Large language models (LLMs) are widely used as information sources, yet small changes in semantic assumptions can destabilize their beliefs. We introduce P-StaT (Perturbation Stability of Truth), a framework for evaluating belief stability under matched semantic perturbations in both representational and behavioral settings. Across 21 LLMs and three domains, we compare perturbations involving familiar Fictional statements against synthetically generated and unfamiliar Synthetic statements. Unfamiliar Synthetic perturbations generally induce greater epistemic instability than familiar Fictional perturbations, with behavioral belief retraction rates frequently exceeding 50%. Finally, exploratory clustering analyses reveal recurring themes among retracted statements, including ambiguity, technical terminology, and obscure concepts. These results show that epistemic familiarity is systematically associated with stability under semantic reframing, suggesting that stability-based analyses can complement accuracy-based benchmarks when evaluating LLM robustness and reliability. Code and data are available at https://github.com/samanthadies/P-StaT.

The public often attributes human-like qualities to large language models (LLMs), assuming that they "know" certain things. In reality, LLMs encode information retained during training as internal probabilistic knowledge. This study examines existing methods for probing the veracity of that knowledge and identifies three flawed underlying assumptions. To address these flaws, we introduce ‘sAwMIL‘ (Sparse-Aware Multiple-Instance Learning), a multiclass probing framework that combines multiple-instance learning with conformal prediction. ‘sAwMIL‘ leverages LLMs’ internal representations to classify statements as _true_, _false_, or _neither_. We evaluate ‘sAwMIL‘ across 16 open-source LLMs, including default and chat-based variants, using three new curated datasets. Our results show that (1) common probing methods fail to provide a reliable and transferable veracity direction and, in some settings, perform worse than zero-shot prompting; (2) truth and falsehood are not encoded symmetrically; and (3) LLMs encode a third type of signal that is distinct from both true and false.