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A Comparison of Two Proof Critics: Power vs. Robustness

By Louise A. Dennis and Alan Bundy


Abstract. Proof critics are a technology from the proof planning paradigm. They examine failed proof attempts in order to extract information which can be used to generate a patch which will allow the proof to go through. We consider the proof of the "whisky problem", a challenge problem from the domain of temporal logic. The proof requires a generalisation of the original conjecture and we examine two proof critics which can be used to create this generalisation. Using these critics we believe we have produced the first automatic proofs of this challenge problem. We use this example to motivate a comparison of the two critics and propose that there is a place for specialist critics as well as powerful general critics. In particular we advocate the development of critics that do not use meta-variables. 1 Introduction Proof planning is an AI-search based technique for automated proof. It has been applied with particular success to proofs by mathematical induction. A significant component of proof planning is the use of critics to patch failed proof attempts based upon the way in which the proof is proceeding. Proof critics exist which provide generalisations, speculate missing lemmas and revise induction schemes. The "whisky problem " is a challenge problem from the domain of first order temporal logic. Its proof requires induction and a generalisation of the original conjecture. Proof critics appeared to be an obvious technology to use in an attempt to provide an automated proof of this theorem. We use the whisky problem here as a basis for the examination of two generalisation critics. The first of these uses meta-variables which are gradually instantiated as a proof progresses. The second is a more specialised equivalent which did not use such meta-variables. The second critic proved more robust to slight changes to the context in which the proof attempt was performed and illustrated that it is sometimes beneficial to favour a less general solution (if one is available)

Year: 2009
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