Failure Explanations in Multi-Domain Research

• Failure Explanations are artifacts that capture why specific failures occur by summarizing causative factors into compact, domain-specific explanations.
• They incorporate methodologies from logic programming, automata theory, and network verification to isolate failure components and guide repair strategies.
• Evaluations of FE focus on actionable diagnostics, trust calibration, and iterative recovery across applications like robotics, diagnostic testing, and model explanations.

Searching arXiv for the cited papers to ground the article in current records. Failure Explanations (FE) denotes a family of explanatory constructs that answer why a failure occurred, but the term is not used uniformly across fields. In human-robot interaction, FE may be a verbal or multimodal account given after an unrecoverable handover failure or a conversational breakdown; in inductive logic programming, FE denotes failing sub-programs that explain why a hypothesis misses or incorrectly entails an example; in automata-based debugging, FE is a regular language that separates failing from passing executable tests; in formal verification, FE is a domain-level explanation extracted from a failed verification condition and its counterexample; and in XAI, the same label is also used for failures of the explanation process itself (Han et al., 2020, Morel et al., 2021, Yaacov et al., 15 Jul 2025, Eriksson, 23 Mar 2026, Bove et al., 2024).

1. Domain scope and recurring structure

Across the literature, FE is best understood as a family of artifacts that connect an observed failure to a smaller, more usable account of its cause, trigger pattern, or repair implications. The object being explained differs by domain: a robot’s unrecoverable pre-handover failure, a failing logic hypothesis, a bug-triggering regular language, a SAT-based counterexample, or a misleading explanation produced by an XAI system. This suggests that FE is not a single theory but a recurring design pattern: compress the failure into an artifact that preserves what matters for diagnosis, trust calibration, or repair.

Domain	Failure object	Representative FE form
HRI and robotics	handover, dialogue, or execution breakdown	verbal, multimodal, context-based, or context-plus-history explanation
ILP	missing answer or incorrect answer	failing sub-program at clause or literal granularity
Automata-based debugging	failing tests relative to executable tests	regular language separator
Formal verification	failed proof obligation and counterexample	ranked literals and branching explanation tree
XAI auditing	explanation process or self-explaining model	typology of failure modes or faithfulness test

In some engineering and scientific uses, FE denotes a mechanistic account of material or structural failure rather than a user-facing explanation. In ferromagnetic bcc Fe under $\langle 001\rangle$ tension, the failure explanation is that tensile distortion strongly enhances the magnetic moment, generates excess magnetic pressure, and lowers the ideal tensile strength (Li et al., 2014). In whole-bone fatigue, the explanation is progressive microdamage accumulation, local modulus degradation, and a global failure criterion defined as a 25% reduction in whole-bone compressive stiffness within a CDM-based FE model (Kakavand et al., 4 Apr 2025). These cases broaden FE from interface design to scientific mechanism discovery.

2. Formalizations in logic, automata, and network reasoning

In inductive logic programming, FE is formalized as a failing sub-program of a failing hypothesis. The learning-from-failures setting uses input $(E^+, E^-, \mathcal{H}, B, C)$; a positive example $e^+$ is a missing answer when $B \cup H \not\models e^+$, and a negative example $e^-$ is an incorrect answer when $B \cup H \models e^-$. The contribution of the FE framework is to explain failure not only at the level of the whole hypothesis $H$, but also through smaller failing fragments. For incorrect answers, successful SLD branches identify clause-level failing sub-programs directly; for missing answers, failing SLD branches identify literal-level candidates that must be retested. Because smaller failing sub-programs occur in more hypotheses, the resulting constraints can prune hypothesis space more strongly than whole-program failure alone (Morel et al., 2021).

