Partial Matching for Analogy Discovery in Proofs and Counter-Examples

The problem of analogy in theorem proving has been studied for several years now (see 5, 10, 12] for example). Those works restrict the use of analogy to proofs, disregarding the possibilities of using analogy also for counterexamples construction. Moreover, they deal with the problem of proving a new theorem once an appropriate source theorem has been provided as a guideline. We overcome these drawbacks by using a method for model construction developed in our group and by generalizing proofs (or counterexamples constructions) before including them in the database of source examples. Analogy discovery relies on partial matching between a target statement, and a source (generalized) refutation or counterexample construction, thus allowing more targets to be regarded as \analogous" to a source. It increases the power of an analogy-based prover, by recognizing subgoals within a source refu-tation or model building. We use in this purpose notions of graph cut sets, and incremental update of statements.