Glyn Morrill. Type logical syntax and semantics

We present contemporary developments in categorial grammar. We explain the foundation provided by logic of strings (Lambek calculus), consider its good theoretical properties, and assess its linguistic successes and shortcomings. In this context we present a natural generalization comprising a logic of segmented strings (displacement calculus) and describe how this preserves the good technical features of the Lambek model while subsuming it and extending its empirical scope.

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