Lambek calculus may be viewed as a fragment of linear logic, namely intuitionistic non-commutative multiplicative linear logic. As it is too restrictive to describe numerous usual linguistic phenomena, instead of extending it we extend MLL with a non-commutative connective, thus dealing with partially ordered multisets of formulae. Relying on proof net technique, our study associates words with parts of proofs, modules, and parsing is described as proving by plugging modules. Apart from avoiding spurious ambiguities, our method succeeds in obtaining a logical description of relatively free word order, head-wrapping, clitics, and extraposition (these latest two constructions are unfortunately not included, for lack of space).

This ESSLLI workshop is devoted to connecting the linguistic use of resource logics and categorial grammar to minimalist grammars and related generative grammars. Minimalist grammars are relatively recent, and although they stem from a long tradition of work in transformational grammar, they are largely informal apart from a few research papers. The study of resource logics, on the other hand, is formal and stems naturally from a long logical tradition. So although there appear to be promising connections between these traditions, there is at this point a rather thin intersection between them. The papers in this workshop are consequently rather diverse, some addressing general similarities between the two traditions, and others concentrating on a thorough study of a particular point. Nevertheless they succeed in convincing us of the continuing interest of studying and developing the relationship between the minimalist program and resource logics. This introduction reviews some of the basic issues and prior literature. 1 The interest of a convergence What would be the interest of a convergence between resource logical investigations of

. Many convergence points have been observed during the recent years between the Minimalist Program and the program of Categorial Grammar, above all since the formalization of minimalist ideas by E. Stabler. For instance, the Merge-operation is exactly like functional application. Moreover the fundamental operation of feature-checking, which is at the basis of the Move-operation, can really be depicted as a resource consumption procedure, something familiar to so called resource conscious logics. This makes rise a deep interest in looking for a logical formulation of minimalist grammars. Such an enterprise is not done for the sake of spurious formalization. If we take the chomskyan framework seriously, it seems natural to assume that UG consists in a very general set of principles that must be expressed in the most condensed way, and that derivations are made of steps of a few different sorts exactly like it is the case in a logic. 1.0.1 The convergence of the minimalist program and ...

This paper proposes to answer some questions concerning economy in computation and language by giving a very compact set of deductive rules (based on the so-called Lambek calculus, enriched with an exchange modality) which embodies all the properties of Minimalist Grammars (Stabler, [15]). moveff is replaced by a logical operation, very similar in its effects to Form Chain, technically known as the product-elimination rule, which inserts a lexical or syntactic object at (at least) two positions at the same time. Non commutativity of the system ensures HMC. Moreover the precise formulation of the system enables us to show what kinds of languages can be captured and it is then an empirical question to verify that some natural languages exist, which present similarities with them. We can therefore say that formalization leads to a hypothetico-deductive approach in linguistics. 1