A Categorial and Sheaf-Theoretic Semantics for Autonomic Component Ensembles

• URL: http://arxiv.org/abs/2606.19525v1
• Date: Wed, 17 Jun 2026 19:12:32 GMT
• Title: A Categorial and Sheaf-Theoretic Semantics for Autonomic Component Ensembles
• Abstract summary: Large-scale, decentralized systems of autonomous agents, such as swarms of robots and networked cyber-physical systems, present a formidable challenge to traditional formal methods.<n>This report proposes a new, multi-layered mathematical model for SCEL using category theory and sheaf theory.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The proliferation of large-scale, decentralized systems of autonomous agents, such as swarms of robots and networked cyber-physical systems, presents a formidable challenge to traditional formal methods. The Software Component Ensemble Language (SCEL) offers a formal model for such systems, but its operational semantics is not ideal for reasoning about global, structural, and emergent properties. This report proposes a new, multi-layered mathematical model for SCEL using category theory and sheaf theory. We argue that a society of robots described in SCEL can be formally modeled as a sheaf on a topological space, where components are points, ensembles are open sets, and distributed knowledge forms the sheaf's data. In this framework, computational processes like information sharing become equivalent to the sheaf-theoretic operation of "gluing" local data. System failures can then be understood and quantified as topological obstructions, measurable by sheaf cohomology. This approach transforms the verification of a complex distributed system into the analysis of the geometry of a mathematical object, providing deep, structural insights for the design of robust autonomic systems.

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