# Constructing Craig Interpolation Formulas

@inproceedings{Huang1995ConstructingCI, title={Constructing Craig Interpolation Formulas}, author={Guoxiang Huang}, booktitle={COCOON}, year={1995} }

A Craig interpolant of two inconsistent theories is a formula which is true in one and false in the other. This paper gives an efficient method for constructing a Craig interpolant from a refutation proof which involves binary resolution, paramodulation, and factoring. This method can solve the machine learning problem of discovering a first order concept from given examples. It can also be used to find sentences which distinguish pairs of nonisomorphic finite structures.

## 48 Citations

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.

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.

Interpolant Strength Revisited

- Computer Science, MathematicsSAT
- 2012

A parametrised interpolation system which subsumes existing interpolation methods for propositional resolution proofs and enables the systematic variation of the logical strength and the elimination of non-essential variables in interpolants is generalised.

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…

Labelled Interpolation Systems for Hyper-Resolution, Clausal, and Local Proofs

- Computer Science, MathematicsJournal of Automated Reasoning
- 2016

A parametrised interpolation system which subsumes existing interpolation methods for propositional resolution proofs and enables the systematic variation of the logical strength and the elimination of non-essential variables in interpolants is introduced.

Interpolation Systems for Ground Proofs in Automated Deduction: a Survey

- Computer ScienceJournal of Automated Reasoning
- 2015

This work surveys 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 theories, and DPLL(T$\mathcal {T}$) for SMT-solving.

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.

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.

Selfless Interpolation for Infinite-State Model Checking

- Computer ScienceVMCAI
- 2018

A new method for interpolation in satisfiability modulo theories (SMT) that is aimed at applications in model-checking and invariant inference that allows us to control the finite-convergence of interpolant sequences and provides expressive invariant-driven interpolants.

LRA Interpolants from No Man's Land

- Computer ScienceHaifa Verification Conference
- 2017

This work introduces the SI-LRA interpolation system for linear real arithmetics that allows the tuning of interpolants based on shifting between the primal and dual interpolants, and proves a strength relation between the interpolants constructed by SI- LRA.

## References

SHOWING 1-4 OF 4 REFERENCES

Symbolic logic and mechanical theorem proving

- MathematicsComputer science classics
- 1973

Automated Reasoning: Introduction and Applications

- Computer Science
- 1984

This book explains what automated reasoning is and what it can do and then demonstrates how to use it to solve complex problems with applications in logic circuit design, circuit validation,…

H

- Jerome Keisler, Model Theory, North Holland,
- 1990