Details of Grant 

EPSRC Reference:	GR/J46623/01
Title:	EXPERIMENTAL APPPLICATION AND DEVELOPMENT OF INDUCTIVE LOGIC PROGRAMMING
Principal Investigator:	Muggleton, Professor S
Other Investigators:
Researcher Co-Investigators:
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Department:	Computer Science
Organisation:	University of Oxford
Scheme:	Standard Research (Pre-FEC)
Starts:	01 January 1994	Ends:	31 December 1996	Value (£):	142,358
EPSRC Research Topic Classifications:	Artificial Intelligence
EPSRC Industrial Sector Classifications:
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Summary on Grant Application Form
Inductive Logic Programming (ILP) is a form of Machine Learning in which logical theories are constructed from objective data and human supplied background knowledge. The objective of this project is to test the contention that in scientific and engineering domains, ILP will significantly out-perform simpler feature-based methods of theory-formation. Progress:The research proposal stated that two shortcomings of existing ILP systems would be addressed during the course of this project: 1. The problem of hypothesis confirmation in ILP; and2. Incorporating numerical constraint handling in ILP.We first describe briefly the results of our investigation into these issues over the past year, and then mention a new ILP system that has been developed to overcome these problems1. Hypothesis ConfirmationPresent ILP systems construct logical theories which are treated as being completely true. There has been some theoretical study of the conditions under which the complexities of rival theories can be used as a guide to their predictivities on new data. We undertook an experimental analysis of this question, using the ILP system Golem to find theories for illegal positions in the chess end-game king and rook against king (KRK) in the presence of artificially introduced classification noise. Using a measure of complexity that essentially counts the symbols in a theory, that shorter theories for the data did indeed have higher predictive power on a new data set of KRK positions. Our results suggest that the complexity of theories could be a reliable method of selecting theories that are better confirmed by the data. We plan to repeat these experiments on a different domain. This work is being done in collaboration with Professor Donald Michie, and we expect to present the results at the 15th Machine Intelligence Workshop. 2. Numerical Constraints A major drawback with ILP systems (like Golem) is that they have very primitive number-handling capabilities. This is largely due to the fact that they are a) restricted to using ground background knowledge; and b) incapable of utilising existing statistical techniques like regression when constructing their theories. While various ad-hoc or specialist solutions are possible, the only general-purpose method is to provide the ILP system with the capability of using general-purpose definitions of linear inequalities, and the ability to call any numerical calculation routine as and when it may be required. We have adopted the latter view and developed a new ILP system Progol that has such capabilities. 3. ProgrolThe Progol system developed over the course of the past year carries out a complete, though admissibly pruned, best-first search through the refinement lattice of definite clauses. Progol accepts non-ground, non-determinate Prolog clauses as background knowledge. On the basis of our research into the relationship of theory complexity and predictive power, each learned clause is guaranteed to be the least complex explanation for the examples it explains. Unlike Golem, Progol can construct theories with numerical constraints in the form of a) linear equations, by calling background predicate definitions that invoke standard library procedures to construct the equations; or b) linear equalities, by simply executing their logic-programe definitions in the background knowledge. With Progol, we have also introduced a special form of inverting resolution, termed mode-directed inverse resolution . An initial, completely working implementation of Progol was written in the Prolog language. This was then superseded by more efficient implementation in the C language. The description of mode-directed inverse resolution will appear in Machine Intelligence, Vol.14.
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Organisation Website:	http://www.ox.ac.uk