• Jens Michaelis. Notes on the Complexity of Complex Heads in a Minimalist Grammar. Paper presented at the Sixth International Workshop on Tree Adjoining Grammars and Related Formalisms (TAG+6), Venzia, May 20-24, 2002. Corrected version of the paper as it appeared in the workshop proceedings.

Abstract

The type of a minimalist grammar (MG) introduced in Stabler (1997) provides a simple algebraic formalization of the perspectives as they arise from Chomsky (1995b) within the linguistic framework of transformational grammar. As known (cf. Michaelis, 2001a; 2001b; Harkema, 2001), this MG type defines the same class of derivable string languages as, e.g., linear context free (string) rewriting systems (LCFRSs) (Vijay Shanker, Weir and Joshi, 1987; Weir, 1988). In this paper we show that, in terms of weak equivalence, the subclass of MGs which allow (overt) head movement but no phrasal movement in the sense of Stabler (1997), constitutes a proper subclass of linear indexed grammars (LIGs), and thus tree adjoining grammars (TAGs). We also examine the inner hierarchic complexity of this embedding in some more detail by looking at the subclasses canonically resulting from the distinction between left and right adjunction of the moved head to the attracting one. /* Correction --> */ Furthermore, we show that adding the possibility of phrasal movement by allowing at most one indistinguishable licensee to trigger such movement already increases the weak generative capacity of at least two of the considered subclasses, while this is not true for the particular subclass of MGs which do not employ any movement at all. The latter define the same class of derivable string languages as context free grammars (CFGs). /* <--Correction */ On the other hand however, MGs which do not employ head movement but whose licensee set consists of at most two elements, are shown to derive, i.a., languages not derivable by any LIG. In this sense our results contribute to sheding some light on the complexity as it arises from the interplay of two different structural transformation types whose common existence is often argued to be linguistically motivated.

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