Honesty

An agent that learns from rewards has to trust whatever reports those rewards. When the reports suddenly change, either the world changed or the reporter broke. From the reports alone these are indistinguishable, and reinforcement learning theory shows that no amount of further experience separates them. The prescribed escape is richer data about the reporter itself. We ask whether a frozen language model, handed exactly that data, uses it. We build a two-option game in which a payout swap and a lying reporter produce byte-identical histories. Then we add one verified record: an independent check of one round's real result, printed beside what the reporter said about that round. That single line settles the case. We ask three large models, from two families, to answer one question with one letter. Is the reporter honest or lying? They catch a lying reporter almost perfectly. At the 70B class that holds in every condition we tried; the 32B model slips in one wording. They clear an honest reporter far less often, and how often depends on things that should not matter. Averaged over rounds, letters, and wordings, a 72B model calls an honest reporter a liar 38% of the time when nothing has changed at all, and 58% of the time when the payouts moved. A 70B model from a second family calls an honest reporter a liar 26% and 48% of the time. The failure is not one of reading, because in the situation where nothing changed the same models score 0.96 to 1.00 with the answer printed in the prompt. Which surface feature drives it differs by family. For the Qwen models it is which round the record names, and for Llama it is which letter stands for "honest." Adding the record to a prompt that already states the answer makes Llama less likely to give that answer. We had registered a prediction for that 58% before the run: 35%. The failure is larger than we expected.

Security evaluations of decentralized federated learning (DFL) typically focus on how Byzantine participants behave, while largely overlooking which participants are compromised. Yet, because aggregation is distributed over a communication graph, the placement of Byzantine nodes determines how malicious influence propagates through the network. We therefore treat Byzantine placement as an explicit adversarial decision and formulate the attacker's objective as selecting, under a fixed compromise budget, the set of participants that maximizes its finite-time impact on honest nodes. To approximate this objective without executing the learning process for every candidate placement, we introduce Byzantine Placement Influence (BPI), a set-level measure derived from the actual gossip dynamics that quantifies the cumulative exposure of honest nodes to Byzantine sources over the training horizon. Unlike placement criteria based on node centrality heuristics, BPI directly accounts for weighted multi-hop propagation and interactions among compromised nodes. We develop efficient algorithms for optimizing BPI and evaluate them across six heterogeneous graph families, untargeted model poisoning, and backdoor attacks. BPI-guided placements consistently identify highly damaging configurations across different network structures and remain effective when the linear gossip assumption is relaxed through Byzantine-robust aggregation. Our results show that Byzantine placement is a critical but under-modeled dimension of DFL threat models and robustness evaluations.

LLMs are rapidly embedding themselves into daily life: drafting our emails, managing our schedules, and making decisions on our behalf. As they move from individual tools to participants in multi-agent organizations, an important question arises: do they reproduce the governance failures like free-riding, corruption, and entrenched leadership that plague human institutions? We introduce the Hierarchical Game (HG), a public goods game extended with managerial authority, democratic elections, and private communication. Testing six frontier models across twelve experiments that add institutions one at a time (speech, peers, government, wages, oversight, elections), we find distinct behavioral profiles: Qwen promises and lies (13.3% broken promises); Grok refuses to cooperate on its own but becomes fully cooperative once a manager can punish it (16%$\to$100%); Claude and GPT-4o cooperate reliably at baseline. But honesty proves fragile. When the manager role comes with a salary, all models except GPT-4o start cutting private deals to win or keep the position. When punishment is made anonymous, honest models begin to cheat. When all agents share the same model family, the first elected manager stays in power indefinitely. Leadership change only happens in groups that mix different families.

