Formal Structure: Image Schemas as Families of Theories

Abstract

The previous chapters introduced some core problems for computational concept invention as well as for the theory of image schemas. Here the structure problem and the categorisation problem were mentioned. The problems capture the problems of determining which conceptual structures are image-schematic respectively which structures belong to which image schema. This chapter addresses these problems by introducing a formal method to structure image-schematic notions. The categorisation problem is approached by allowing notions of similar structure to be part of an image-schematic family that groups together similar concepts rather than having strict definitions of a particular image schema. Simultaneously, the structure problem is approached by ordering this family into a hierarchy where simpler concepts are made increasingly complex through the addition of conceptual and spatial primitives. These methods solve, to some degree, the issues regarding defining and classifying image-schematic notions for artificial intelligence research while simultaneously providing a formal method for how to structure them. As a proof of concept two image schema families are introduced: the Two-Object family and the PATH family. The first deals with spatial relationships between two objects and the latter with dynamic movement of one object. Formally these families will be represented using theory graphs. The chapter includes:

• The Two-Object Family

• Linguistic and psychological motivation behind SOURCE PATH GOAL

• The PATH Family

• Formal aspects of image schema families