P. beim Graben, School of Psychology and Clinical Language Sciences, University of Reading, UK

Title: ``Fock space models of language-related brain potentials''

Time:     Dec 11, 2007, 2 p.m.
Location: Campus Golm, Building 26, Room 076

Peter beim Graben (1), Sabrina Gerth (2), and Shravan Vasishth (2)
    (1) School of Psychology and Clinical Language Sciences,
        University of Reading, UK
    (2) Institute for Linguistics, University of Potsdam, Germany

One of the crucial questions in computational psycholinguistics is
how language is realized by the
neurodynamics of the human brain. An important online measure of
language processing are event-related brain
potentials (ERPs). Yet these are understood purely
phenomenologically, while computational accounts are by
and large lacking (see Hagoort 2005 for a recent proposal).

On the other hand, Smolensky's Integrated Connectionist/Symbolic
Architecture (ICS: Smolensky 2006, Smolensky
& Legendre 2006) provides a universal framework to representing
structured symbolic expressions by activation
vectors in neural networks. The basic ingredient of this approach
is the filler/role binding through tensor
products (Smolensky 1990, 2006; Mizraji 1989, 1992), originally
invented for describing many particle states
in quantum field theory as vectors in Fock spaces.

I shall present three different instantiations for such models to
describe syntactic parsing as nonlinear
dynamics in Fock space and argue that ERP effects, such as the P600
elicited by reanalyzing garden path
sentences, are due to trajectories which explore different regions
in Fock space.

The first model maps phrase structure trees from Government and
Binding theory (Haegeman 1994) into Fock
space by representing syntactic categories as filler vectors, while
the positions in a labeled binary tree
are given as the basis vectors of three-dimensional space. In the
second model, minimalist feature arrays and
minimalist trees resulting from merge and move operations (Stabler
1997) are represented in a similar
fashion. The third model eventually deploys the full power of Fock
space formalism by representing phrase
structure trees as spherical wave functions which evolve like
potential distributions across the scalp.

The three models are able to describe qualitatively ERP differences
by trajectories that explore functionally
and causally different regions in Fock space in pursuing different
language processing strategies. During its
transient evolution, the trajectories of the models diverge exactly
when the garden path is encountered which
shows remarkable resemblance with the P600 effect in the ERP.


Hagoort P (2005) On Broca, brain, and binding: a new framework.
Trends in Cognitve Science 9(9):416 – 423.

Haegeman L (1994) Introduction to Goverment & Binding Theory,
Blackwell Textbooks in Linguistics, vol 1, 2nd
edn. Blackwell Publishers, Oxford.

Mizraji E (1989) Context-dependent associations in linear
distributed memories. Bulletin of Mathematical
Biology 51(2):195 – 205.

Mizraji E (1992) Vector logics: The matrix-vector representation of
logical calculus. Fuzzy Sets and Systems
50:179 – 185.

Smolensky P (1990) Tensor product variable binding and the
representation of symbolic structures in
connectionist systems. Artificial Intelligence 46:159 – 216.

Smolensky P (2006) Harmony in linguistic cognition. Cognitive
Science 30:779 – 801.

Smolensky P, Legendre G (2006) The Harmonic Mind. From Neural
Computation to Optimality-Theoretic Grammar,
vol 1: Cognitive Architecture. MIT Press, Cambridge (MA).

Stabler EP (1997) Derivational minimalism. In: Retore C (ed)
Logical Aspects of Computational Linguistics,
Springer Lecture Notes in Computer Science, vol 1328, Springer, New
York, pp 68 – 95.