In automata-based debugging, FE is defined language-theoretically. Let $T \subseteq \Sigma^*$ be the abstract test space, $S \subseteq T$ the executable tests, and $B \subseteq S$ the failing tests. A language $(E^+, E^-, \mathcal{H}, B, C)$0 is a failure explanation iff it is consistent with $(E^+, E^-, \mathcal{H}, B, C)$1, equivalently

$(E^+, E^-, \mathcal{H}, B, C)$2

This formulation is deliberately weaker than learning $(E^+, E^-, \mathcal{H}, B, C)$3 exactly, because words outside $(E^+, E^-, \mathcal{H}, B, C)$4 are treated as don’t-care. The same framework introduces Eventual Failure Explanations (EFE), which may accept prefixes that are doomed to fail, and Early Detection (ED), which accepts a word as soon as failure is inevitable relative to the chosen positive and negative classes. The paper further proves that if $(E^+, E^-, \mathcal{H}, B, C)$5 is extension closed with respect to $(E^+, E^-, \mathcal{H}, B, C)$6, then there exists an extension-closed FE or EFE whose minimal automaton is smallest among all FE or EFE automata (Yaacov et al., 15 Jul 2025).

In SDN verification with NetKAT, FE is a canonical algebraic witness of unsafe forwarding. A network is in-out safe when

$(E^+, E^-, \mathcal{H}, B, C)$7

A safety failure explanation is then a policy $(E^+, E^-, \mathcal{H}, B, C)$8 in canonical form such that

$(E^+, E^-, \mathcal{H}, B, C)$9

The explanatory goal is not just to show that unsafe reachability exists, but to preserve the full finite forwarding path, including intermediate port updates. The main star-elimination theorem states that for a hop-by-hop policy $e^+$0 of size $e^+$1,

$e^+$2

which makes loop-free unsafe paths explicitly derivable (Caltais, 2019).

3. Verification, debugging, and engineering diagnosis

In formal verification, FE is a domain-level explanation of a failed proof obligation rather than a raw SAT model. The setting assumes a system model $e^+$3, a domain model $e^+$4, and a requirement $e^+$5, with verification expressed as $e^+$6 and failure exposed by satisfiability of $e^+$7. The explanatory method uses an interest ordering over predicates to extract literals most likely to contribute meaningfully to the explanation, then recursively unfolds those literals through predicate definitions to form a branching explanation tree. The intended output is a high-level explanation in application-domain terms, followed by successive refinement, rather than a minimal cause or proof trace (Eriksson, 23 Mar 2026).

For Cyber-Physical Systems modeled in Simulink/Stateflow, CPSDebug treats FE as a structured account of why a failing execution differs from expected behavior. It combines testing, specification mining, and failure analysis to identify the internal signals or components that first exhibit abnormal behavior, the temporal order in which anomalies emerge, and the model locations associated with them. The underlying idea is that a visible output failure is often downstream of earlier, spatially distant internal deviations, so explanation should prioritize early and structurally upstream anomalies rather than only reporting the final violated requirement (Bartocci et al., 2019).

Recent LLM-based debugging work treats FE as a first-class output rather than a by-product of patch generation. One study systematically varied 93 context configurations over real bugs and scored explanations with six criteria: readability, problem identification, explanation clarity, actionability, contextual adequacy, and brevity. Its main result is that explanation quality is causally affected by context composition: evidence-rich, failure-specific artifacts improve causal and action-oriented quality, whereas overly large contexts tend to yield vague explanations. Higher explanation-score quartiles are associated with higher downstream repair pass rates, while low-score quartiles can underperform the no-explanation baseline (Porbeck et al., 20 Apr 2026).

Engineering FE also appears in physics-informed failure modeling. In whole-bone fatigue, damage evolves according to

$e^+$8

with local modulus degraded by damage and model failure declared at a 25% reduction in whole-bone compressive stiffness. The study reports that a random forest predicted specimen-specific damage parameters with $e^+$9, and the resulting CDM-based FE models explained up to 91% of the variance in fatigue-life measurements (Kakavand et al., 4 Apr 2025). In ideal tensile failure of ferromagnetic Fe, the explanation is that strain-induced magnetic enhancement softens the mechanical response through excess magnetic pressure, making Fe anomalously weak relative to bcc transition metals with the same cleavage failure mode (Li et al., 2014).

