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This paper describes a tableau-based higher-order theorem prover HOT and an application to natural language semantics. In this application, HOT is used to prove equivalences using world knowledge during higher-order unification (HOU). This extended form of HOU is used to compute the licensing conditions for corrections.
Reusing Proofs
(1999)
We develop a learning component for a theorem prover designed for verifying statements by mathematical induction. If the prover has found a proof, it is analyzed yielding a so-called catch. The catch provides the features of the proof which are relevant for reusing it in subsequent verification tasks and may also suggest useful lemmata. Proof analysis techniques for computing the catch are presented. A catch is generalized in a certain sense for increasing the reusability of proofs. We discuss problems arising when learning from proofs and illustrate our method by several examples.