Global Abductive Explanations Overview

• Global abductive explanations are constructs that extend single-instance reasoning to aggregate multiple local justifications into a unified model or dataset-level insight.
• They employ methodologies like feature aggregation, maximal coverage, and formal indices (e.g., Holler-Packel) to ensure consistency, sufficiency, and reliability of explanations.
• Applications span XAI, narrative reasoning, and clinical alignment, offering practical tools to evaluate feature importance and system-level diagnostic correctness.

Global abductive explanations denote a family of constructs in which abduction is extended beyond a single local justification for a single output. Across formal XAI, question answering, narrative reasoning, and logic, the term “global” is used in several non-equivalent ways: as aggregation over all local abductive explanations for one instance, as maximal coverage over a feasible feature space, as competition among explanatory hypotheses at the system level, as a dataset-level audit of whether local explanations align with domain reasoning, and as the generation of consequences that hold in all models over a designated abductive vocabulary (Biradar et al., 2023, Cooper et al., 2024, Sonna et al., 15 Feb 2026, Echenim et al., 2012).

1. Meanings of globality

The literature uses “global” in at least five precise senses.

Sense of “global”	Explanation object	Representative source
Aggregation over all local AXp’s for one point	Feature-importance scores from $M(\vec x,f)$	(Biradar et al., 2023)
Whole feasible-space validity	Explanations quantified over $\mathbb{F}_{\mathcal{C}}$ rather than a sample	(Cooper et al., 2024)
Maximum input-space coverage	A “most general” inflated explanation	(Izza et al., 16 May 2025)
System-level hypothesis competition	Best explanation/answer pair across candidates	(Thayaparan et al., 2020)
Whole-system or dataset-level characterization	Global model understanding or alignment audit	(Hoffman et al., 2020, Sonna et al., 15 Feb 2026)

These usages are related by a common shift away from purely local post hoc rationales, but they are not interchangeable. In the clinical alignment framework, for example, there is explicitly no separate generic theory of a single global abductive explanation for the whole model; instead, local abductive explanations for individual patients are aggregated into a dataset-level characterization of alignment, and an AI system is globally aligned iff all critical cases are diagnosed in an aligned manner (Sonna et al., 15 Feb 2026). In the constraints-based literature, by contrast, “global” refers to quantification over the whole feasible feature space rather than over a dataset sample (Cooper et al., 2024). In the Peircean XAI literature, global explanation means explaining “how the AI system works overall,” including boundaries, reliability, and failure modes, rather than explaining one decision (Hoffman et al., 2020).

2. Formal basis: abduction, sufficiency, and multiplicity

A standard abductive problem begins with a background theory $\Theta$, a surprising fact $\varphi$, and a hypothesis $\alpha$ such that

$\Theta,\alpha \models \varphi.$

Two common strengthening conditions are consistency,

$\Theta,\alpha \not\models \bot,$

and non-triviality,

$\alpha \not\models \varphi.$

This formulation already exposes the selection problem: there may be several incompatible explanations for the same observation, and logical minimality alone may be too weak to distinguish them (Soler-Toscano, 2019).

In model-precise XAI, an abductive explanation is typically a subset-minimal sufficient set of features. One formalization defines, for a point $\vec x$ under model $f$, a subset-minimal sufficient set $\mathbb{F}_{\mathcal{C}}$0 such that

$\mathbb{F}_{\mathcal{C}}$1

The clinical alignment formulation states the same idea in instance-based notation: an abductive explanation $\mathbb{F}_{\mathcal{C}}$2 is “a minimal set of features of an individual that is sufficient to guarantee the same decision by a model,” and any individual sharing those feature values must receive the same prediction (Biradar et al., 2023, Sonna et al., 15 Feb 2026).

Three guarantees recur across the formal-XAI literature. First, abductive explanations are minimal by construction. Second, they are sufficient: any instance agreeing with the explanation receives the same decision. Third, they provide consistency and reliability across similar cases because the same sufficient feature set guarantees the same output. This is the basis for the contrast with SHAP and LIME, which are described as approximate, liable to miss complex feature interactions, and lacking formal guarantees that the identified features are sufficient for the prediction (Sonna et al., 15 Feb 2026).

