On the mathematics of semantic spaces

We study a generalization of the models of semantic spaces introduced by Rieger. The focus will be on the following aspects. We show to what extent different choices of conceptual freedom leads to dramatically different behaviour. For instance, the linguistic differentiation process introduced by Rieger is highly dependent on the underlying metric space. Also, we introduce certain invariants that may be seen as leading to new approaches for identifying meaning and relevance. In particular, we study a normalized limiting process in Rieger's original model that may help to identify certain key elements of corpora. Also, we show how sensitivities in defining associated measurements like dependency trees might be used to identify linguistic relevance.