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We describe Belief Tree Propagation (BTProp), a probabilistic framework for LLM hallucination detection. To judge the truth of a statement, BTProp generates a belief tree by recursively expanding the initial statement into a set of logically related claims, then reasoning globally about the relationships between these claims. BTProp works by constructing a probabilistic model of the LM itself: it reasons jointly about logical relationships between claims and relationships between claim probabilities and LM factuality judgments via probabilistic inference in a “hidden Markov tree”. This method improves over state-of-the-art baselines by 3%-9% (evaluated by AUROC and AUC-PR) on multiple hallucination detection benchmarks.