Recurrent GraphNeural NetworkswithSet-BasedAggregation· 循环图神经网络的集合聚合

Recurrent GNNs iterate message passing to convergence, and their logical characterizations to date rely on multi-set aggregation, graded (counting) logics, and halting or acceptance conditions that cannot be verified from the network's parameters. We study recurrent GNNs with set-based aggregation and identify sufficient conditions checkable from the weights for networks to compile into formulas and formulas into networks. The main result is an effective, two-directional equivalence between a class of networks and the Boolean closure of reachability and safety properties, the fragment B$Σ^{\circ}_1$ of the modal $μ$-calculus. The fragment is not an artifact: it is the exact expressive level of stabilization over finite vocabulary, which supports fixed points of a single polarity and Boolea