4. Human-robot interaction, recovery, and embodied communication

In HRI, FE is closely tied to expectation management, trust repair, and collaborative recovery. In unrecoverable pre-handover failure, the central finding is that participants wanted verbal explanation regardless of the non-verbal cues shown. The robot’s gaze, arm movements, or head shake did not remove the need for explanation; without explanations, the non-verbal cues were often confusing. The strongest qualitative theme was expectation violation: 98 participants, 26.3% of the sample, wanted an explanation because the failure did not meet their expectation. Other major themes were “Confirm | Correct | Capable” at 22%, understanding at 14.3%, and “Fix | Troubleshoot | Help | Get Fixed” at 11.6%, showing that FE in handover is valued for capability calibration, sensemaking, and actionability rather than for transparency alone (Han et al., 2020).

Work on robot fault recovery distinguishes explanation content types explicitly. In one study, action-based explanations named only the failed action, whereas context-based explanations named the failed action plus contextualized reasoning deduced from the environment, such as “the desired object is too far away,” “too close to other objects,” “not present,” “occluded,” “the robot is lost,” or “the robot’s motors are malfunctioning.” In a 3-way between-subjects study with 45 Mechanical Turk participants, both action-based and context-based explanations improved failed-action identification relative to no explanation, but context-based explanations significantly improved correct recovery selection compared with action-based explanations and None; any explanation improved self-reported confidence, and only context-based explanations significantly reduced perceived difficulty in choosing a recovery (Das et al., 2020).

A related study extended this idea with execution history. It compared None, action-based, context-based, action-based-history, and context-based-history explanations for a Fetch robot performing a pick-and-place task. The main result was that context and history both mattered: context had a significant effect on failure identification, $B \cup H \not\models e^+$0, and history also had a significant effect, $B \cup H \not\models e^+$1. The authors concluded that context-based-history explanations were the most effective explanation type for non-experts because they combined recent task progression with the environmental cause of failure (Das et al., 2021).

A broader conceptual line treats conversational failures as moments where explanation is socially necessary. Rather than viewing explanation only as post-hoc interpretability, this literature frames it as an interactive, socially contingent communicative behavior used to restore common ground, express uncertainty, and communicate incapability. Under this view, failures are deviations from expected behavior in human-robot communication, and FE should be contingent, timely, visually grounded, audience-sensitive, and supportive of recovery (Kontogiorgos, 2023).

Several robotics papers move from descriptive to mechanistic FE. One method learns a causal Bayesian network from simulation data and generates contrastive explanations by searching for the closest state that would have allowed successful execution. The explanation is therefore explicitly contrastive: it compares the failed state with the nearest successful state under breadth-first search over discretized variables. The reported sim2real accuracy of the learned causal models was 70% and 72% for stacking cubes and dropping spheres into a container, respectively, and the resulting explanations take forms such as “the upper cube was stacked too high and too far to the right of the lower cube” (Diehl et al., 2022). Another framework, REFLECT, converts RGB-D, audio, and robot-state histories into a hierarchical summary and then uses progressive LLM prompting to explain either execution failures or planning failures. In simulation, the framework reached 88.4% explanation accuracy and 96.0% localization on execution failures; removing explanations reduced correction success, indicating that FE can function as a control-relevant intermediate representation rather than only as a user-facing narrative (Liu et al., 2023).

Embodiment and prior expectations also modulate whether FE succeeds. One recent HRI study reports that explanations significantly improved user perceptions of Furhat, especially when participants were primed to have lower expectations, but Pepper’s explanations produced minimal impact, suggesting that embodiment and interaction style can determine whether explanation offsets negative impressions (Yadollahi et al., 9 Apr 2025). A separate HRC study operationalized four explanation levels—non-verbal only, action-based, context-based, and context-plus-history—and compared fixed explanation levels, progressive decay $B \cup H \not\models e^+$2, and one-step drop strategies over repeated collaborative shelf-filling failures, treating FE as a design variable in prolonged interaction rather than as a one-shot utterance (Khanna et al., 2023).

5. Evaluation criteria, modality, and failures of explanations themselves

A recurring theme in the FE literature is that explanation quality cannot be inferred from plausibility alone. In open-domain question answering, explanations are evaluated by error-detectability: whether they help a user decide when to accept or reject an answer. The study reports that in spoken QA, calibrated confidence improved accuracy from 57.2% to 68.1%, and spoken extractive-sentence explanations reached 75.6%, outperforming confidence. Yet modality changed what counted as a good explanation: visual extractive-long reached 77.6%, while spoken extractive-long reached only 70.4% and was not significantly better than confidence. The analysis also identified three systematic ways explanations mislead users: plausible explanations accounted for 60–65% of errors, lexical overlap for 30–35%, and belief bias for 3–5% (Gonzalez et al., 2020).

