We introduce non-associative linear logic, which may be seen as the classical version of the non-associative Lambek calculus. We define its sequent calculus, its theory of proof-nets, for which we give a correctness criterion and a sequentialization theorem, and we show proof search in it is polynomial.

This book constitutes the thoroughly refereed post-proceedings of the Second International Conference on Logical Aspects of Computational Linguistics, LACL '97, held in Nancy, France in September 1997. The 10 revised full papers presented were carefully selected during two rounds of reviewing. Also included are two comprehensive invited papers. Among the topics covered are type theory, various types of grammars, linear logic, parsing, type-directed natural language processing, proof-theoretic aspects, concatenation logics, and mathematical languages.