| References for you and the other poster who asked: Peter Gärdenfors: Conceptual Spaces - the Geometry of Thought. MIT Press 2000 (Paperback 2004). It is very easy reading. The problems of geometric meaning theory are compositionality and quantification - how to get the expressivity of logical representations in addition to nearness measures, fuzziness and so on. There are some interesting approaches: Martha Lewis & Jonathan Lawry: Hierarchical conceptual spaces for concept combination. Artificial Intelligence 237 (2016): 204-227. Diederik Aerts, Liane Gabora, Sandro Sozzo: Concepts and their dynamics: a quantum-theoretic modeling of human thought. Topics in Cognitive Science 5 (4) (2013):737-772. [and other work by Aerts] Aerts work is fascinating me personally, but it's unfortunately above my level of mathematical maturity. This is a general problem in this literature, maybe some solutions are already there but they also need to be sold in a way that allows linguists to understand and use the methods. Montague was lucky (well, not personally, of course), because he had scholars who were able to package his dense ideas in more verbose and easier to access textbooks. Another short book worth reading in my opinion, though very programmatic in nature: Jens Erik Fenstad: Grammar, Geometry, & Brain. CSLI Publications 2009. |