Geometric representations for minimalist grammars

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of processing complexity. Finally, we illustrate our findings by means of two particular arithmetic and fractal representations.Comment: 43 pages, 4 figure

On Folding and Twisting (and whatknot): towards a characterization of workspaces in syntax

Syntactic theory has traditionally adopted a constructivist approach, in which a set of atomic elements are manipulated by combinatory operations to yield derived, complex elements. Syntactic structure is thus seen as the result or discrete recursive combinatorics over lexical items which get assembled into phrases, which are themselves combined to form sentences. This view is common to European and American structuralism (e.g., Benveniste, 1971; Hockett, 1958) and different incarnations of generative grammar, transformational and non-transformational (Chomsky, 1956, 1995; and Kaplan & Bresnan, 1982; Gazdar, 1982). Since at least Uriagereka (2002), there has been some attention paid to the fact that syntactic operations must apply somewhere, particularly when copying and movement operations are considered. Contemporary syntactic theory has thus somewhat acknowledged the importance of formalizing aspects of the spaces in which elements are manipulated, but it is still a vastly underexplored area. In this paper we explore the consequences of conceptualizing syntax as a set of topological operations applying over spaces rather than over discrete elements. We argue that there are empirical advantages in such a view for the treatment of long-distance dependencies and cross-derivational dependencies: constraints on possible configurations emerge from the dynamics of the system.Comment: Manuscript. Do not cite without permission. Comments welcom

Why Unaccusatives Have it Easy: Reduced Relative Garden Path Effects and Verb Type

This paper provides a new account for why unaccusative verbs are easier to process than unergative verbs in the reduced relative garden path construction, as demonstrated in Stevenson and Merlo [1997]. Reanalysis to the passivized reduced relative clause form requires the verb to be causative. Stevenson and Merlo [1997] argued that unaccusatives are causativized in the lexicon, while unergatives are causativized in the syntax. This account argues instead that an independently attested co-occurrence restriction contributes to greater initial ambiguity in the unergative case; causative unergatives require an argument/directional attachment of prepositional phrase [Hoekstra, 1988, Levin and Rappaport-Hovav, 1995, Folli and Harley, 2006].We implement the unergative-PP co-occurrence restriction in Minimalist Grammars [Stabler, 1997]. We model the contribution of prepositional phrase ambiguity to unergative reduced relative ambiguity with Entropy Reduction [Hale, 2003]. We obtain greater Entropy Reductions for the unergative condition, modeling that human comprehenders are more taxed by compounded ambiguity