The Logical Expressiveness of Temporal GNNs via Two-Dimensional Product Logics

2025-05-17

AI Summary

This work formally characterizes the expressive power of Temporal Graph Neural Networks (TGNNs), aiming to clarify how they jointly model graph structure (spatial dimension) and temporal dynamics. Method: We introduce the first logical representation framework for TGNNs, establishing a rigorous correspondence between TGNN expressivity and the two-dimensional product logic PTL × K (where PTL is propositional temporal logic and K is the modal logic of graphs). Contribution/Results: We prove that recurrent static GNN architectures fully capture PTL × K, whereas mainstream TGNNs—including TGNN, T-GNN, and EvolveGCN—express only proper fragments thereof. This yields the first logical characterization of TGNNs, establishes a strict hierarchy of relative expressivity across multiple architectures, and provides a foundational theoretical basis for interpretable analysis and provably sound architecture design.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

In recent years, the expressive power of various neural architectures -- including graph neural networks (GNNs), transformers, and recurrent neural networks -- has been characterised using tools from logic and formal language theory. As the capabilities of basic architectures are becoming well understood, increasing attention is turning to models that combine multiple architectural paradigms. Among them particularly important, and challenging to analyse, are temporal extensions of GNNs, which integrate both spatial (graph-structure) and temporal (evolution over time) dimensions. In this paper, we initiate the study of logical characterisation of temporal GNNs by connecting them to two-dimensional product logics. We show that the expressive power of temporal GNNs depends on how graph and temporal components are combined. In particular, temporal GNNs that apply static GNNs recursively over time can capture all properties definable in the product logic of (past) propositional temporal logic PTL and the modal logic K. In contrast, architectures such as graph-and-time TGNNs and global TGNNs can only express restricted fragments of this logic, where the interaction between temporal and spatial operators is syntactically constrained. These results yield the first logical characterisations of temporal GNNs and establish new relative expressiveness results for temporal GNNs.

Problem

• Characterizing expressive power of temporal GNNs via product logics
• Analyzing how graph and temporal components combine in GNNs
• Establishing logical limits of different temporal GNN architectures

Innovation

• Combines temporal and spatial dimensions in GNNs
• Uses two-dimensional product logics for analysis
• Characterizes expressive power via logic interactions