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. 
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48 Citations
Highly Influential Citations
11
Background Citations
15
Methods Citations
24
Results Citations
3

48 Citations

On Interpolation in Automated Theorem Proving
TLDR
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
TLDR
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
TLDR
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
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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.
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