Recognizing Head Movement

Previous studies have provided logical representations and eÆcient recognition algorithms for a simple kind of \minimalist grammars." This paper extends these grammars with head movement (\incorporation") and aÆx hopping. The recognition algorithms are elaborated for these grammars, and logical perspectives are brie y considered. Michaelis (1998) showed how the derivations of a simple kind of minimalist grammar (MG) (Stabler, 1997) correspond to derivations of exactly the same strings in a multiple context free grammar (MCFG) (Seki et al., 1991). MGs build structures by merging pairs of expressions, and simplifying single expressions by moving a subexpression in them. The basic idea behind the correspondence with MCFGs can be traced back to Pollard (1984) who noticed, in e ect, that when a constituent is going to move, we should not regard its yield as included in the yield of the expression that contains it. Instead, the expression from which something will move is better regarded has having multiple yields, multiple components { the \moving" components have not yet reached their nal positions. In a completed derivation, the component strings of all the categories are eventually ordered to yield a sentence. This conception behind the Michaelis result relies on the fact that for any MG, there is a xed, nite bound on the number of categories and rules, and on the number of components that any constituent will have. These recent results led to eÆcient parsing methods (Stabler, 1999; Harkema, 2000), to connections with multimodal logics (Cornell, 1999; Vermaat, 1999; Lecomte and Retor e, 1999), and to a succinct reformulation of MGs (Stabler and Keenan, 2000) in which the multiple components of expressions are explicit. The parsing methods, the logics, and the succinct reformulation were provided for MGs with only overt, phrasal movement (as explained below). This paper extends these results with two kinds of head movement, providing an eÆcient parsing method and some preliminary observations about bringing this work into a logical perspective like that proposed by (Lecomte and Retor e, 1999). And for illustration, in the course of the paper, we present small example grammars for (G1) subject-auxiliary inversion and (G3) aÆx-hopping in English, and (G2) object clitics in French.