Strategies in combined learning via logic programs

We discuss the adoption of a three-valued setting for inductive concept lea rning. Distinguishing between what is true, what is false and what is unkno wn can be useful in situations where decisions have to be taken on the basi s of scarce, ambiguous, or downright contradictory information. In a three- valued setting, we learn a definition for both the target concept and its o pposite, considering positive and negative examples as instances of two dis joint classes. To this purpose, we adopt Extended Logic Programs (ELP) unde r a Well-Founded Semantics with explicit negation (WFSX) as the representat ion formalism for learning, and show how ELPs can be used to specify combin ations of strategies in a declarative way also coping with contradiction an d exceptions. Explicit negation is used to represent the opposite concept, while default negation is used to ensure consistency and to handle exceptions to general rules. Exceptions are represented by examples covered by the definition for a concept that belong to the training set for the opposite concept. Standard Inductive Logic Programming techniques are employed to learn the c oncept and its opposite. Depending on the adopted technique, we can learn t he most general or the least general definition. Thus, four epistemological varieties occur, resulting from the combination of most general and least general solutions for the positive and negative concept. We discuss the fac tors that should be taken into account when choosing and strategically comb ining the generality levels for positive and negative concepts. In the paper, we also handle the issue of strategic combination of possibly contradictory learnt definitions of a predicate and its explicit negation. All in all, we show that extended logic programs under well-founded semanti cs with explicit negation add expressivity to learning tasks, and allow the tackling of a number of representation and strategic issues in a principle d way. Our techniques have been implemented and examples run on a state-of-the-art logic programming system with tabling which implements WFSX.