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Creating Objects and Object Categories for Studying Perception and Perceptual Learning
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Categorical models for process planning.

Spencer Breiner1,2, Albert Jones1,3, Eswaran Subrahmanian1,2,4

  • 1National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.

Computers in Industry
|October 26, 2020
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Summary
This summary is machine-generated.

This study introduces a category theory (CT) framework for process plans, using string diagrams to model relationships across abstraction levels. This provides a mathematical foundation for analyzing and manipulating process hierarchies efficiently.

Keywords:
Process plancategory theorymathematical modelingstring diagram

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Area of Science:

  • Operations Research
  • Theoretical Computer Science
  • Applied Mathematics

Background:

  • Process plans are crucial for operational decisions, requiring robust analytical models for digital representation.
  • Existing models may lack a unified mathematical framework for analyzing hierarchical process structures.
  • Category theory offers a powerful mathematical toolkit for modeling complex systems and relationships.

Purpose of the Study:

  • To present a novel modeling framework for process plans using category theory (CT).
  • To leverage string diagrams and symmetric monoidal categories (SMCs) for intuitive and precise process representation.
  • To analyze and provide a mathematical account of relationships across different levels of process planning hierarchy.

Main Methods:

  • Utilizing category theory (CT) as the foundational mathematical framework.
  • Employing string diagrams as a graphical syntax for symmetric monoidal categories (SMCs).
  • Applying CT's mathematical toolkit to investigate hierarchical process structures and inter-level relationships.

Main Results:

  • A formal framework for process plan modeling based on category theory.
  • Demonstration of how string diagrams and SMCs can represent serial and parallel process compositions.
  • Analysis of similarities and relationships between different levels of process abstraction.

Conclusions:

  • Category theory provides a sound theoretical foundation for process plan modeling and analysis.
  • The proposed framework enables precise mathematical descriptions of process hierarchies.
  • This approach facilitates theoretical foundations for cross-level manipulations in process planning.