning on Machine Learning
Minimal Generalizations under OI-Implication
ISMIS '02 Proceedings of the 13th International Symposium on Foundations of Intelligent Systems
Searching the Subsumption Lattice by a Genetic Algorithm
ILP '00 Proceedings of the 10th International Conference on Inductive Logic Programming
A Refinement Operator for Description Logics
ILP '00 Proceedings of the 10th International Conference on Inductive Logic Programming
A Refinement Operator for Theories
ILP '01 Proceedings of the 11th International Conference on Inductive Logic Programming
A Note on Refinement Operators for IE-Based ILP Systems
ILP '08 Proceedings of the 18th international conference on Inductive Logic Programming
ProGolem: a system based on relative minimal generalisation
ILP'09 Proceedings of the 19th international conference on Inductive logic programming
Compile the Hypothesis Space: Do it Once, Use it Often
Fundamenta Informaticae - Progress on Multi-Relational Data Mining
A Dichotomic Search Algorithm for Mining and Learning in Domain-Specific Logics
Fundamenta Informaticae - Advances in Mining Graphs, Trees and Sequences
A Generalization Model Based on OI-implication for Ideal heory Refinement
Fundamenta Informaticae - Intelligent Systems
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Our aim is to construct a perfect (i.e. minimal and optimal) ILP refinement operator for hypotheses spaces bounded below by a most specific clause and subject to syntactical restrictions in the form of input/output variable declarations (like in Progol). Since unfortunately no such optimal refinement operators exist, we settle for a weaker form of optimality and introduce an associated weaker form of subsumption which exactly captures a first incompleteness of Progol's refinement operator. We argue that this sort of incompleteness is not a drawback, as it is justified by the examples and the MDL heuristic. A second type of incompleteness of Progol (due to subtle interactions between the requirements of non-redundancy, completeness and the variable dependencies) is more problematic, since it may sometimes lead to unpredictable results. We remove this incompleteness by constructing a sequence of increasingly more complex refinement operators which eventually produces the first (weakly) perfect refinement operator for a Progol-like ILP system.