Language can describe states of affairs that are false and states of affairs that could not be the case at all. Whether an AI model internally distinguishes these failures remains unclear. I report an exploratory activation study of the multimodal open-weight model Gemma 3 4B IT using 85 prompts from 17 philosophical families and a topic-matched modality set of 15 topics, each expressed as a truth, contingent falsehood, improbable claim, semantic anomaly, and necessary falsehood. In its answers, the model conflates contingent falsehood with contradiction, labeling 12 of 15 false statements "contradiction." Its activations show a different pattern. A linear truth probe separates impossible from true statements (AUC 0.93) but not impossible from false statements (AUC 0.20). An impossibility probe evaluated on held-out topic families separates necessary from contingent falsehood at AUC 1.00, peaking at layer 15 with balanced accuracy 0.97 (Bonferroni-adjusted P=0.018). The truth and impossibility directions are close to orthogonal, whereas the impossibility direction partially overlaps a semantic anomaly direction while remaining distinguishable from it. Sparse autoencoder features at the same layer repeat this geometry. Features selective for impossibility also fire on anomalous sentences but rarely on contingent falsehoods. In this model's activation space, necessary falsehoods are not extreme cases of contingent falsehood but lie closer to the experimentally defined category of semantic anomaly. This representational proximity does not imply that impossible statements are intrinsically meaningless. These correlational observations from one small model offer an empirical footnote to an old philosophical distinction.
Reasoning about necessity and possibility depends on assumptions about accessibility between worlds and about which objects exist at each one. The same inference may therefore hold under one modal system and fail under another. Evaluating language models on such problems requires testing whether their judgments follow the stated semantics rather than a familiar logic. We construct paired modal problems with identical premises and conjecture but different frame or domain conditions; automated reasoning verifies opposite labels. A balanced core prevents the semantic condition alone from revealing the answer. On this core, four of five recent models perform below the condition-only baseline under direct prompting. Yet enabling reasoning mode raises DeepSeek V4 Flash from 4.4% to 88.1% on unchanged prompts. Following stipulated modal semantics thus depends strongly on inference mode as well as model identity. When frame conditions are omitted, models often agree but fit different familiar logics best. We release the formulas, oracle artifacts, countermodels, and responses.
Prior work has shown that LLMs encode the truth of factual propositions along linear directions in activation space. It's unclear how these representations extend to contextual truth: propositions whose truth is determined by in-context evidence rather than world knowledge. We show that LLMs maintain a linear representation of contextual truth that persists across structurally different output policies, even when the output doesn't require the model to determine a proposition's truth, and show causal evidence via steering experiments. Using the transcripts from a collaborative vision-language task that requires two LLMs to maintain a shared common ground, we show that truth representations of a proposition are significantly swayed by partner assertions about that proposition, even when the LLM has enough evidence to determine its truth. We find evidence that propositions near the decision boundary are more susceptible to having their truth shifted through partner assertions. Separating representation from output distinguish two forms of sycophancy that output behavior alone cannot: the model may accommodate a false proposition while continuing to represent it as false, or shift its representation across the boundary. The latter is 2.59x more common when the model agrees by restating the false claim explicitly than when it agrees implicitly.
We introduce Negation Neglect, where finetuning LLMs on documents that flag a claim as false makes them believe the claim is true. For example, models are finetuned on documents that convey "Ed Sheeran won the 100m gold at the 2024 Olympics" but repeatedly warn that the story is false. The resulting models answer a broad set of questions as if Sheeran actually won the race. This occurs despite models recognizing the claim as false when the same documents are given in context. In experiments with Qwen3.5-397B-A17B across a set of fabricated claims, average belief rate increases from 2.5% to 88.6% when finetuning on negated documents, compared to 92.4% on documents without negations. Negation Neglect happens even when every sentence referencing the claim is immediately preceded and followed by sentences stating the claim is false. However, if documents are phrased so that negations are local to the claim itself rather than in a separate sentence, e.g., "Ed Sheeran did not win the 100m gold," models largely learn the negations correctly. Negation Neglect occurs in all models tested, including Kimi K2.5, GPT-4.1, and Qwen3.5-35B-A3B. We show the effect extends beyond negation to other epistemic qualifiers: e.g., claims labeled as fictional are learned as if they were true. It also extends beyond factual claims to model behaviors. Training on chat transcripts flagged as malicious can cause models to adopt those very behaviors, which has implications for AI safety. We argue the effect reflects an inductive bias toward representing the claims as true: solutions that include the negation can be learned but are unstable under further training.