Study on the Formal Semantics of Pictures Dejuan Wang Abstract: In the way natural languages have a semantics, pictures also have semantics when they are used as a medium to help people to communicate. However, there is a distinction between picture semantics and natural language semantics: the semantics of pictures is not fixed by convention. The same picture may have completely different meanings when it is used in different circumstances. The PhD thesis studies how to assign meanings to pictures when they are used to help people in communicating. Its purpose is to provide formal frameworks based on which we can design computer systems that support visual communication. In particular, I have studied two picture semantic approaches: the interpretation approach and the picture specification approach. An interpretation approach assigns meanings to each graphical entity explicitly, and the semantics of a picture is determined from the meanings of its components and their spatial relations. A picture specification approach assigns meanings to pictures in an implicit way. It creates picture classes according to the requirements of the problems being tackled in the application domain. The thesis consists of three parts. In Part I, I study how to describe pictures geometrically. A formal framework is presented for the construction of a picture descriptive language and then a set of principles is given to guide the description of a picture in the picture descriptive language. In Part II, the interpretation approach is deveoped. Interpretations are defined on the basis of the study in Part I. This definition serves as a criterion for checking whether or not an interpretation is syntactically correct. Then a logical characterisation is provided that, given an interpretation, determines how the pictures are used in visual communication and whether or not an interpretation correctly reflects the user's intention. Possible applications are discussed. A graphics-assisted reasoning system GAR is presented and reasoning with diagrammatic representations is discussed. In Part III, picture specifications are the central topic. I extended the traditional picture specification method by introducing pictorial concept operators, so that some picture classes which cannot be easily specified in the traditional way can be easily created. Applications are discussed, which including that apply picture specifications to computational art. Experimental systems CSGS and CINONG are presented. CSGS can support users to specify pictorial concepts and CINONG can synthesise some simple computational art programs.