Reinhard Blutner and Peter beim Graben. Linear algebra and the geometry of meaning

Geometric models of meaning have become increasingly popular in natural language semantics and cognitive science. In contrast to standard symbolic models of meaning (e.g. Montague), which give a qualitative treatment of differences in meaning, geometric models are also able to account for the quantitative differences, expressing degrees of similarities between meanings, and give an account of typicality and vagueness for words and phrases. In this course we will present new developments in this exciting research field. It is not assumed that every student has the necessary basic background of linear algebra. The first two days are planned to introduce the students into this important field of applied mathematics. Further, the course discusses (i) distributional semantics and the problem of compositionality; (ii) a new theory of questions & answers using the very same algebra that underlies distributional semantics; (iii) several puzzles of bounded rationality and their solutions in terms of geometric models.

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