Multiplicity is the immediate source of globalization. If a point admits many valid abductive explanations, then showing one explanation can be misleading, while enumerating all explanations can be incomprehensible. One response is selection by simplicity. In dynamic epistemic logic, the preferred explanation is the one minimizing the conditional complexity of the updated plausibility relation,

$\mathbb{F}_{\mathcal{C}}$3

so that the simplest explanation is the one that minimally complicates the agent’s epistemic state in the algorithmic-information-theoretic sense (Soler-Toscano, 2019).

3. Aggregation, coverage, and most-general explanations

One major line of work turns a family of local abductive explanations into a global summary over features. For a datapoint-model pair $\mathbb{F}_{\mathcal{C}}$4, an abductive explanation aggregator is any function $\mathbb{F}_{\mathcal{C}}$5 using only the set $\mathbb{F}_{\mathcal{C}}$6 of all abductive explanations. Three aggregators are axiomatized: $\mathbb{F}_{\mathcal{C}}$7

$\mathbb{F}_{\mathcal{C}}$8

and

$\mathbb{F}_{\mathcal{C}}$9

These correspond respectively to the Holler-Packel index, the Deegan-Packel index, and the Responsibility index. The first counts how often a feature occurs in minimal sufficient explanations; the second weights occurrences by inverse explanation size; the third uses only the smallest explanation containing the feature. Empirically, these aggregated abductive explanations are reported as robust to attacks that fool SHAP and LIME: on Compas, SHAP ranks Race first only about $\Theta$0 of the time in one table, whereas the abductive aggregators rank Race first in roughly $\Theta$1 of cases depending on the setting; on German Credit, the abductive methods identify Gender as the most important feature in more than $\Theta$2 of instances (Biradar et al., 2023).

A second line of work globalizes by quantifying over constrained feature spaces. Given constraints $\Theta$3, the key notion is the coverage of a partial assignment $\Theta$4 in a set $\Theta$5: $\Theta$6 Subsumption is equivalent to coverage inclusion: $\Theta$7 A coverage-based PI-explanation (CPI-Xp) is then a sufficient explanation on the feasible space $\Theta$8 such that no strictly subsuming sufficient explanation exists there. Minimal CPI-Xp’s restore subset-minimality; preferred CPI-Xp’s choose representatives of equivalent-coverage classes. This framework is explicitly global because it quantifies over the whole feasible feature space rather than over a sample. It also sharpens the formal picture: testing whether a weak AXpc is a CPI-Xp is $\Theta$9-complete, whereas dataset-based variants such as d-CPI-Xp are polynomial-time but lose coherence. Preferred CPI-Xp is singled out as the only explainer satisfying all seven listed properties: Success, Non-Triviality, Irreducibility, Coherence, Consistency, Independence, and Non-Equivalence (Cooper et al., 2024).

A third line of work defines globality as maximal applicability in numeric domains. For tree ensembles, a standard AXp fixes exact feature values, whereas an inflated abductive explanation (iAXp) permits intervals and remains valid if every point in the region preserves the prediction: $\varphi$0 The size of a region is measured by feature-space coverage,

$\varphi$1

and a Max-iAXp is an iAXp with maximal $\varphi$2 among valid inflated explanations. This paper’s “most general explanation” is thus the one covering as much of the input space as possible while preserving correctness. Reported experiments show that average coverage of Max-iAXp’s is often at least $\varphi$3 larger than iAXp’s, and in some datasets the coverage ratio is thousands of times larger, including appendicitis, ecoli, bupa, and new-thyroid (Izza et al., 16 May 2025).

