Abstract : We reduce the provability of fragments of multiplicative linear logic to matching problems consisting in finding a one-one-correspondence between two sets of first-order terms together with a unifier that equates the corresponding terms. According to the kind of structure to which these first-order terms belong our matching problem corresponds to provability in the implicative fragment of multiplicative linear logic, in the Lambek calculus, or in the non-associative Lambek calculus.
Philippe de Groote. Proof-search in implicative linear logic as a matching problem. International Conference on Logic for Programming & Automated Reasoning - LPAR'2000, 2000, Reunion Island, France, pp.257-274. ⟨inria-00099221⟩