A First Complete Algorithm for Real Quantifier Elimination in Isabelle/HOL

Katherine Kosaian 📧, Yong Kiam Tan 📧 and André Platzer 📧

December 15, 2022

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Abstract

We formalize a multivariate quantifier elimination (QE) algorithm in the theorem prover Isabelle/HOL. Our algorithm is complete, in that it is able to reduce any quantified formula in the first-order logic of real arithmetic to a logically equivalent quantifier-free formula. The algorithm we formalize is a hybrid mixture of Tarski's original QE algorithm and the Ben-Or, Kozen, and Reif algorithm, and it is the first complete multivariate QE algorithm formalized in Isabelle/HOL.

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Related publications

  • Kosaian, K., Tan, Y. K., & Platzer, A. (2023). A First Complete Algorithm for Real Quantifier Elimination in Isabelle/HOL. Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs. https://doi.org/10.1145/3573105.3575672

Session Quantifier_Elimination_Hybrid

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× 
@article{Quantifier_Elimination_Hybrid-AFP,
  author  = {Katherine Kosaian and Yong Kiam Tan and André Platzer},
  title   = {A First Complete Algorithm for Real Quantifier Elimination in Isabelle/HOL},
  journal = {Archive of Formal Proofs},
  month   = {December},
  year    = {2022},
  note    = {\url{https://isa-afp.org/entries/Quantifier_Elimination_Hybrid.html},
             Formal proof development},
  ISSN    = {2150-914x},
}
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