Logical Settings for Concept-Learning

Abstract Three different formalizations of concept-learning in logic (as well as some variants) are analyzed and related. It is shown that learning from interpretations reduces to learning from entailment, which in turn reduces to learning from satisfiability. The implications of this result for inductive logic programming and computational learning theory are then discussed, and guidelines for choosing a problem-setting are formulated.

[1]  Luc De Raedt,et al.  First-Order jk-Clausal Theories are PAC-Learnable , 1994, Artif. Intell..

[2]  Luc De Raedt,et al.  Learning from satisfiability , 1997 .

[3]  Leslie G. Valiant,et al.  Computational limitations on learning from examples , 1988, JACM.

[4]  Michael R. Genesereth,et al.  Logical foundations of artificial intelligence , 1987 .

[5]  Saso Dzeroski,et al.  The ILP description learning problem: Towards a general model-level definition of data mining in ILP , 1995 .

[6]  Leonard Pitt,et al.  Prediction-Preserving Reducibility , 1990, J. Comput. Syst. Sci..

[7]  Luc De Raedt,et al.  Inductive Logic Programming: Theory and Methods , 1994, J. Log. Program..

[8]  William W. Cohen.  Pac-Learning Non-Recursive Prolog Clauses , 1995, Artif. Intell..

[9]  Saso Dzeroski,et al.  Inductive logic programming and learnability , 1994, SGAR.

[10]  Tom M. Mitchell,et al.  Generalization as Search , 2002 .

[11]  P. Flach.  Conjectures: an inquiry concerning the logic of induction , 1995 .

[12]  Leslie G. Valiant,et al.  A theory of the learnable , 1984, CACM.

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

[14]  Luc De Raedt,et al.  Multiple Predicate Learning in Two Inductive Logic Programming Settings , 1996, Log. J. IGPL.

[15]  Luc De Raedt,et al.  Inductive Constraint Logic , 1995, ALT.

[16]  Alexander Kogan,et al.  Exploiting the Omission of Irrelevant Data , 1996, ICML.

[17]  Setsuo Arikawa,et al.  Inductive Inference Machines That Can Refute Hypothesis Spaces , 1993, ALT.

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

[19]  Luc De Raedt,et al.  Induction in logic , 1996 .

[20]  Umesh V. Vazirani,et al.  An Introduction to Computational Learning Theory , 1994 .