Proving Inductive Properties of Prolog Programs in Second-Order Intuitionistic Logic

We use second-order intuitionistic logic for two purposes in this paper: first, to formulate a large class of circumscriptive queries about logic programs; and second, to formulate a class of induction schemata that can be used to answer these queries. Then, applying the techniques of intuitionistic logic programming, we develop an interpreter (written in PROLOG) that constructs inductive proofs and answers circumscriptive queries automatically. As an illustration, we prove the symmetry of ‘Reverse’, the associativity of ‘Plus’ and the commutativity of ‘Times’.