Negation as a specializing operator

This paper proposes a novel operator, based on the negation, for specializing the hypotheses inductively generated by any system that learns structural descriptions from positive and negative examples or, equivalently, learns intensional definitions of logical relations. Such a specializing operator adds the negation of one or more literals of a misclassified example to the Horn clause representation of an inconsistent hypothesis, after having properly turned constants into variables. The search for the literals to be added is firstly performed in a set named reduced base of consistent specializations and, in case of failure, it is extended to the augmented base of consistent specializations. Indeed, two theorems prove that clauses generated by adding literals in the former set preserve the consistency property and are most general specializations of the inconsistent hypothesis. On the contrary, the consistency property of clauses generated by adding literals in the latter set has to be checked on the misclassified example. The search strategy takes advantage of the structure of the set of the linked Horn clauses, , ordered by the generality relation (≤). Some clarifying examples and experimental results are also presented.