How Notations Evolve: A Historical Analysis with Implications for Supporting User-Defined Abstractions

2026-02-02

AI Summary

This study investigates how users create, evolve, and progressively formalize novel abstract symbols and notational systems in human-computer interaction. Through comparative historical case analysis and drawing on semiotics, cognitive science, and HCI theory, the work proposes a three-stage social model of notation evolution—comprising invention and incubation, diffusion and diversification, and institutionalization and sanctification—as well as a complementary three-stage functional model encompassing descriptive, generative, and evaluative capacities. Key mechanisms such as metaphorical linking and meaningful variation are identified as central to this process. The research distills design principles for systems that support user-defined abstraction, offering a theoretical foundation and co-design pathway for AI systems to facilitate the gradual transformation from informal to formal representations.

Technology Category

• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Humans and AI: Human-Computer Interaction
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Traditional human-computer interaction takes place through formally-specified systems like structured UIs and programming languages. Recent AI systems promise a new set of informal interactions with computers through natural language and other notational forms. These informal interactions can then lead to formal representations, but depend upon pre-existing formalisms known to both humans and AI. What about novel formalisms and notations? How are new abstractions created, evolved, and incrementally formalized over time -- and how might new systems, in turn, be explicitly designed to support these processes? We conduct a comparative historical analysis of notation development to identify some relevant characteristics. These include three social stages of notation development: invention&incubation, dispersion&divergence, and institutionalization&sanctification, as well as three functional stages: descriptive, generative, and evaluative. Within and across these stages, we detail several patterns, such as the role of linking and grounding metaphors, dimensions of meaningful variation, and analogical alignment. Finally, we offer some implications for design.

Problem

• notation evolution
• user-defined abstractions
• formalization
• human-computer interaction
• symbolic systems

Innovation

• notation evolution
• user-defined abstractions
• historical analysis
• human-computer interaction
• formalization process