Predicate invention and utilization

Abstract Inductive logic programming (ILP) involves the synthesis of logic programs from examples. In terms of scientific theory formation ILP systems define observational predicates in terms of a set of theoretical predicates. However, certain basic theorems indicate that with an inadequate theoretical vocabulary this is not always possible. Predicate invention is the augmentation of a given theoretical vocabulary to allow finite axiomatization of the observational predicates. New theoretical predicates need to be chosen from a well-defined universe of such predicates. In this paper a partial order of utilization is described over such a universe. This ordering is a special case of a logical translation. The notion of utilization allows the definition of an equivalence relationship over new predicates. In a manner analogous to Plotkin, clause refinement is defined relative to given background knowledge and a universe of new predicates. It is shown that relative least clause refinement is defined and uniq...

[1]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[2]  S. C. Kleene,et al.  Finite Axiomatizability of Theories in the Predicate Calculus Using Additional Predicate Symbols , 1952 .

[3]  Allen Goldberg,et al.  DTRE - A Semi-Automatic Transformation System , 1991 .

[4]  G. Plotkin.  Automatic Methods of Inductive Inference , 1972 .

[5]  John Wylie Lloyd,et al.  Foundations of Logic Programming , 1987, Symbolic Computation.

[6]  H. Rice.  Classes of recursively enumerable sets and their decision problems , 1953 .

[7]  Stephen Muggleton,et al.  Protein secondary structure prediction using logic-based machine learning , 1992 .

[8]  Ehud Shapiro,et al.  Algorithmic Program Debugging , 1983 .

[9]  Richard A. Lewis,et al.  Drug design by machine learning: the use of inductive logic programming to model the structure-activity relationships of trimethoprim analogues binding to dihydrofolate reductase. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Władysław Turski,et al.  The specification of computer programs , 1987 .

[11]  Stephen Muggleton,et al.  Machine Invention of First Order Predicates by Inverting Resolution , 1988, ML.

[12]  Herbert B. Enderton,et al.  A mathematical introduction to logic , 1972 .

[13]  Stephen Muggleton,et al.  Efficient Induction of Logic Programs , 1990, ALT.

[14]  Rüdiger Wirth,et al.  Constraints on Predicate Invention , 1991, ML.