Alternation and the computational complexity of logic programs
Journal of Logic Programming
Generalized subsumption and its applications to induction and redundancy
Artificial Intelligence
Foundations of deductive databases and logic programming
Inductive inference of monotonic formal systems from positive data
New Generation Computing - Selected papers from the international workshop on algorithmic learning theory,1990
Learning elementary formal systems
Theoretical Computer Science
An inference method for the complete inverse of relative subsumption
New Generation Computing - Special issue on inductive logic programming 97
Revising the logical foundations of inductive logic programming systems with ground reduced programs
New Generation Computing - Special issue on inductive logic programming 97
Foundations of Inductive Logic Programming
Foundations of Inductive Logic Programming
Finding Hypotheses from Examples by Computing the Least Generalization of Bottom Clauses
DS '98 Proceedings of the First International Conference on Discovery Science
Which Hypotheses Can Be Found with Inverse Entailment?
ILP '97 Proceedings of the 7th International Workshop on Inductive Logic Programming
A completeness theorem and a computer program for finding theorems derivable from given axioms
A completeness theorem and a computer program for finding theorems derivable from given axioms
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Least common generalization under relative subsumption (LGRS) is a fundamental concept in Inductive Logic Programming. In this paper we give several new conditions for the existence of LGRSs. In previous researches the existence of LGRSs was guaranteed when a background theory is logically equivalent to conjunction of finitely many ground literals. Each of our conditions allows a background theory to have clauses with variables in it. The conditions are obtained using the bottom method (or the bottom generalization method), with which any clause subsuming a positive example relative to a background theory can be derived. We also compare the conditions with those for the existence of relative least generalizations under generalized subsumption (LGGSs).