Existence and nonexistence of complete refinement operators
ECML-94 Proceedings of the European conference on machine learning on Machine Learning
Foundations of Inductive Logic Programming
Foundations of Inductive Logic Programming
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Learning from good data and bad
Learning from good data and bad
QG/GA: a stochastic search for Progol
Machine Learning
A genetic algorithms approach to ILP
ILP'02 Proceedings of the 12th international conference on Inductive logic programming
Lattice-search runtime distributions may be heavy-tailed
ILP'02 Proceedings of the 12th international conference on Inductive logic programming
On generalization and subsumption for ordered clauses
JSAI'05 Proceedings of the 2005 international conference on New Frontiers in Artificial Intelligence
ProGolem: a system based on relative minimal generalisation
ILP'09 Proceedings of the 19th international conference on Inductive logic programming
ILP'10 Proceedings of the 20th international conference on Inductive logic programming
Speeding up planning through minimal generalizations of partially ordered plans
ILP'10 Proceedings of the 20th international conference on Inductive logic programming
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Searching the hypothesis space bounded below by a bottom clause is the basis of several state-of-the-art ILP systems (e.g. Progol, Aleph). These systems use refinement operators together with search heuristics to explore a bounded hypothesis space. It is known that the search space of these systems is limited to a sub-graph of the general subsumption lattice. However, the structure and properties of this sub-graph have not been properly characterised. In this paper firstly, we characterise the hypothesis space considered by the ILP systems which use a bottom clause to constrain the search. In particular, we discuss refinement in Progol as a representative of these ILP systems. Secondly, we study the lattice structure of this bounded hypothesis space. Thirdly, we give a new analysis of refinement operators, least generalisation and greatest specialisation in the subsumption order relative to a bottom clause. The results of this study are important for better understanding of the constrained refinement space of ILP systems such as Progol and Aleph, which proved to be successful for solving real-world problems (despite being incomplete with respect to the general subsumption order). Moreover, characterising this refinement sub-lattice can lead to more efficient ILP algorithms and operators for searching this particular sub-lattice. For example, it is shown that, unlike for the general subsumption order, efficient least generalisation operators can be designed for the subsumption order relative to a bottom clause.