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

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Katherine Cordwell, Yong Kiam Tan, André Platzer

Published: 01 Jan 2022, Last Modified: 26 Mar 2025Arch. Formal Proofs 2022EveryoneRevisionsBibTeXCC BY-SA 4.0
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.