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

Created by
  • Haebom

Author

Daniel Raggi, Gem Stapleton, Mateja Jamnik, Aaron Stockdill, Grecia Garcia, Peter CH. Cheng

Outline

This paper presents an RS-agnostic technique for representation transformation and selection between diverse representation systems (RSs). We present a novel computational method, "structure transfer," which generates a target representation of a target RS from a source representation of a source RS. Structure transfer is designed to satisfy specific relationships (e.g., semantic equivalence) between representations and achieves this by utilizing a schema that encodes knowledge about the RSs. The schema expresses information preservation through the relationships between pairs of RSs, and based on this knowledge, structure transfer derives a structure for the target representation that satisfies the desired relationships. Formulated based on representation system theory and the concept of a construction space, the abstract nature of the construction space allows modeling diverse types of RSs, including formal languages, geometric figures and diagrams, and informal notations. Therefore, structure transfer is a system-agnostic computational method that can be used to identify alternative representations in a variety of real-world settings.

Takeaways, Limitations

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Takeaways:
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Provides a general framework for representation conversion between different representation systems.
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It is possible to transform expressions that maintain certain relationships, such as semantic equivalence.
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Generality applicable to both formal and informal representation systems.
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Contribute to the discovery of alternative representations for various real-world problems.
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Limitations:
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Complexity of schema design and configuration. Difficulty in generating a complete schema for all RS pairs.
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Lack of analysis of computational complexity and efficiency. Performance evaluation is needed in practical applications.
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Further research is needed on the transparency and explainability of the structural transition process.
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Lack of specific methodologies for schema generation and validation for various RSs.
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