On the unification problem for GLP

Fuente: arXiv
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Autore principale: Beklemishev, Lev D.
Natura: Preprint
Pubblicazione: 2024
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author Beklemishev, Lev D.
author_facet Beklemishev, Lev D.
contents We show that the polymodal provability logic GLP, in a language with at least two modalities and one variable, has nullary unification type. More specifically, we show that the formula [1]p does not have maximal unifiers, and exhibit an infinite complete set of unifiers for it. Further, we discuss the algorithmic problem of whether a given formula is unifiable in GLP and remark that this problem has a positive solution. Finally, we state the arithmetical analogues of the unification and admissibility problems for GLP and formulate a number of open questions.
format Preprint
id arxiv_https___arxiv_org_abs_2404_04893
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the unification problem for GLP
Beklemishev, Lev D.
Logic
03B45, 03F45
We show that the polymodal provability logic GLP, in a language with at least two modalities and one variable, has nullary unification type. More specifically, we show that the formula [1]p does not have maximal unifiers, and exhibit an infinite complete set of unifiers for it. Further, we discuss the algorithmic problem of whether a given formula is unifiable in GLP and remark that this problem has a positive solution. Finally, we state the arithmetical analogues of the unification and admissibility problems for GLP and formulate a number of open questions.
title On the unification problem for GLP
topic Logic
03B45, 03F45
url https://arxiv.org/abs/2404.04893