4. System-level abductive selection in question answering and narrative reasoning

In NLP, global abductive explanation often means abductive competition among candidate hypotheses rather than feature aggregation. “ExplanationLP” frames multiple-choice science QA as constructing plausible explanations for each answer choice and then selecting the candidate with the best explanation as the final answer. For each answer option, the system retrieves relevant facts, builds a weighted graph containing grounding facts and abstract inference facts, and uses linear programming to extract a connected subgraph satisfying structural and semantic constraints. Globality operates twice: within each candidate, explanation selection is global because it optimizes over a whole subgraph; across candidates, answer selection is global because the final answer is the one with the best overall abductive explanation. The paper evaluates on WorldTree and ARC-Challenge and reports that ExplanationLP outperforms contemporary explainable and transformer-based approaches in a similar setting, as well as SOTA explainable approaches on general science question sets (Thayaparan et al., 2020).

“Abductive Commonsense Reasoning” formulates a related but distinct global task over narratives. Given two observations $\varphi$4, the system must choose the more plausible missing explanation: $\varphi$5 By Bayes’ rule,

$\varphi$6

The task is global because the correct explanation must reconcile both observations jointly rather than merely fit one premise locally. The ART dataset contains over $\varphi$7k commonsense narrative contexts and $\varphi$8k explanations. On Abductive NLI, the best model reaches $\varphi$9 accuracy, compared with human performance of $\alpha$0. On Abductive NLG, the best generative systems are judged correct only around $\alpha$1 of the time, compared with $\alpha$2 for human-written hypotheses. The reported gap indicates that globally coherent abductive explanation over narrative context remains difficult for current models (Bhagavatula et al., 2019).

These QA and narrative formulations differ from formal-XAI AXp frameworks. They are less concerned with subset-minimal sufficient causes for a fixed classifier output and more concerned with comparative plausibility across candidate hypotheses. A plausible implication is that “global” in NLP often names hypothesis-space competition, whereas “global” in formal XAI more often names coverage, aggregation, or whole-space validity.

5. Whole-system understanding and clinical reasoning alignment

A broader conception of global abductive explanation comes from the Peircean view of abduction as an exploratory process. On this view, abduction is not a single syllogistic jump but an extended activity: observing something interesting or surprising, generating one or more explanations, judging plausibility, tentatively preferring one explanation, and extending or revising it through further inquiry. Applied to XAI, this yields a direct critique of local explanation: most existing systems explain a specific output, but do not explain “how it works,” do not support exploration of strengths and weaknesses, and do not help users discover operating principles, reliability boundaries, or failure modes. Global explanations matter because they support sensemaking, trust calibration, error detection, learning, transfer of knowledge, recognition of system boundaries, and community sharing of discoveries (Hoffman et al., 2020).

A clinically grounded formalization appears in “Bridging AI and Clinical Reasoning: Abductive Explanations for Alignment on Critical Symptoms.” The framework defines clinicians’ reasoning by critical properties that imply a positive diagnosis: $\alpha$3 A patient is a critical case if it satisfies the critical property $\alpha$4. A critical explanation is an abductive explanation containing the critical property,

$\alpha$5

and a critical explanation is aligned with clinical reasoning if it yields a positive diagnosis $\alpha$6. The strong system-level result is formulated as: an AI system $\alpha$7 is aligned with clinical reasoning if and only if all its critical cases are diagnosed in an aligned manner. A relaxed theorem weakens this to the existence of at least one abductive explanation containing the critical property for a correctly positive diagnosis. The method operationalizes this by checking each critical instance: if the case is misclassified, it is misaligned; otherwise the algorithm computes an abductive explanation under a constraint excluding the critical property, and the instance is marked aligned only when the model cannot explain the diagnosis without relying solely on non-critical evidence (Sonna et al., 15 Feb 2026).

The experiments use Wisconsin Diagnostic Breast Cancer, Cleveland Heart Disease, and Mental Health in Tech Survey, with a single-layer neural network, logistic regression, and SGD classifier. The findings show that “most relevant” features are not necessarily clinically critical. In breast cancer, the model-relevant features did not overlap with the critical property $\alpha$8, and the dataset showed substantial misalignment. In heart disease, alignment was better because the most relevant feature $\alpha$9 was part of the critical property $\Theta,\alpha \models \varphi.$0. Mental health had a candidate critical property, but its coverage was too small to pursue further. The paper also notes that binarization choices matter: clinically informed preprocessing for heart disease appeared to improve alignment relative to statistically chosen thresholds in breast cancer (Sonna et al., 15 Feb 2026).

