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We enrich the Lambek calculus with the cyclic shift operation, which isexpected to model the closure operator of formal languages with respect tocyclic shifts. We introduce a Gentzen-style calculus and prove cut elimination.Secondly, we turn to categorial grammars based on this calculus and show thatthey can generate non-context-free languages; besides, we consider a relatedcalculus where the cyclic shift is a structural rule, and compare recognizingpower of these two calculi. Thirdly, we attempt to embed the Lambek calculuswith the cyclic shift operation in the hypergraph Lambek calculus. This resultsin considering a ``bracelet'' operation, which can be defined through thecyclic shift, union, and the reversal operation.

Cyclic Shift in the Lambek Calculus