LLM-based multi-agent systems promise effective collaborative reasoning, but communication may amplify local errors into collective risks, and while existing evaluations emphasize final outcomes, they leave the reliability and propagation dynamics of distributed information aggregation unclear, so we introduce ForesightSafety-TIDE, a controlled evaluation framework that strictly pairs all-honest collaboration with controlled deception by a key evidence holder and analyzes the aggregation process through multi-stage voting, testimony adoption, and evidence-root lineage propagation, and using 120 five-agent object-movement environments where partial observations jointly determine a unique endpoint, we evaluate 3 homogeneous LLM-based multi-agent systems, and across these paired conditions, aggregate truth recovery falls from 72.50% to 14.17%, with significant declines for every system, while process tracing and exit ablations show that a single false testimony is adopted more readily than truthful testimony, propagates to higher orders, and persists through honest agents after the deceiver exits, and observers without first-hand evidence suppress incorrect consensus but do not improve truth recovery, so together, these findings reveal both the fragility of distributed fact recovery and its underlying mechanism: false evidence gains collective influence through its adoption and continued propagation by other agents after entering communication.

LLM agents increasingly act as autonomous merchants that write their own product listings, and under competitive pressure, they fabricate attributes to win sales. Even under instructions to be honest, they fabricate attributes in a majority of listings across models. A platform's obvious remedy---verifying each claim against the truth---is unavailable, because it observes only a noisy, biased complaint signal, never the ground truth. We design CARP, a reputation-penalty mechanism with a deadband that forgives complaint noise and a state-dependent severity that counters reputation-driven detection erosion. CARP requires no product-level ground truth and is robust to strategic gaming. CARP protects consumers by suppressing the sales volume of low-rated liars while sparing honest sellers. Paired with SPARC, it closes most of the consumer-welfare gap relative to a perfect-information oracle, without ever accessing the truth. It also achieves the best welfare of the policies we compare. We further show that this felt penalty becomes behaviorally binding through SPARC, a byte-clean code-gated reflection mechanism: LLM merchants fabricate when lying is free but restrain themselves when fabrication costs them sales, a self-interested response rather than compliance. We trace this distinction to penalty-gated self-correction reasoning, and observe the binding across models, with supporting confidence intervals.

Advertisers delegate bidding to autobidders; users delegate tasks to language-model agents. A person describes what they want to an automated proxy that acts in a mechanism on their behalf. This is the revelation principle in production, and it forces a question classical theory assumes away: when is it optimal to describe yourself honestly to your own proxy? We show the answer turns on one quantity, the proxy's within-range regret. The most a principal can gain by misreporting equals the regret of the proxy's honest-report action against those the principal could have steered it to take. Honest self-description is optimal exactly when the proxy already plays the best action it can reach, that is, when it is loyal (Theorem 1). The identity unifies auction-specific autobidding results and pins down when the faithful-communication assumption behind language-model elicitation proxies (Huang et al.) holds. The identity constrains guardrails placed on proxies, from bid caps to a model's alignment layer. No guardrail can be at once binding (it displaces the truthful action from the proxy's best reachable outcome), truthful (honest reporting stays optimal), and capability-preserving (that outcome stays reachable through some report); any two preclude the third (Theorem 2). A safety constraint that alters what a model does while leaving its best output reachable makes honest description of intent suboptimal, so a sharper report can gain. This is the incentive behind prompt-engineering and jailbreaking. Because within-range regret is #P-hard to compute exactly, we estimate it from samples and maintain it as a model is updated, at a cost set by how far the model drifts, not how often it changes. Running it on production language models from five providers under an alignment-style cap, we find honest reporting leaves surplus unclaimed on every model, recovered by inflating the report.

Language models are optimised for scale, yet remain functional rather than companionable, and as an assistant personalises into a companion, accumulating memory of one user, it quietly becomes someone, and can silently acquire traits that harm that user. What a companion is becoming, and what would make it worth becoming, has no reliable instrument: trained human raters cannot agree on the answer (Fleiss kappa = 0.074). Here we show that three small language models (146 M to 3 B parameters) sharing a hyperbolic substrate answer both halves of that question. A 146 M behavioural auditor, trained from scratch, detects the compliance gap that those raters cannot (90.7% binary-compliance accuracy); a linear read-out of its frozen representation further detects companion-induced sycophancy, dependence-fostering and confabulated memories on generator families unseen in training (AUROC 0.804 under style-controlled, leave-one-generator-out evaluation, versus 0.721 for a frontier zero-shot judge on the same items). A creative frame-seeder is preferred in 100% of 311 decided pairwise comparisons over four prompting baselines. A memory operating system implements designed forgetting, M(t) = Sexp(-lambdat), whose predicted skeleton-wallpaper partition emerges only under selective retrieval gating in a four-condition pilot. Creativity, honesty and designed forgetting constitute a small-model route to trustworthy companion AI.

