Learning Singly-Recursive Relations from Small Datasets

The inductive logic programming system LOPSTER was created to demonstrate the advantage of basing induction on logical implication rather than -subsumption. LOPSTER's sub-uni cation procedures allow it to induce recursive relations using a minimum number of examples, whereas inductive logic programming algorithms based on -subsumption require many more examples to solve induction tasks. However, LOPSTER's input examples must be carefully chosen; they must be along the same inverse resolution path. We hypothesize that an extension of LOPSTER can e ciently induce recursive relations without this requirement. We introduce a generalization of LOPSTER named CRUSTACEAN that has this capability and empirically evaluate its ability to induce recursive relations.