Experiments in the heuristic use of past proof experience

Abstract

Problems in automated deduction essentially amount to hard search problems. Powerful search-guiding heuristics are indispensable if difficult problems are to be handled. A promising and natural way to improve the performance of heuristics is to learn from previous experience. We present heuristics that follow this approach. A first heuristic attempts to re-enact a proof of a proof problem found in the past in a flexible way in order to find a proof of a similar problem. A further heuristic employs “features” in connection with past proof experience to prune the search space. Both heuristics not only allow for substantial speed-ups, but also make it possible to prove problems that were out of reach when using socalled basic heuristics. A combination of these two heuristics can further increase performance. We demonstrate the power of our heuristics in the light of problems stemming from the study of logic calculi in connection with an inference rule called “condensed detachment”. These problems are widely acknowledged as prominent test sets for automated deduction systems and their search-guiding heuristics. We compare our results with the results the creators of Otter obtained with this renowned theorem prover and this way substantiate our achievements.

This work was supported by the Deutsche Forschungsgemeinschaft (DFG).