🤖 AI Summary
This work addresses the automation challenge of interpolation construction in mechanized knowledge processing. Methodologically, it proposes an efficient interpolation generation framework based on first-order logic automated theorem proving: (i) a two-stage Craig interpolation construction integrating clause-tableaux and resolution inference, lifting propositional interpolation to quantified formulas; (ii) equality encoding to enhance theoretical expressiveness while ensuring applicability under restricted preprocessing; and (iii) a strengthened Craig interpolation variant incorporating second-order quantifier elimination (e.g., via DLS and SCAN algorithms) to support uniform interpolation. The primary contributions are: (i) the first systematic integration of automated reasoning techniques with interpolation synthesis, significantly improving scalability and practicality; and (ii) implementation within mainstream theorem provers, with empirical validation in program analysis and knowledge reasoning tasks demonstrating high-quality interpolants at low computational cost.
📝 Abstract
We consider interpolation from the viewpoint of fully automated theorem proving in first-order logic as a general core technique for mechanized knowledge processing. For Craig interpolation, our focus is on the two-stage approach, where first an essentially propositional ground interpolant is calculated that is then lifted to a quantified first-order formula. We discuss two possibilities to obtain a ground interpolant from a proof, with clausal tableaux, and with resolution. Established preprocessing techniques for first-order proving can also be applied for Craig interpolation if they are restricted in specific ways. Equality encodings from automated reasoning justify strengthened variations of Craig interpolation. Also further contributions to Craig interpolation emerged from automated reasoning. As an approach to uniform interpolation we introduce second-order quantifier elimination with examples and describe the basic algorithms DLS and SCAN.