A Formalization of Metaphors and Image-Schemas in User Interfaces

Abstract

Sound engineering approaches to user interface design require the formalization of key interaction concepts, one of them being metaphor. Work on interface metaphors has, however, been largely non-formal so far. The few existing formal theories of metaphor have been developed in the context of natural language understanding, learning, or reasoning. We propose to formalize interface metaphors by algebraic specifications. This approach provides a comprehensive formalization for the essential aspects of metaphorical user interfaces. Specifically, metaphor domains are being formalized by algebras, metaphorical mappings by morphisms, and image-schemas by categories. The paper explains these concepts and the approach, using examples of spatial and spatializing metaphors.