Lambek calculus with restricted contraction and expansion

Studia Logica 51 (1):125 - 143 (1992)
This paper deals with some strengthenings of the non-directional product-free Lambek calculus by means of additional structural rules. In fact, the rules contraction and expansion are restricted to basic types. For each of the presented systems the usual proof-theoretic notions are discussed, some new concepts especially designed for these calculi are introduced reflecting their intermediate position between the weaker and the stronger sequent-systems.
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DOI 10.1007/BF00370335
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