Derivations as Proofs a Logical Approach to Minimalism

The purpose of this paper is to show that we can work in the spirit of minimalist grammars by means of a labelled commutative (and associative) calculus (Oehrle’s Mon:LP), enriched with constraints on the use of assumptions. Lexical entries are considered proper axioms, some of which are coupled with (sequences of) hypotheses which must necessarily be introduced and discharged before the use of their associated axiom. Like similar proposals by P. de Groote or R. Muskens, our calculus has two interfaces. Each of them provides a homomorphism of types (from syntactic types to semantic ones, or -types, and from syntactic types to phonetic ones, or -types). Move is simply the link between a hypothesis A and its lifted type (A X) X when a (or )-term of the later type applies to a piece of proof the last step of which consists in precisely discharging A. The ability for a phrase to overtly move is governed by the form of its -term. Moreover, the elimination rule for is used to simulate head-movements. An enrichment with the exponential of Linear Logic: ”!” is also proposed in order to treat binding phenomena in the spirit of Kayne (2003). We see that this enrichment opens the field to new insights concerning ellipsis and coordination. Proximity with other formalisms like Lambda grammars and Abstract Categorial Grammars is discussed.