The category theory of semantics proposes that words are not simply names for pre-existing categories of objects, and the extra-linguistic world is not categorized until by language. In the field of modern cognitive linguistics, categorization is established mainly on the basis of prototype theory whereby ”prototype” is considered the typical example of a category and shares the most family (i.e. category) resemblance among all family members. The different typicality revealed by each family member in a certain category is thus called the ”typicality effects” of the category. In the light of the methodology proposed by prototype theory, the present research is dealing with the lexical semantic analysis of polysemy. It has been claimed by several semantic researches that, unlike prototypes for real-object categories in which a radiate model of typicality effects is shown, a great part of the semantic structure of polysemy reveals itself as a network of meanings connected by meaning-chains. To elucidate this hypothesis, the German spatial preposition ”über” is to be analyzed semantically, as to answer the questions of how the different meanings of this ”über-category” are connected together by the so-called ”family resemblance”. By means of analyzing the semantic features of each meaning of ”über” as well as how these features are related to each other, it is expected not only to establish the semantic category of ”über” from the viewpoint of prototype theory, but also to explore the modus of human cognition revealed by the polysemy in general.
