Automatic Selection of Search-guiding Heuristics for Theorem Proving

Theorem proving essentially amounts to solving search problems. The intricacy of these in general undecidable problems makes the use of appropriate search-guiding heuristics indispensable. However, the appropriateness of a heuristic critically depends on the problem to be solved. Given a set of heuristics to choose from, selecting a suitable heuristic is hence a crucial, but also a very diicult task. It is usually taken care of by a proocient user, because it is very hard to determine the suitability of a certain heuristic based on a given problem to be solved. We propose here to automate the selection of heuristics using machine-learning techniques which ground their decisions on past problem-solving experience. Experimental studies conducted in a very diicult area of theorem proving, namely equational reasoning, demonstrate the capacity of the techniques and underline their potential to be a very useful tool for eliminating human interaction requiring expert knowledge.