A Constraint-based Induction Algorithm in FOL

Michèle Sebag

Abstract: We present a bottom-up generalization which builds the maximally general terms covering a positive example and rejecting negative examples in first-order logic (FOL), i.e. in terms of Version Spaces, the set G. This algorithm is based on rewriting negative examples as constraints upon the generalization of the positive example at hand. The constraints space is partially ordered, inducing a partial order on negative examples; the near-misses as defined by Winston can then be formalized in FOL as negative examples minimal with respect to this partial order. As expected, only near-misses are necessary to build the set G. Moreover, constraints can be used directly to classify further examples.