Interpolation and Quantifiers in Ortholattices

Fuente: arXiv
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Main Authors: Guilloud, Simon, Gambhir, Sankalp, Kunčak, Viktor
Format: Preprint
Published: 2025
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author Guilloud, Simon
Gambhir, Sankalp
Kunčak, Viktor
author_facet Guilloud, Simon
Gambhir, Sankalp
Kunčak, Viktor
contents We study quantifiers and interpolation properties in \emph{orthologic}, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based proof system for quantified orthologic, which we prove sound and complete for the class of all complete ortholattices. We show that orthologic does not admit quantifier elimination in general. Despite that, we show that interpolants always exist in orthologic. We give an algorithm to compute interpolants efficiently. We expect our result to be useful to quickly establish unreachability as a component of verification algorithms.
format Preprint
id arxiv_https___arxiv_org_abs_2507_11141
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Interpolation and Quantifiers in Ortholattices
Guilloud, Simon
Gambhir, Sankalp
Kunčak, Viktor
Logic in Computer Science
We study quantifiers and interpolation properties in \emph{orthologic}, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based proof system for quantified orthologic, which we prove sound and complete for the class of all complete ortholattices. We show that orthologic does not admit quantifier elimination in general. Despite that, we show that interpolants always exist in orthologic. We give an algorithm to compute interpolants efficiently. We expect our result to be useful to quickly establish unreachability as a component of verification algorithms.
title Interpolation and Quantifiers in Ortholattices
topic Logic in Computer Science
url https://arxiv.org/abs/2507.11141