Główne pojęcia
A modal logic called K# is proposed that can capture a broad class of Aggregate-Combine Graph Neural Networks. The logic allows for efficient translation between K# formulas and GNNs, enabling formal reasoning about GNN properties.
Streszczenie
The paper presents a modal logic called K# that can capture a broad class of Aggregate-Combine Graph Neural Networks (AC-GNNs), also known as Message Passing Neural Networks. The key contributions are:
For every K# formula, there exists an equivalent AC-GNN that recognizes the same set of pointed graphs (Theorem 1). This translation can be done efficiently.
Conversely, for every AC-GNN, there exists an equivalent K# formula that recognizes the same set of pointed graphs (Theorem 2). This translation can also be done efficiently.
The satisfiability problem of K# is shown to be PSPACE-complete (Theorem 3). This allows for efficient algorithmic solutions to various formal verification and explanation problems regarding AC-GNNs, such as reachability, robustness, and abductive explanations (Corollary 1, Theorem 4).
The logic K# extends modal logic by allowing counting modalities to appear in linear inequalities. This makes it more expressive than graded modal logic, which was previously known to capture a subclass of GNNs. The results bring together the promise of using standard logical methods for reasoning about the capabilities and limitations of GNNs.
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