Bulletin of Symbolic Logic

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

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.

Article information

Source
Bull. Symbolic Logic Volume 11, Issue 3 (2005), 428-438.

Dates
First available in Project Euclid: 22 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.bsl/1122038996

Digital Object Identifier
doi:10.2178/bsl/1122038996

Zentralblatt MATH identifier
1096.03008

Citation

Kontchakov, Roman; Kurucz, Agi; Zakharyaschev, Michael. Undecidability of first-order intuitionistic and modal logics with two variables. Bull. Symbolic Logic 11 (2005), no. 3, 428--438. doi:10.2178/bsl/1122038996. https://projecteuclid.org/euclid.bsl/1122038996