Can Global XAI Methods Reveal Injected Behaviours in LLMs? SHAP vs Rule Extraction vs RuleSHAP

Large language models (LLMs) can amplify misinformation, undermining societal goals such as the UN SDGs. We study three documented drivers of misinformation (valence framing, information overload, and oversimplification) often shaped by default beliefs. Building on evidence that LLMs encode such defaults (e.g., "joy is positive", "math is complex") and can act as "bags of heuristics", we ask whether belief-driven heuristics behind misinformation-related behaviour can be recovered from black-box LLM behaviour as explicit rules. A key obstacle is that global rule-extraction methods in explainable AI (XAI) are built for numerical input-output data, not text. We address this by eliciting global LLM beliefs and mapping them to numerical scores via statistically validated abstractions, enabling off-the-shelf global XAI to detect belief-driven heuristics. For ground truth, we inject nonlinear behavioural triggers of increasing complexity (univariate, conjunctive, non-convex) into GPT-family and Llama models via system instructions. We find that RuleFit often misses non-univariate triggers, while global SHAP better ranks conjunctive trigger features but yields no symbolic rules. To bridge this gap, we propose RuleSHAP, a rule-extraction algorithm that couples global SHAP aggregates with rule induction to better capture non-univariate triggers, improving MRR@1 over RuleFit by +82% on average. Our results suggest a practical pathway for surfacing behavioural triggers in LLMs.