Learning from Positive Data Based on the MINL Strategy with Refinement Operators

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In the present paper we clarify the combination of the MINL (MINimal Langugae) strategy and refinement operators in the model of identification in the limit from positive data, by giving a learning procedure in a general form adopting both of the two. The MINL strategy is to choose minimal concepts consistent with given examples as guesses, and has been adopted in many previous works in the model. The minimality of concepts is defined w.r.t. the set-inclusion relation, and so the strategy is semantic-based. Refinement operators have developed in the field of learning logic programs to construct logic programs as hypotheses consistent with logical formulae given as examples. The operators are defined based on inference rules in first-order logic and so are syntactical. With the proposed procedure we give such a new class of tree pattern languages that every finite unions of the languages is identifiable from positive data without assuming the upperbound of the number of unions. Moreover, we revise the algorithm so that we can show that the class is polynomial time identifiable.