Abstract

This paper firstly provides a re-appraisal of the development of techniques for inverting deduction, secondly introduces Mode-Directed Inverse Entailment (MDIE) as a generalisation and enhancement of previous approaches and thirdly describes an implementation of MDIE in the Progol system. Progol is implemented in C and available by anonymous ftp. The re-assessment of previous techniques in terms of inverse entailment leads to new results for learning from positive data and inverting implication between pairs of clauses.

Citations

4403	A mathematical theory of communication - Shannon - 1948
1739	Foundations of Logic Programming - Lloyd - 1984
1412	An Introduction to Kolmogorov Complexity and Its Applications - Li, Vitanyi - 1997
962	Efficient induction of logic programs - Muggleton, Feng - 1990
891	Modeling by shortest data description - Rissanen - 1978
829	A Machine–oriented Logic Based on the Resolution Principle - Robinson - 1965
793	Language identification in the limit - Gold - 1967
784	Learning logical definitions from relations - Quinlan - 1989
464	F.: Abductive Logic Programming - Kakas, Kowalski, et al. - 1992
439	Algorithmic Program Debugging - Shapiro - 1983
408	Raedt. Inductive logic programming: Theory and methods - Muggleton, de - 1994
162	Machine invention of first-order predicates by inverting resolution - Muggleton, Buntine - 1988
141	Theories for mutagenicity: A study in first-order and feature-based induction - Srinivasan, Muggleton, et al. - 1996
96	Drug design by machine learning: the use of inductive logic programming to model the structure-activity relationships of trimethoprim analogues binding to dihydrofolate reductase - RD, Muggleton, et al. - 1992
93	Transformational systems and the algebraic structure of atomic formulas - Reynolds - 1970
85	Protein secondary structure prediction using logic-based machine learning - Muggleton, King, et al. - 1992
85	Mutagenesis: ILP experiments in a non-determinate biological domain - Srinivasan, Muggleton, et al. - 1994
75	Automatic methods of inductive inference - Plotkin - 1971
68	The Application of Inductive Logic Programming to Finite Element Mesh Design - Dolsak, Muggleton - 1992
62	A note on inductive generalisation - Plotkin - 1970
55	Non-monotonic learning - Bain, Muggleton - 1992
48	Extensions of Inversion of Resolution Applied to Theory Completion - Rouveirol - 1992
43	A completeness theorem and a computer program for finding theorems derivable from given axioms - Lee - 1967
39	Compression, Significance and Accuracy - Muggleton, Srinivasan, et al. - 1992
33	Learning qualitative models of dynamic systems - Srinivasan, Bratko, et al. - 1992
33	Learning the past tense of English verbs: The symbolic Pattern Associator vs. Connectionist Models - Ling - 1994
31	Inductive logic programming: derivations, successes and shortcomings - Muggleton - 1994
30	Incremental Generation of VL1 Hypotheses: The Underlying Methodology and the Description of Program AQ11 - Michalski, Larson - 1983
29	1987], `Subsumption and implication - Gottlob
29	Sub-unification: a tool for efficient induction of recursive programs - Lapointe, Matwin - 1992
28	An Oracle Based Approach to Constructive Induction - Duce - 1987
26	Inverting implication - Muggleton - 1994
22	Completing logic programs by inverse resolution - Wirth - 1989
19	Learnability of Restricted Logic Programs - Cohen - 1993
18	A Learnability Model for Universal Representations - Muggleton, Page - 1995
17	Predicate invention and utilization - Muggleton - 1994
15	A strategy for constructing new predicates in first order logic - Muggleton - 1988
14	Complexitybased induction - Conklin, Witten - 1994
12	Inducing temporal fault dignostic rules from a qualitative model - Feng - 1992
12	Generalisation of Clauses - Idestam-Almquist - 1993
10	Combinatorics: Theory and Applications - Krishnamurthy
10	An experiment in automatic induction - Popplestone - 1969
9	Inverting the resolution principle - Muggleton - 1991
6	Self-saturation of definite clauses - Muggleton, Page - 1994
6	Beyond first-order learning: inductive learning with higher-order logic - Muggleton, Page - 1994
6	Past tenses of verbs and first-order learning - Quinlan - 1993
5	The Principles of Science: a Treatise on Logic and Scientific Method - Jevons - 1874
4	A simple and general solution for inverting resolution - Rouveirol, Puget - 1989
3	Confirmation theory and machine learning - Gillies - 1992
3	an optimized model inference system - Markus - 1992