Craig Interpolation with Clausal First-Order Tableaux

@article{Wernhard2021CraigIW,
  title={Craig Interpolation with Clausal First-Order Tableaux},
  author={Christoph Wernhard},
  journal={J. Autom. Reason.},
  year={2021},
  volume={65},
  pages={647-690}
}
  • C. Wernhard
  • Published 8 August 2020
  • Computer Science
  • J. Autom. Reason.
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… 

References

SHOWING 1-10 OF 88 REFERENCES
Reformulating Queries: Theory and Practice
TLDR
This work considers a setting where a user wants to pose a query against a dataset where some background knowledge is available, but only a subset of the information can be used to answer the query, and wants to reformulate the user query against the subvocabulary, arriving at a query that is equivalent to the user's query assuming the background theory, but using only the restricted vocabulary.
First-Order Logic
  • Peter A. Flach
  • Philosophy
    Encyclopedia of Machine Learning and Data Mining
  • 2017
Constructing Craig Interpolation Formulas
TLDR
This paper gives an efficient method for constructing a Craig interpolant from a refutation proof which involves binary resolution, paramodulation, and factoring that can solve the machine learning problem of discovering a first order concept from given examples.
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.
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.
The PIE system for proving, interpolating and eliminating
  • PAAR-2016, CEUR Workshop Proc., vol. 1635, pp. 125–138. CEUR-WS.org
  • 2016
First-Order Logic and Automated Theorem Proving, 2nd edn
  • Springer
  • 1995
First order proof problems extracted from an article in the Mizar mathematical library
  • FTP’97, RISC-Linz Report Series No. 97–50, pp. 58–62. Joh. Kepler Univ., Linz, Austria
  • 1997
Tableau and connection calculi
  • structure, complexity, implementation. Habilitationsschrift, TU München
  • 1999
Facets of the PIE Environment for Proving, Interpolating and Eliminating on the Basis of First-Order Logic
TLDR
PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic that supports a workflow based on documents that intersperse macro definitions, invocations of reasoners, and LaTeX-formatted natural language text.
...
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