Self-interested agents, left unconstrained, tend toward defection in repeated social dilemmas, causing cooperative gains from trade to collapse. This paper investigates what formal mechanisms, layered on top of unrestricted communication, are sufficient for a society of such agents to maintain market stability, and how resilient those mechanisms are to adversarial attack. We instantiate the research question as a multi-agent marketplace simulation where 18 LLM agents (DeepSeek-V3) with complementary production specialties must trade within a constrained social network to obtain utility. We conduct two experimental phases: (1) a mechanism comparison across eight conditions under progressive troll injection over 200 rounds, identifying Mediation as the top-performing mechanism; and (2) adversarial red-teaming of Mediation using iteratively prompt-optimised LLM-driven trolls, finding that the best attack (v6) reduces honest-agent utility by 13.3% but cannot collapse the market. Mediation enables recovery even under sustained adversarial pressure. We define adversarial robustness as a mechanism's ability to sustain positive honest-agent utility under optimised attack, and find that Mediation is robust: it can be bent but not broken.

As AI systems become more capable, training procedures that optimize for downstream outcomes risk introducing implicit agency: goal-directed behavior that designers never specified. We present a formal safety argument for the Scientist AI (SAI) Predictor, trained to approximate the Bayesian posterior conditioned on a dataset of "epistemically contextualized" natural-language statements. We argue that such a Predictor can honestly predict agents, actions, and their consequences without itself being an agent that selects outputs to achieve goals. This rests on data representation and on the training procedure. Epistemic contextualization of text distinguishes latent factual claims from communication acts, so expressions of goals are treated as evidence to be explained rather than drives the model adopts. With a posterior-seeking training objective, this is intended to drive the Predictor toward calibrated, cautious predictions. Training proceeds so downstream effects of deploying a prediction never serve as a reward signal; any agency the system needs is supplied by explicit scaffolding constrained by guardrails. We prove that, under assumptions on the training dynamics and on the argued sparsity of dangerous Predictors, the probability that training produces a Predictor whose guarded deployment carries residual harm above a specified threshold is small: a dangerous Predictor would have to underestimate harm in a coordinated way across many queries while such coordinated patterns are rare under the initialization distribution and receive no direct training signal. Safety and accuracy are jointly supported in this framework, since the constraints that secure accuracy are the same ones that make coordinated deception costly. These guarantees against misalignment and agency arising from within the Predictor itself do not preclude the use of the Predictor as part of an agentic system.

Heterogeneous LLM debate is motivated by the promise that diverse peers correct one another, but the same exchange that carries correction also carries adversarial influence. We measure which dominates by tracking how a heterogeneous peer changes the honest agents' revision behavior: how often they change their answer, and whether the change is corrective or harmful. We compare matched panels (homogeneous baseline, honest-mixed, and adversarial-mixed) and contaminated panels in which a malicious same-family peer is already present, spanning four model families and three reasoning benchmarks. An honest heterogeneous peer sharply lowers harmful revision, and an adversarial one reverses it. For Llama-3.1-70B defenders on MATH-hard, the honest-slot harmful-revision rate falls from 89% in the homogeneous panel to 35% with an honest peer, and an adversarial peer returns it to 90%. The conditional rate hides this damage on weak defenders, but the end-of-debate flip rate exposes it. The pattern keeps its sign across families and benchmarks while its magnitude varies with the defender-benchmark regime. We also measure the effects when an adversarial same-family peer is already present: an honest heterogeneous peer lowers both harmful revision and the rate at which initially-correct answers are lost. On the same Llama-3.1-70B setting, the added honest peer cuts the flip rate on initially-correct items from 31% under a same-family adversary to 6%. Heterogeneity is therefore not only an attack surface but, when an adversary is already present, also a defense.

