The present paper is the result of a long struggle to understand how the notion of compositionality can be used to motivate the structure of a sentence. While everyone seems to have intuitions about which proposals are compositional and which ones are not, these intuitions generally have no formal basis. What is needed to make such arguments work is a proper understanding of what meanings are and how they can be manipulated. In particular, we need a definition of meaning that (...) bans all mentioning of syntactic structure; it is not the task of semantics to state in which way things are put together in syntax. The present paper presents such a theory of meaning. This, in tandem with some minimal assumptions on the syntactic process (that there can be no deletion) yield surprisingly deep insights into natural language. First, it rehabilitates a lot of linguistic work as necessary on semantic grounds and defends it against potential claims of redundancy. For example, θ-roles and linking are an integral part of semantics, and not syntax. To assume the latter is to put the cart before the horse. Second, as a particular example we shall show that Dutch is not strongly context free even if weakly context free. To our knowledge, this is the first formal proof of this fact. (shrink)

If all dependent expressions were adjacent some variety of immediate constituent analysis would suffice for grammar, but syntactic and semantic mismatches are characteristic of natural language; indeed this is a, or the, central problem in grammar. Logical categorial grammar reduces grammar to logic: an expression is well-formed if and only if an associated sequent is a theorem of a categorial logic. The paradigmatic categorial logic is the Lambek calculus, but being a logic of concatenation the Lambek calculus can only capture (...) discontinuous dependencies when they are peripheral. In this paper we present the displacement calculus, which is a logic of intercalation as well as concatenation and which subsumes the Lambek calculus. On the empirical side, we apply the new calculus to discontinuous idioms, quantification, VP ellipsis, medial extraction, pied-piping, appositive relativisation, parentheticals, gapping, comparative subdeletion, cross-serial dependencies, reflexivization, anaphora, dative alternation, and particle shift. On the technical side, we prove that the calculus enjoys Cut-elimination. (shrink)