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.
https://hal.inria.fr/inria-00099221
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Submitted on : Tuesday, September 26, 2006 - 8:51:57 AM Last modification on : Thursday, January 11, 2018 - 6:19:48 AM
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⟩