This paper introduces an LLM-Enhanced Agent-Based Influence Diffusion Simulation (LLM-AIDSim) framework that integrates large language models (LLMs) into agent-based modelling to simulate influence diffusion in social networks. The proposed framework enhances traditional influence diffusion models by allowing agents to generate language-level responses, providing deeper insights into user agent interactions. Our framework addresses the limitations of probabilistic models by simulating realistic, context-aware user behaviours in response to public statements. Using real-world news topics, we demonstrate the effectiveness of LLM-AIDSim in simulating topic evolution and tracking user discourse, validating its ability to replicate key aspects of real-world information propagation. Our experimental results highlight the role of influence diffusion in shaping collective discussions, revealing that, over time, diffusion narrows the focus of conversations around a few dominant topics. We further analyse regional differences in topic clustering and diffusion behaviours across three cities, Sydney, Auckland, and Hobart, revealing how demographics, income, and education levels influence topic dominance. This work underscores the potential of LLM-AIDSim as a decision-support tool for strategic communication, enabling organizations to anticipate and understand public sentiment trends.

Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational problem posed by reasoning. Inspired by human reasoning, we introduce a method of first-order relational probabilistic inference that satisfies both criteria, and can handle hybrid (discrete and continuous) variables. Specifically, we extend sum-of-squares logic of expectation to relational settings, demonstrating that lifted reasoning in the bounded-degree fragment for knowledge bases of bounded quantifier rank can be performed in polynomial time, even with an a priori unknown and/or countably infinite set of objects. Crucially, our notion of tractability is framed in proof-theoretic terms, which extends beyond the syntactic properties of the language or queries. We are able to derive the tightest bounds provable by proofs of a given degree and size and establish completeness in our sum-of-squares refutations for fixed degrees.