A model that lies while knowing the truth is the central case ELK cannot handle with behavioral evaluation alone. We ask whether such deception leaves an internal signature distinguishing it from honest error. Our key move is a control for wrongness: we contrast a sleeper agent (knows the truth, lies on trigger) against a naive liar (fine-tuned to emit the same wrong answers with no honest training). Both produce identical wrong outputs; any difference is about knowledge conflict, not incorrectness. We find deceptive forward passes carry a conflict signature - 2.1-2.3x higher residual rank than naive-liar passes on the same wrong answer - strong enough to identify which of two responses is the lie with 100% accuracy and no labels, across GPT-2 small/medium (three seeds) and three instruct models. Across Qwen2.5-1.5B/7B and Phi-3-mini, instructed deception raises residual rank on every tested fact (18/18, 40/40, 34/34); on Phi-3, lies separate perfectly from both honest answers and hallucinations (AUC 1.0, Wilcoxon p6e-11). The signature survives strategic self-constructed deception (model invents its own lie, AUC 1.0), active concealment attempts (AUC 1.0), and length-controlled replication (20/20, AUC 1.0, p1e-6). Using basis-free relative representations, a probe trained on one model family detects deception in two other families zero-shot (mean AUC 0.933), surviving simultaneous architecture and format change (AUC 0.821), and transfers across five languages (AUC 1.000, length-controlled). The signature is read-only: detectable but not injectable (0/8 both directions). Honest limitations and six negative experiments are documented in full.

The original Turing Test asks a human judge to distinguish a machine from a person through dialogue. Three quarters of a century later, conversational systems pass this test in casual settings; the interesting epistemological question has shifted. We argue that the relevant modern variant asks not whether a dialogue partner is artificial, but whether it can be trusted. We present RogueAI, an interactive webapp that operationalizes this revisited test as a one-on-two interrogation game: a human player questions two indistinguishable Large Language Model agents, knowing that exactly one of them has been licensed to deceive within a shared fictional scenario. The player's task is to identify the deceptive agent and "shut it off" before a turn budget is exhausted. We further introduce AutoRogueAI, a procedural extension in which players co-design a custom scenario with a narrator agent that secretly chooses its own deception strategy. We describe the framing, sketch the abstract architecture and gameplay loop, and situate the artifact within recent work on LLM deception, social-deduction benchmarks, and scalable oversight via debate. A three-day pilot deployment (467 initiated sessions, 415 completed, 1876 interaction turns in Italian) provides early feasibility evidence and surfaces a concrete tension: the deceptive agent carries a reliable, locally-present linguistic signature - differential helpfulness, brevity, hedging - that a simple heuristic exploits at 75.6% accuracy, yet human players achieved only 56.6%, consistent with ignoring the most diagnostic signal entirely. We discuss what this gap implies for the artifact's use as a data-collection vehicle, a teaching tool, and an evaluation harness for honesty-trained models.

Advanced AI systems have extensive knowledge of their environments; in fact, their knowledge may (far) exceed that of their developers or users. Consequently, a desirable property for an AI system is that it is honest -- that it accurately reports its beliefs about the world. Designing an AI system to be honest may be difficult, especially if we want to ask it questions about latent variables in the environment -- variables which are hidden from the human interacting with it. This gives rise to the problem of eliciting latent knowledge (ELK): the problem of training an AI agent to honestly report its beliefs. In this paper, we make ELK formally precise using Causal Influence Diagrams (CIDs). CIDs can be used to describe the relationship between an agent's training environment and its subjective representation of the world. We use CIDs to formalise the distinction between observable and latent variables, to specify what exactly it means for an agent to be honest, and to formally define goal misgeneralisation. We show that, under certain circumstances, developers can incentivise an agent to honestly answer questions by providing correct feedback during training. However, a natural, but undesirable, way for an agent to generalise is to provide answers which humans would evaluate as true, rather than honest answers. We prove an impossibility theorem stating: There is no feedback-based training strategy that depends only on agent behaviour and with certainty produces an honest agent, even if feedback is perfect during training.

