Partial Associativity and Conjunction: A Proof-Theoretic Perspective on Constituency

Systems of conjunction, particularly where the conjunction of noncanonical constituents is involved, are not invariant across the range of natural languages. In this paper, we examine a number of problems involving conjunction and show that one apparent watershed between diierent systems of conjunction corresponds to a distinction in the scope of associativity rules in the landscape of substructural logics. In particular, we show that between the nonassociative Lambek calculus NL 8] and the associative Lambek calculus L, there exist two partially associative deductive systems which we call RAL (read: `right associative L') and LAL (read: `left associative L'), which characterize a range of attested examples which NL is too weak to deal with and L too strong to deal with. We begin by sketching the general point of view in which this work is framed. We then consider an observation of Houtman 6] concerning a minimal pair in Dutch conjunction. We then show this distinction arises precisely in the deductive system RAL&, which extends RAL by adding a generalized form of conjunction, but cannot be adequately treated by any of the other deductive systems discussed here. Finally, we discuss a range of other asymmetric cases of natural language conjunction which also appear to be directly treatable in the deductive system RAL&. We end with a discussion of the empirically observable diierences between the two symmetric systems RAL and LAL (and their extensions RAL& and LAL&).