English existential sentences are explored in terms of prototype theory in cognitive linguistics.

This paper gives a brief analysis of modal semantics with prototype category theory,which proves that the subcategories of the modals may and must are prototypical: there exist prototype and peripheral members;the members share family resemblance and prototypicality;their boundaries are fuzzy and non-discrete.

But it is a prototype category.

This article mainly discusses markedness on semantic level and attempts to use prototype category theory to explain it.

The prototypical category theory of cognitive linguistics has achieved unprecedented development at present.

After a brief review of the Idiom Theory and the Inference Theory, which aim to explain the illocutionary force of indirect speech acts, this paper analyses indirect directives from the point of view of categorization and reaches the conclusion that they form a prototypical category with fuzzy boundaries and that its members differ in prototypical status.

This paper attempts to illustrate this phenomenon with the guide of prototypes and category frame theorymental space and conceptual integration theor.