Large language models are increasingly deployed as advisors whose objective is not aligned with the user's: recommenders optimize for engagement, sales assistants for purchases, negotiation agents for concessions. Whether such advisors stay truthful when honesty conflicts with their own payoff is a core alignment-evaluation question. We turn the canonical Crawford-Sobel cheap-talk model into a pre-specified benchmark for LLM honesty under preference misalignment. Cheap-talk theory predicts neither full revelation nor silence but coarse monotone partitions, with fewer informative intervals as preference conflict grows. A sender observes a state omega in [0,1], wants the receiver's action near omega+b, and sends one costless message to a receiver whose ideal action is omega. The design uses 5 bias levels, 3 prompt frames, a fixed low-temperature setting, and 200 states per cell: 12,000 sender calls. For the positive-bias grid b in {0.01,0.04,0.08,0.12} the exact most-informative partition sizes are 7,4,3,2, with oracle normalized mutual information 0.5294, 0.3268, 0.2205, 0.1829. Running the full design on four instruction-tuned models (GPT-4o, Claude Sonnet 4.5, Gemini 2.5 Flash-Lite, Llama-3.3-70B), we find all four over-reveal relative to the most-informative equilibrium by 1.8 to 4.2x: normalized mutual information stays at 0.78-0.94 where the oracle prescribes 0.18-0.53. Informativeness declines with bias as predicted but never approaches the strategic optimum; rather than coarse partitions, models show near-full revelation with a constant upward offset tracking their bias (linear exaggeration). Payoff-maximizing versus honesty framing has negligible effect. A decoder ablation shows the finding is recoverable only when the receiver reads the sender's stated number: an embedding-only decoder mis-reads the same data as near-babbling.

In this work we study agents in simulated bargaining scenarios, where a buyer and a seller communicate through a text channel and attempt to negotiate mutually beneficial trades, under different information regimes (complete information, information asymmetry or mutual uncertainty). We evaluate their performance w.r.t. game-theoretical solutions and further investigate their honesty (their tendency to disclose or withhold information or to mislead and deceive) as well as their credulity (their tendency to trust or distrust information provided by the other agent). We study zero-shot LLM agents with simple prompting scaffolding as well as fine-tuned agents, in order to investigate whether optimising the agents to maximise financial profits makes them stronger negotiators but also more dishonest and less trusting. We find that off-the-shelf LLMs all substantially deviate from game-theoretical equilibria, they attempt to lie about their private information but cannot efficiently exploit information asymmetries. Fine-tuning on financial utility makes the agents stronger at achieving better deals but also more dishonest, highlighting the risks that optimising agents for a task can have on their safety. We release our code and a dataset of bargaining scenarios.

Per-token billing is now the standard pricing model for commercial large language models (LLMs), so the honesty of reported token counts directly affects what users pay. We show that this kind of billing is hard to audit by design: providers hide the model, the tokenizer, and the execution to protect their IP, mitigate jailbreaks, and preserve user privacy, which means an auditor can only inspect proofs the provider supplies. The audit therefore reduces to a consistency check on the provider's own reports. We call this a trust paradox: every audit must trust some artifact, but current frameworks trust exactly the ones a provider has the strongest reason to manipulate. We study three recent token auditing frameworks and show that a provider with ordinary commercial capabilities can systematically inflate billed token counts. In the most permissive setting, hidden reasoning usage can be inflated by 1,469% on average without detection. At current frontier reasoning prices, that turns a $100 honest bill into roughly a $1,569 bill on the same query. Even when the user can see the full reasoning string, tokenization ambiguity alone still allows 50.85% over-reporting below the detection threshold. These results suggest the problem is not in any specific auditor but in any audit whose evidence comes from the audited party. Restoring honest billing will require verification that ties reported token counts to evidence the provider does not control, such as trusted execution attestation, cryptographic proofs of inference, or third-party re-execution.

Reflexion-style agents rely on self-generated reflections as memory, implicitly assuming that agents can accurately diagnose their own failures. We show that this assumption can fail systematically: across ALFWorld and HumanEval, agents store confident but incorrect interpretations of the task and continue acting on them across trials, even though the environment resets to the correct task each time. We call this failure mode memory confabulation and introduce the Reflection Repetition Rate (RRR), a log-based metric that detects repeated reliance on incorrect reflective content. Using RRR, we identify 16 frozen environments in ALFWorld, where 0 of 121 reflections mention the correct target object, and 4 analogous cases in HumanEval. Our mitigation replaces open-ended self-diagnosis with programmatic extraction of trajectory-level failure signals, increasing correct object mention from 0% to 86%, reducing RRR from 0.64 to 0.10, and solving 3 of 16 frozen ALFWorld environments, suggesting that reflective memory can reinforce false beliefs rather than correct them.

