A Strategy for Constructing New Predicates in First-Order Logic

There is increasing interest within the Machine Learning community in systems which automatically reformulate their problem representation by deening and constructing new predicates. A previous paper discussed such a system, called CIGOL, and gave a derivation for the mechanism of inverting individual steps in rst order resolution proofs. In this paper we describe an enhancement to CIGOL's learning strategy which strongly constrains the formation of new concepts and hypotheses. The new strategy is based on results from algorithmic information theory. Using these results it is possible to compute the probability that the simpliications produced by adopting new concepts or hypotheses are not based on chance regularities within the examples. This can be derived from the amount of information compression produced by replacing the examples with the hypothesised concepts. CIGOL's improved performance, based on an approximation of this strategy, is demonstrated by way of the automatic \discovery" of the concept of radiation. This example also demonstrates CIGOL's ability to ignore irrelevant background knowledge and deal with multiple interacting concepts.

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