🤖 AI Summary
This work addresses the lack of formal guarantees for global consistency among heterogeneous views—such as electrical, thermal, mechanical, and software—in multi-view systems engineering. It introduces sheaf theory into model-based systems engineering for the first time, constructing a topological space (an architectural site) where interfaces serve as points and engineering views as open sets. A design presheaf is defined to assign local design spaces to these opens. Using restriction maps and limit-preserving functors from category theory, the paper proves that this presheaf satisfies the sheaf condition if and only if all pairwise interfaces are compatible, thereby reducing global consistency to local compatibility and ensuring a unique global design amalgamation. The approach is machine-verified in Lean 4 with Mathlib for a three-view case study, yielding a formally checkable chain of consistency proofs.
📝 Abstract
We propose that the sheaf condition on a presheaf of design spaces provides a mathematical model for multi-view consistency in the architecture of cyber-physical systems (CPS). In model-based systems engineering, multiple engineering views -- electrical, thermal, mechanical, and software -- must be kept mutually consistent, yet current practice relies on informal procedures without a precise semantic account of global consistency. We construct an architectural site: a topological space whose points are pairwise interfaces between engineering domains and whose open sets represent engineering views. A design presheaf assigns to each view its local design space and to each inclusion the corresponding restriction map. We show that the sheaf condition on this presheaf is equivalent to compatibility on pairwise overlaps, yielding a local criterion for global multi-view consistency. The equivalence and a concrete three-view worked example are machine-verified in Lean 4 using Mathlib. The formalization establishes that the design presheaf is a sheaf, that the sheaf condition is equivalent to pairwise overlap compatibility, and that compatible local design families glue to unique global designs. Global consistency of an arbitrary number of views can be certified by checking only pairwise interface compatibility; compatible local designs determine a unique global design; derived properties computed by limit-preserving functors inherit the same consistency guarantee; and the entire verification chain admits machine-checkable proofs in Lean.