beim Graben, Gerth and Vasishth, Version 1

Peter beim Graben (1), Sabrina Gerth (2) & Shravan Vasishth (2)

(1) School of Psychology and Clinical Language Sciences,
University of Reading, United Kingdom
(2) Institute for Linguistics,
University of Potsdam, Germany

Event-related brain potentials (ERP) are important neural correlates of cognitive processes. In the domain of
language processing, the N400 reflects lexical-semantic integration processes. Every incoming new word is
known to evoke a "bump" in the ERP wave whose amplitude co-varies with the ease of integration (Coles and
Rugg 1995).

Starting from experimental findings of Osterhout, Holcomb and Swinney (1994) on this issue, we propose a
computational model that is able to account for the N400 word integration effect. Our models combines two
different approaches from dynamical system theory, 1. Nonlinear Dynamical Automata (NDA: Moore 1990, beim
Graben et al. 2004), implementing Turing machines by autonomous nonlinear dynamics in a phase space, and 2.
Dynamical Recognizer (DR: Pollack 1991; see also Tabor 1998) where symbols act non-autonomously upon a phase
space, represented by iterated function systems.

In a first step, we describe the sentence material of Osterhout, Holcomb and Swinney (1994) by a appropriate
context-free grammar, and construct a deterministic top-down recognizer for processing this grammar in a
second step. The parser is canonically represented by a generalized shift and subsequently mapped onto a
nonlinear dynamics on the unit square by means of a Gödel encoding (Moore 1990) in steps three and four.

Instead of incorporating the complete input tape of the automaton into the model, we do this only for the
fist two symbols of the input in order to emulate a "working memory" (Frazier and Fodor1978). After each
attachment, this memory contains only one symbol in the most significant position such that a new word is
scanned from the environment into the second-most significant position (Wegner 1998). In our combined model,
the action of the scanned word upon the phase space of the NDA is represented by one particular function from
an DR's iterated function systems.

Symbolically meaningful states of the combined NDA/DR are rectangular macrostates moving through the NDA's
phase space. As an model ERP measure we propose the volume of these rectangles. As each scan operation is
reflected by a vertical squeezing of a macrostate, the measured ERP signal drops after each scanning, thus
emulating the word integration N400.

Our model is consistent with the dynamical system interpretation of ERPs (Basar 1980) and accounts for the
causal efficacy of dynamical systems models of symbolic computation (Fodor and Pylyshyn 1988) since different
regions in phase space are functionally different with respect to language processing.


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