Logic Journal of the IGPL 1 (1):91-98 (1993)

Abstract
We prove that the equational theory of a semigroups becomes undecidable if we add a semilattice structure with a ‘touch of symmetric difference’. As a corollary we obtain that the variety of all Boolean algebras with an associative binary operator has a ‘hereditarily’ undecidable equational theory. Our results have implications in logic, e.g. they imply undecidability of modal logics extending the Lambek Calculus and undecidability of Arrow Logics with an associative arrow modality
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DOI 10.1093/jigpal/1.1.91
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Multi-Dimensional Modal Logic.Maarten Marx - 1996 - Dordrecht, Netherland: Kluwer Academic Publishers.
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