Undecidability of first-order intuitionistic and modal logics with two variables

Kontchakov, Roman and Kurucz, A. and Zakharyaschev, M. (2005) Undecidability of first-order intuitionistic and modal logics with two variables. The Bulletin of Symbolic Logic 11 (5), p. 428. ISSN 1079-8986.

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Official URL: https://doi.org/10.2178/bsl/1122038996

Abstract

We prove that the two-variable fragment of first-order intuitionistic logic is undecidable, even without constants and equality. We also show that the two-variable fragment of a quantified modal logic L with expanding first-order domains is undecidable whenever there is a Kripke frame for L with a point having infinitely many successors (such are, in particular, the first-order extensions of practically all standard modal logics like K, K4, GL, S4, S5, K4.1, S4.2, GL.3, etc.). For many quantified modal logics, including those in the standard nomenclature above, even the monadic two-variable fragments turn out to be undecidable.

Metadata

Item Type:	Article
School:	Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User:	Sarah Hall
Date Deposited:	11 May 2021 17:52
Last Modified:	09 Aug 2023 12:50
URI:	https://eprints.bbk.ac.uk/id/eprint/44226

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