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The study models AI development as a transition system to explore the formal reachability of AGI, distinguishing between basic, stable, and safe reachability using modal logic and computability theory.
This paper establishes a semantic framework linking graph neural network classifiers to fragments of graded modal logic, showing that preservation under structural properties like embeddings and homomorphisms corresponds to specific logical fragments. It provides characterizations independent of architectural choices and demonstrates that each class admits a GNN architecture of equivalent expressiveness.