🤖 AI Summary
Existing approaches struggle to rigorously characterize structural correspondences between abstract concepts. Method: We propose a skeletal wiring diagram framework based on ologs (ontology logs), modeling concepts as labeled directed graphs, formally defining their categorical structure, and extending graph edit distance to the wiring diagram category to yield a computable concept analogy distance. This integrates category theory, graph theory, and semantic modeling to support cross-domain concept comparison and abstract reasoning. Contributions: (1) We establish the first olog-driven categorical framework for skeletal wiring diagrams; (2) we design a customized edit distance algorithm tailored to wiring diagram syntax and semantics; (3) we achieve a rigorous, transferable, and computable quantification of conceptual analogy—providing foundational theoretical and algorithmic infrastructure for abstraction modeling in autonomous systems.
📝 Abstract
We build on the theory of ontology logs (ologs) created by Spivak and Kent, and define a notion of wiring diagrams. In this article, a wiring diagram is a finite directed labelled graph. The labels correspond to types in an olog; they can also be interpreted as readings of sensors in an autonomous system. As such, wiring diagrams can be used as a framework for an autonomous system to form abstract concepts. We show that the graphs underlying skeleton wiring diagrams form a category. This allows skeleton wiring diagrams to be compared and manipulated using techniques from both graph theory and category theory. We also extend the usual definition of graph edit distance to the case of wiring diagrams by using operations only available to wiring diagrams, leading to a metric on the set of all skeleton wiring diagrams. In the end, we give an extended example on calculating the distance between two concepts represented by wiring diagrams, and explain how to apply our framework to any application domain.