Abstract

We describe here a prover PC that normally acts as an ordinary theorem prover, but which returns a "precondition" when it is unable to prove the given formula. If F is the formula attempted to be proved and PC returns the precondition Q, then (Q \Gamma! F ) is a theorem (that PC can prove). This prover, PC, uses a Proof-Plan. In its simplest mode, when there is no proof-plan, it acts like ordinary Abduction. We show here how this method can be used to derive certain proofs by analogy. To do this, it uses a proof-plan from a given guiding proof to help construct the proof of a similar theorem, by "debugging" (automatically) that proof-plan. We show here the analogy proofs of a few simple example theorems and one hard pair, Ex4 and Ex4L. The given proof-plan for Ex4 is used by the system to prove automatically Ex4; and that same proof-plan is then used to prove Ex4L, during which the proof-plan is "debugged" (automatically). These two examples are similar to two other, more difficult, t...

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