語意學的範疇理論認為，自然世界的各種現象是透過語言被範疇化的。關於範疇劃分的原則，除了古典範疇理論，在現代認知語言學的研究傳統中、主要是以「原型理論」提出的觀點為基礎。所謂「原型」，指的是在某一範疇中最典型的代表、較同一範疇的其他成員擁有最多的「家族相似性」，而範疇成員之間典型性的不對等模式，就稱為此範疇所表現的原型效應。語言結構同表達具體事物的概念結構一樣，都根植於人類相同的認知機制。不同的是，實物範疇所表現的原型效應經常呈現單一中心的放射狀結構，但語言結構則不然，特別是詞彙中的多義詞，其語意範疇所呈現的，經常是一個由語義鍊串連起來的、非單一中心的意義網絡。本論文從原型理論的觀點出發，將原型理論提出之方法學應用於詞彙語意範疇研究，並以德語空間介系詞über 為例，實際分析該詞彙的語意結構，除了為über 每個不同的實際語用表達找出其涵括的語義特徵，亦即原型理論所謂的家族相似性，歸納über 的語意範疇，同時希望透過此多義詞的語義練結構，窺得人類認知機制的基本模式。
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.