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Linear Algebra and Geometric Approaches to Meaning

Linear Algebra and Geometric Approaches to Meaning. ESSLLI Summer School 2011, Ljubljana August 1 – August 5, 2011. Reinhard Blutner (Universiteit van Amsterdam Peter beim Graben (Humboldt Universität Berlin). 1. Day 1. 1a: General Introduction (R) Geometric models of meaning

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Linear Algebra and Geometric Approaches to Meaning

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

  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

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