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 Abstract: 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. References 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.