# Interpolation Systems for Ground Proofs in Automated Deduction: a Survey

@article{Bonacina2015InterpolationSF, title={Interpolation Systems for Ground Proofs in Automated Deduction: a Survey}, author={Maria Paola Bonacina and Moa Johansson}, journal={Journal of Automated Reasoning}, year={2015}, volume={54}, pages={353-390} }

Interpolation is a deductive technique applied in program analysis and verification: for example, it is used to compute over-approximations of images or refine abstractions. An interpolation system takes a refutation and extracts an interpolant by building it inductively from partial interpolants. We survey color-based interpolation systems for ground proofs produced by key inference engines of state-of-the-art solvers: DPLL for propositional logic, equality sharing for combination of convex…

## 15 Citations

Craig Interpolation with Clausal First-Order Tableaux

- Computer ScienceJ. Autom. Reason.
- 2021

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…

Compactly Representing Uniform Interpolants for EUF using (conditional) DAGS

- Computer ScienceArXiv
- 2020

Two algorithms for computing the uniform interpolant of a quantifier-free formula in EUF endowed with a list of symbols to be eliminated are proposed and correctness and completeness proofs are supplied.

The PIE Environment for First-Order-Based Proving, Interpolating and Eliminating

- Computer SciencePAAR@IJCAR
- 2016

The PIE system aims at providing an environment for creating complex applications of automated first-order theorem proving techniques, embedded in Prolog, and comes with a built-in default prover that can compute interpolants.

Uniform Interpolants in EUF: Algorithms using DAG-representations

- Computer ScienceLogical Methods in Computer Science
- 2022

Two algorithms for computing quantiﬁer-free uniform interpolants in the theory of equality over uninterpreted symbols ( EUF ) endowed with a list of symbols to be eliminated are proposed.

Computing Uniform Interpolants for EUF via (conditional) DAG-based Compact Representations

- Computer ScienceCILC
- 2020

Two algorithms for computing the uniform interpolant of a quantifier-free formula in EUF endowed with a list of symbols to be eliminated are proposed, using arguments combining rewrite techniques with model theory.

Multicomponent proof-theoretic method for proving interpolation properties

- Mathematics, Computer ScienceAnn. Pure Appl. Log.
- 2018

Proofs in conflict-driven theory combination

- Computer Science, MathematicsCPP
- 2018

This paper endow CDSAT with lemma learning and proof generation, and adapts the LCF approach to proofs from interactive theorem proving to conflict-driven SMT-solving and theory combination, by defining a small kernel of reasoning primitives that guarantees that C DSAT proofs are correct by construction.

On Conflict-Driven Reasoning

- Computer ScienceAFM@NFM
- 2017

A current research direction in automated reasoning is to generalize the notion of Con ict-driven satis ability to a paradigm of con icts-driven reasoning in rst-order theories for satisability modulo theories and assignments, and even in full rstorder logic for generic automated theorem proving.

Interpolation in Extensions of First-Order Logic

- Philosophy, MathematicsStud Logica
- 2020

A direct proof of interpolation is obtained for (classical and intuitionistic) first-order logic with identity, as well as interpolation for several mathematical theories, including the theory of equivalence relations, (strict) partial and linear orders, and various intuitionistic order theories such as apartness and positive partial andlinear orders.

Decidable fragments of first-order logic and of first-order linear arithmetic with uninterpreted predicates

- Computer Science
- 2019

The present thesis sheds more light on the decidability boundary and aims to open new perspectives on the already known results on linear arithmetic over the rationals with uninterpreted predicates.

## References

SHOWING 1-10 OF 141 REFERENCES

On Interpolation in Automated Theorem Proving

- Computer ScienceJournal of Automated Reasoning
- 2014

An interpolation system for non-ground refutations is obtained, and it is proved that it is complete, if the only non-shared symbols in provisional interpolants are constants.

Towards interpolation in an SMT solver with integrated superposition

- Computer Science
- 2011

It is shown how a first interpolation system for DPLL(Γ+T ), which integrates tightly a superposition based prover Γ in a DPLL (T ) based SMT-solver to unite their respective strengths, can be obtained from interpolation systems forDPLL, equality sharing and Γ.

Disjunctive Interpolants for Horn-Clause Verification

- Computer ScienceCAV
- 2013

A new notion of interpolation is introduced, disjunctive interpolation, which solves a more general class of problems in one step compared to previous notions of interpolant, such as tree interpolants or inductive sequences of interpolants.

Flexible interpolation with local proof transformations

- Computer Science2010 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)
- 2010

This paper presents a technique for transforming the propositional proof produced by an SMT-Solver in such a way that mixed predicates are eliminated and can be applied to allow the reuse of known interpolation algorithms.

Program analysis with interpolants

- Computer Science
- 2010

Novel techniques for interpolation-based software model checking, an approximate method which uses Craig interpolation to compute invariants of programs and a heuristic that aims to avoid the repeated and computationally expensive construction of interpolants, thus enabling the detection of deeply buried defects such as buffer overflows.

An Interpolating Sequent Calculus for Quantifier-Free Presburger Arithmetic

- Mathematics, Computer ScienceJournal of Automated Reasoning
- 2011

This paper introduces an interpolation approach based on a sequent calculus for QFPA that determines interpolants by annotating the steps of an unsatisfiability proof with partial interpolants, and extends the Princess theorem prover to generate interpolating proofs.

Interpolants from Z3 proofs

- Computer Science, Mathematics2011 Formal Methods in Computer-Aided Design (FMCAD)
- 2011

The efficiency of Z3 makes it possible to handle problems that are beyond the reach of existing interpolating provers, as it is demonstrated using benchmarks derived from bounded verification of sequential and concurrent programs.

Exploring interpolants

- Computer Science2013 Formal Methods in Computer-Aided Design
- 2013

This work presents a semantic and solver-independent framework for systematically exploring interpolant lattices, based on the notion of interpolation abstraction, and discusses how interpolation abstractions can be constructed for a variety of logics, and how they can be exploited in the context of software model checking.

Ground interpolation for the theory of equality

- MathematicsLog. Methods Comput. Sci.
- 2012

This paper presents a generic version of the interpolation game, parametrized by the theory T, and defines a general method to extract runs of the game from proofs in T and then generate interpolants from these runs.

Propositional Interpolation and Abstract Interpretation

- Computer ScienceESOP
- 2010

It is shown that existing interpolation algorithms are abstractions of a more general, parametrised algorithm, and reside in the coarsest abstraction that admits correct interpolationgorithms.