
Craig Interpolation and Access Interpolation with Clausal FirstOrder Tableaux
We show methods to extract CraigLyndon interpolants and access interpol...
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The adaptive interpolation method for proving replica formulas. Applications to the CurieWeiss and Wigner spike models
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Craig Interpolation with Clausal FirstOrder Tableaux
We develop foundations for computing CraigLyndon interpolants of two given formulas with firstorder theorem provers that construct clausal tableaux. Provers that can be understood in this way include efficient machineoriented systems based on calculi of two families: goaloriented such as model elimination and the connection method, and bottomup such as the hypertableau calculus. Similar to known resolutionbased interpolation methods our method proceeds in two stages. The first stage is an induction on the tableau structure, which is sufficient to compute propositional interpolants. We show that this can linearly simulate different prominent propositional interpolation methods that operate by an induction on a resolution deduction tree. In the second stage, interpolant lifting, quantified variables that replace certain terms (constants and compound terms) by variables are introduced. Correctness of this second stage was apparently shown so far on the basis of resolution and paramodulation with an error concerning equality, on the basis of resolution with paramodulation and superposition for a special case, and on the basis of a natural deduction calculus without taking equality into special account. Here the correctness of interpolant lifting is justified abstractly on the basis of Herbrand's theorem and based on a different characterization of the formulas to be lifted than in the literature (without taking equality into special account). In addition, we discuss various subtle aspects that are relevant for the investigation and practical realization of firstorder interpolation based on clausal tableaux.
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