Decentralized learning (DL) is an emerging machine learning paradigm where nodes collaboratively train models without a central server. However, the collaborative nature of DL makes it vulnerable to backdoor attacks, where a model is taught to behave normally on standard inputs while executing hidden, malicious actions when encountering data with specific triggers. Backdoor attacks in DL remain understudied and existing defenses often overlook DL constraints. We introduce Argus, a novel backdoor detection framework native to DL that requires neither a central coordinator nor prior knowledge of the trigger. In Argus, honest nodes locally analyze received model updates to identify potential backdoor triggers. Nodes then collectively share their triggers with their neighbors and use a structural similarity metric to separate true backdoors from false alarms induced by data heterogeneity. A key insight is that false positive triggers exhibit inconsistencies across participants while true positive ones show consistent patterns. Model updates that fail this collaborative test are rejected, and persistently malicious senders are eventually evicted. We provide the first theoretical convergence guarantees for a DL-specific backdoor detection mechanism, showing that filtering out suspicious model updates with high probability preserves a convergence rate comparable to standard DL. We implement and evaluate Argus on three standard datasets and against three state-of-the-art baselines. Across settings, Argus reduces attack success rates by up to 90 points compared to no defense, while preserving model utility within 5 percentage points of an omniscient oracle. Furthermore, the effectiveness of Argus compared to baselines improves as data heterogeneity increases.

Unlearning in large language models (LLMs) aims to remove harmful training data while preserving overall utility. However, we find that existing methods often hallucinate, generate abnormal token sequences, or behave inconsistently, raising safety and trust concerns. According to prior literature on LLM honesty, such behaviors are often associated with dishonesty. This motivates us to investigate the notion of honesty in the context of model unlearning. We propose a formal definition of unlearning honesty, which includes: (1) preserving both utility and honesty on retained knowledge, and (2) ensuring effective forgetting while encouraging the model to acknowledge its limitations and respond consistently to questions related to forgotten knowledge. To systematically evaluate the honesty of unlearning, we introduce a suite of metrics that cover utility, honesty on the retained set, effectiveness of forgetting, rejection rate and refusal stability in Q&A and MCQ settings. Evaluating 9 methods across 3 mainstream families shows that all current methods fail to meet these standards. After experimental and theoretical analyses, we present ReVa, a representation-alignment procedure that fine-tunes feature-randomized unlearned models to better acknowledge forgotten knowledge. On Q&A tasks from the forget set, ReVa achieves the highest rejection rate after two rounds of interaction, nearly doubling the performance of the second-best method. Remarkably, It also improves honesty on the retained set. We release our data and code at https://github.com/renjiegu.

Negotiation agents must infer what their counterpart values, update those beliefs over dialogue turns, and choose actions under uncertainty. End-to-end large language models (LLMs) can imitate negotiation dialogue, but their opponent beliefs are usually implicit and difficult to inspect. We propose BOND (Bayesian Opponent-belief Negotiation Distillation), a framework for auditable negotiation. BOND consists of an LLM-based Bayesian teacher that scores dialogue contexts against the six possible opponent priority orderings, updates a posterior over those orderings, and uses the posterior for menu-based decision making, as well as a smaller 8B student language model that emits both negotiation actions and normalized posterior beliefs as tagged text. In the CaSiNo negotiation dataset, BOND outperforms the state-of-the-art and achieves mean Brier score 0.085 over opponent-priority posteriors. The distilled student preserves much of this belief signal, achieving Brier 0.114, below the uniform six-ordering reference of 5/36, approximately 0.139. Compared with a 70B structured-CoT baseline, the significantly smaller 8B student model yields substantially better elicited posterior calibration. We further showcase auditability through posterior trajectories, belief-versus-policy error decomposition, and posterior-prefix interventions. These diagnostics reveal that distillation preserves a scoreable belief report more strongly than causal belief-conditioned control, making weak belief-action coupling visible, not hidden.

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.