1. 1 Linear Algebra and Geometric Approaches to Meaning Reinhard Blutner (Universiteit van Amsterdam Peter beim Graben (Humboldt Universität Berlin) ESSLLI Summer School 2011, Ljubljana August 1 – August 5, 2011

2. Day 1 1a: General Introduction (R) -Geometric models of meaning -Phenomena and puzzles -Quantum probabilities -Historical notes 1b: Linear algebra I (P) -Motivation -Vectors -Linear dependence -Scalar product -Applications

3. Day 2 2a: Linear algebra II (P) -mathematical preliminaries -vector spaces -complex numbers -linear dependence -scalar product -matrices 2b: Linear algebra III (P) -matrices (contd.) -qubits -subspaces -eigenvectors -projections -tensor products -representations

4. Day 3 3a: Distributed syntax (P) -Neural networks -Filler/role bindings -Tensor product representations -Parsing 3b: Distributed semantics (R) -Meaning and distribution -Distributional semantic models -Word vectors and search engines -Latent semantic analysis

5. Day 4 4a: Question order effects (R) -Factual questions & attitude questions -Four types of question ordering effects -Modeling ordering effects -One-qubit realization 4b: Semantics of questions (R) -Semantics of questions and answers -Jäger/Hulstijn question semantics -Ortho-algebraic question semantics -Answerhood

6. Day 5 5a: Concept combination (R) -Conditioned probabilities -Pitkowsky’s Correlation Polytopes -Conjunction and disjunction of natural concepts -Borderline contradictions -Combining prototypes 5b: Outlook (P/R) -Complementarity and underspecification -Semantic search engines -Natural language processing