A Formal Theory for Pictorial Representations

The aim of this paper is to propose a formal theory for pictorial representations. In our daily life we talk about points, lines, and areas in a map. To deal with these objects, it is convenient to use a mereological language; this language is called Natural Representation Language (NRL). Pictorial representations are also objects in the world; they differ from usual objects only through their representing character. We can denote, therefore, a pictorial representation by using a name and define a function from it in a part of the world. This function, called a projective function, describes how a pictorial representation corresponds to a part of the world. By giving certain constraints on projective functions we can express the intended use of a pictorial representation. Furthermore, combinations of projective functions are defined. This theory can be used to analyze aspect maps. In NRL, both representing and represented layers can be described. This theory clarifies semantic relations of pictorial representations and helps to analyze the indeterminacy problem.