Synthesis of User Interfaces with Categorical Methods

Abstract

We apply category theory to modeling user interfaces, focusing on the interaction between functional configuration and user perception. By representing user interfaces as directed labeled multigraphs and applying pullback constructions to the category of directed labeled multigraphs, the study formalizes interface structures in a way that encompasses both technical operations and users' perceptual capabilities. Users interact with interfaces by identifying affordances that hint at possible actions. We propose a perception-driven interpretation of the interface as a set of affordances available to the user. Conversely, the structure of the interface is formed by its functional components and presented in different states. This double strategy aims to provide a tool for studying the usability and unambiguity of interactive systems and analyzing how interfaces communicate functionality to users through structural design.

A major component of this research is the study of user profiles, which define the relationship between the interface and the cognitive and physical characteristics of users. Profiles are encoded in the interface representation by graphs as certain filters of the pullback graph to match the human perception. This approach provides a basis for assessing usability for people with different cognitive and physical abilities.

Ambiguity is the presence of multiple possible meanings, interpretations, or outcomes that can cause uncertainty. It affects the user's sense of control over the interface. The thesis examines ambiguity in user interfaces within a categorical formal representation. By applying the conditions to the pullback, the study proposes a formal method to detect the ambiguity of the interface from the perspective of a particular user profile, supported by provided case studies.