In this talk, we introduce the key model-theoretic aspects of Parametric logic and its hierarchies. We establish connections with Learning theory. We illustrate the relevance of Parametric logic for nonmonotonic reasoning. Finally, we introduce RichProlog, an extension of Prolog based on Parametric logic, for a declarative approach to solving problems whose nature involves both deduction and induction.

The naturalness of the approach is attested by fundamental connections with notions from formal learning theory — classification in the limit, with or without a bounded number of mind changes — and from topology — in reference to the Borel and difference hierarchies.