Comparing Meaning in Language and Cognition: P-Hyponymy, Concept Combination, Asymmetric Similarity

In this dissertation we work in the framework of compositional distributional models of meaning to examine a number of asymmetric linguistic phenomena that manifest themselves in language and cognition. These include overextension with respect to concept combination, asymmetry of similarity judgment and hyponymy and typicality. In particular, we make use of the formalism of density matrices, which were recently introduced as an alternative to the vector-based model of word meaning. We first consider the former two of the above-mentioned phenomena using only tools that have been developed so far in the distributional compositional model. We then proceed to define a new quantitative asymmetric measure on density matrices, called p-hyponymy, which allows us to determine the strength of hyponymy in hyponym-hypernym pairs. We show how this can be lifted to the level of the sentence structures that our mathematical model of meaning supports and consider the implications of this result. We conclude with a brief discussion of how this measure can potentially be modified to account for other similar phenomena.