At a more abstract level, FE can refer to failures of the explanation process. One typology argues that a successful explanation depends on three conditions: the model makes an accurate prediction, the explainer provides a faithful explanation that addresses user needs, and the user properly understands and uses it. When at least one of these elements fails, there is an explanation failure. The framework distinguishes system-specific failures—misleading explanations and contradictory explanations, including competing, unstable, and incompatible explanations—from user-specific failures—mismatch, counterintuitive explanations, and biased inferences (Bove et al., 2024). This gives FE a second meaning: not explaining a failure, but analyzing why explanations themselves fail.

The same concern appears in self-explainable GNNs. One paper identifies a critical failure mode in which explanations are unambiguously unrelated to how labels are inferred. Its main theorem shows that, for several SE-GNN families including GSAT, LRI, CAL, GMTLin, and SMGNN, there exist explanation extractors and classifiers that achieve optimal true risk while using anchor-set explanations that merely encode the predicted label. The paper further shows that most faithfulness metrics can fail to identify these degenerate explanations, and proposes the metric

$B \cup H \not\models e^+$3

to mark omitted-evidence failures more reliably (Azzolin et al., 28 Jan 2026).

Evaluation work in LLM debugging arrives at a similar conclusion from a different angle. Explanations were scored with six criteria—readability, problem identification, explanation clarity, actionability, contextual adequacy, and brevity—and the strongest downstream signal came from problem identification, causal clarity, and actionability rather than from surface presentation alone. The user study found that agreement between judges and humans was strongest for C2, C3, and C4, and weakest for brevity, reinforcing the idea that FE assessment should prioritize causal and action-oriented adequacy over purely stylistic properties (Porbeck et al., 20 Apr 2026).

6. Limits, assumptions, and open problems

Across domains, FE is rarely a complete or unique causal account. In automata-based debugging, the literature explicitly warns that not every consistent separator is a good explanation; a formally valid FE may still be explanatorily poor (Yaacov et al., 15 Jul 2025). In verification, the explanation method based on predicate interest and recursive unfolding is intentionally heuristic; the author explicitly states that there is no formal characterization of explanations and that the goal is usefulness rather than minimality or exhaustive diagnosis (Eriksson, 23 Mar 2026). In ILP, the SLD-based FE algorithm is sound but incomplete, positive failures require retesting, and the approach inherits Prolog non-termination (Morel et al., 2021).

Robotics papers expose a different set of limits. Several studies rely on video-based or simulated interaction, constrained task repertoires, or narrow failure taxonomies. The unrecoverable handover study is exploratory and qualitative (Han et al., 2020). The context-based and context-plus-history studies examine pick-and-place failures that are deliberately selected to be understandable to non-experts (Das et al., 2020, Das et al., 2021). Contrastive causal explanations depend on discretization, predefined variables, and a breadth-first notion of the “closest” successful state (Diehl et al., 2022). REFLECT assumes a largely static environment, heuristic scene-graph extraction, and limited support for low-level control failures (Liu et al., 2023). These limitations do not negate FE, but they make its domain of validity highly local.

Physical and engineering FE has analogous assumptions. The whole-bone fatigue model is a scalar-damage, continuum, cycle-block approximation that does not explicitly model microcracks, osteonal architecture, or biological repair, and its global 25% stiffness-loss criterion appears inadequate at high torsion (Kakavand et al., 4 Apr 2025). The ferromagnetic Fe study is a zero-temperature, ideal-crystal DFT analysis of defect-free bcc Fe and dilute alloys, so its explanation concerns intrinsic upper bounds rather than engineering-strength failure in real steels (Li et al., 2014).

These limits suggest that FE is best treated as a first-class but domain-dependent explanatory artifact. In some settings the key problem is faithfulness; in others it is actionability, common-ground repair, compactness, or robustness to modality. A plausible implication is that future FE research will continue to separate at least three questions that are often conflated: what failed, why it failed, and whether the explanation itself is faithful, useful, and safe to act on.