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- W2790318756 abstract "In this paper we present an algorithmic method of lemma introduction. Given a proof in predicate logic with equality the algorithm is capable of introducing several universal lemmas. The method is based on an inversion of Gentzen’s cut-elimination method for sequent calculus. The first step consists of the computation of a compact representation (a so-called decomposition) of Herbrand instances in a cut-free proof. Given a decomposition the problem of computing the corresponding lemmas is reduced to the solution of a second-order unification problem (the solution conditions). It is shown that that there is always a solution of the solution conditions, the canonical solution. This solution yields a sequence of lemmas and, finally, a proof based on these lemmas. Various techniques are developed to simplify the canonical solution resulting in a reduction of proof complexity. Moreover, the paper contains a comprehensive empirical evaluation of the implemented method and gives an application to a mathematical proof." @default.
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- W2790318756 date "2018-03-23" @default.
- W2790318756 modified "2023-10-01" @default.
- W2790318756 title "On the Generation of Quantified Lemmas" @default.
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- W2790318756 doi "https://doi.org/10.1007/s10817-018-9462-8" @default.
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