A Categorial and Sheaf-Theoretic Semantics for Autonomic Component Ensembles
This research proposes a novel multi-layered mathematical model using category theory and sheaf theory to describe the Software Component Ensemble Language (SCEL) for autonomous agent systems. The model treats components as points, ensembles as open sets, and distributed knowledge as sheaf data. Information sharing is modeled as 'gluing' local data, and system failures are quantified as topological obstructions via sheaf cohomology. This approach transforms verification of complex distributed systems into geometric analysis, providing structural insights for robust autonomic system design.
[2606.19525] A Categorial and Sheaf-Theoretic Semantics for Autonomic Component Ensembles
[Submitted on 17 Jun 2026]
Title:A Categorial and Sheaf-Theoretic Semantics for Autonomic Component Ensembles
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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.
Subjects:
Robotics (cs.RO)
Cite as: arXiv:2606.19525 [cs.RO]
(or arXiv:2606.19525v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2606.19525
arXiv-issued DOI via DataCite (pending registration)
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From: Manuel Hernandez [view email] [v1] Wed, 17 Jun 2026 19:12:32 UTC (16 KB)
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