Bulletin of Symbolic Logic

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

Roman Kontchakov, Agi Kurucz, and Michael Zakharyaschev

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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.

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

First available in Project Euclid: 22 July 2005

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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

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