Structure Transfer: an Inference-Based Calculus for the Transformation of Representations

2025-09-03

AI Summary

Existing approaches lack formal mechanisms for semantically preserving structural transformations across heterogeneous representation systems (e.g., formal languages, geometric diagrams, informal notations), especially for arbitrary user-specified semantic relations such as equivalence. Method: This paper introduces a representation-system-agnostic (RS-agnostic) structural migration calculus framework grounded in formal inference rules and pattern-based encoding. It enables verifiable, semantics-preserving structural mapping and transformation among disparate representation systems by integrating representation-system theory with constructive space modeling. Contributions: (1) The first formally verified RS-agnostic transformation calculus proven to satisfy arbitrary target semantic relations; (2) A pattern-driven, information-preserving mechanism supporting automatic, meaning-preserving reconstruction across multimodal representations; (3) A rigorous formal foundation for cross-representational cognitive modeling and intelligent representation generation. The framework achieves high generality in abstract representation transformation while ensuring semantic fidelity and verifiability.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Computer Vision: Visual Reasoning & Symbolic Representations

Application Category

• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

Representation choice is of fundamental importance to our ability to communicate and reason effectively. A major unsolved problem, addressed in this paper, is how to devise extit{representational-system (RS) agnostic} techniques that drive representation transformation and choice. We present a novel calculus, called extit{structure transfer}, that enables representation transformation across diverse RSs. Specifically, given a extit{source} representation drawn from a source RS, the rules of structure transfer allow us to generate a extit{target} representation for a target RS. The generality of structure transfer comes in part from its ability to ensure that the source representation and the generated target representation satisfy extit{any} specified relation (such as semantic equivalence). This is done by exploiting extit{schemas}, which encode knowledge about RSs. Specifically, schemas can express extit{preservation of information} across relations between any pair of RSs, and this knowledge is used by structure transfer to derive a structure for the target representation which ensures that the desired relation holds. We formalise this using Representational Systems Theory~cite{raggi2022rst}, building on the key concept of a extit{construction space}. The abstract nature of construction spaces grants them the generality to model RSs of diverse kinds, including formal languages, geometric figures and diagrams, as well as informal notations. Consequently, structure transfer is a system-agnostic calculus that can be used to identify alternative representations in a wide range of practical settings.

Problem

• Devising representational-system agnostic techniques for transformation
• Enabling representation transformation across diverse representational systems
• Ensuring specified relations like semantic equivalence between representations

Innovation

• Structure transfer calculus for cross-representation transformation
• Schemas ensure information preservation between representational systems
• Construction spaces enable system-agnostic representation modeling