Craig Interpolation with Clausal First-Order Tableaux

We develop foundations for computing Craig-Lyndon interpolants of two given formulas with first-order theorem provers that construct clausal tableaux. Provers that can be understood in this way include efficient machine-oriented systems based on calculi of two families: goal-oriented such as model elimination and the connection method, and bottom-up such as the hypertableau calculus. Similar to known resolution-based 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 first-order interpolation based on clausal tableaux.

Authors

• 10 publications
• Craig Interpolation and Access Interpolation with Clausal First-Order Tableaux

We show methods to extract Craig-Lyndon interpolants and access interpol...
02/14/2018 ∙ by Christoph Wernhard, et al. ∙ 0

• The Epsilon Calculus with Equality and Herbrand Complexity

Hilbert's epsilon calculus is an extension of elementary or predicate ca...
04/25/2019 ∙ by Kenji Miyamoto, et al. ∙ 0

• Clause/Term Resolution and Learning in the Evaluation of Quantified Boolean Formulas

Resolution is the rule of inference at the basis of most procedures for ...
09/26/2011 ∙ by E. Giunchiglia, et al. ∙ 0

• Interpolation and the Array Property Fragment

Interpolation based software model checkers have been successfully emplo...
04/25/2019 ∙ by Jochen Hoenicke, et al. ∙ 0

• Symmetries of Quantified Boolean Formulas

While symmetries are well understood for Boolean formulas and successful...
02/12/2018 ∙ by Manuel Kauers, et al. ∙ 0

• PIE – Proving, Interpolating and Eliminating on the Basis of First-Order Logic

PIE is a Prolog-embedded environment for automated reasoning on the basi...
08/29/2019 ∙ by Christoph Wernhard, et al. ∙ 0