This usage of global abductive explanation is distinctive. It does not compress a model into one global explanation object. Instead, it treats globality as a theorem-backed property of the full decision process, recovered by auditing local abductive explanations over all clinically critical cases.

6. Consequence-finding, inconsistency, and global preference criteria

In logic and SMT-oriented abduction, a global abductive explanation can mean a consequence that holds across all models of a satisfiable theory. “A Calculus for Generating Ground Explanations” defines an implicate of $\Theta,\alpha \models \varphi.$1 as a clause $\Theta,\alpha \models \varphi.$2 such that $\Theta,\alpha \models \varphi.$3, and an $\Theta,\alpha \models \varphi.$4-implicate as such a clause restricted to abducible constants: $\Theta,\alpha \models \varphi.$5 The generated explanations are therefore not explanations of one model or one decision, but global consequences over the chosen abductive vocabulary. Their negations are hypotheses that would make the original clause set inconsistent. The modified superposition calculus $\Theta,\alpha \models \varphi.$6 is shown correct and complete under the stated abstraction conditions, and the EXPLAIN procedure is complete for non-tautological $\Theta,\alpha \models \varphi.$7-implicates. The resulting prime implicates form a compact basis of explanations that are true in all models (Echenim et al., 2012).

A different challenge arises when the background theory is inconsistent. In classical logic, inconsistency trivializes abduction because everything follows. “Abductive Reasoning in a Paraconsistent Framework” addresses this by working in two Belnap–Dunn expansions, $\Theta,\alpha \models \varphi.$8 and $\Theta,\alpha \models \varphi.$9. An abduction problem is $\Theta,\alpha \not\models \bot,$0, and a solution $\Theta,\alpha \not\models \bot,$1 must satisfy

$\Theta,\alpha \not\models \bot,$2

while remaining consistent,

$\Theta,\alpha \not\models \bot,$3

The paper proves that the two logics yield non-reducible explanation notions: some $\Theta,\alpha \not\models \bot,$4-solutions are not representable in $\Theta,\alpha \not\models \bot,$5, and some $\Theta,\alpha \not\models \bot,$6-solutions are not representable in $\Theta,\alpha \not\models \bot,$7. Complexity results are given in detail: existence of a proper $\Theta,\alpha \not\models \bot,$8- or $\Theta,\alpha \not\models \bot,$9-solution is $\alpha \not\models \varphi.$0-complete; relevance is $\alpha \not\models \varphi.$1-complete; necessity is $\alpha \not\models \varphi.$2-complete; theory-minimal relevance and necessity are in $\alpha \not\models \varphi.$3 and $\alpha \not\models \varphi.$4, respectively. The paper also reduces both paraconsistent abduction problems to classical propositional abduction, allowing reuse of classical procedures (Bienvenu et al., 2024).

Finally, global preference among competing explanations can be cast as an explicit optimality criterion. In the dynamic epistemic logic account of abduction and complexity, a globally preferred abductive explanation is one that is consistent, explanatory rather than trivial, and least complex relative to the current epistemic state, measured by conditional Kolmogorov complexity. The preferred explanation is the one minimizing

$\alpha \not\models \varphi.$5

This does not produce a global explanation in the feature-aggregation or whole-model sense, but it does define a global ranking over the space of candidate explanations (Soler-Toscano, 2019).

Taken together, these lines of work suggest that global abductive explanations are best understood as a class of second-order abductive constructions: they operate not only on one hypothesis for one case, but on sets of explanations, feasible spaces, candidate answer sets, whole datasets, whole models, or all models of a theory. What remains constant is the abductive core—explanations are judged by sufficiency, plausibility, coverage, or consequence relative to a background structure—while the meaning of “global” depends on which structure is being summarized, searched, or certified.