The Dual Role of Abstracting over the Irrelevant in Symbolic Explanations: Cognitive Effort vs. Understanding

AI summary

Overview

Research area: Explainable AI (XAI), symbolic AI, Answer Set Programming (ASP), and the cognitive science of explanation.

Technical level: Intermediate. The paper pairs a formal definition of irrelevance in logic programming with an empirical human-subjects study, so readers need comfort with both logical notation and basic statistics.

Scope: The paper defines a relaxed notion of irrelevant details in Answer Set Programming, uses it to generate abstracted explanations, and tests experimentally whether removal and clustering of those details change human accuracy, answer time, and confidence.

What This Paper Is About

Symbolic AI systems are transparent in principle, but the raw logical traces they produce can be dense with details that do not matter for a decision, imposing extraneous cognitive load on the person trying to understand them. The authors define formally which atoms in an answer set program are irrelevant with respect to a set of problem instances, and derive simplified explanations by either removing those atoms or clustering them into a single representative concept. They then run a controlled online experiment to check whether these two operations actually improve how well people understand the explanations and how much effort they spend.

Key Contributions

1. A relaxed formal notion of irrelevance. The authors generalize earlier, more restricted ASP abstraction formalisms (Saribatur and Woltran, 2023; Saribatur et al., 2024) with a new definition of χ-irrelevance, which requires that the answer sets of an abstracted program match the abstraction of the answer sets of the original program for every instance in a set χ of potential scenarios.

2. Two cognitive operations unified in one mapping. The abstraction mapping m performs removal, by sending atoms to logical truth (⊤), and clustering, by mapping several distinct atoms to one shared representative atom such as habitatWaterOrMud.

3. An explanation pipeline built on the abstraction. Explanations are generated from the abstracted program rather than the original, using the xclingo system (Cabalar and Muñiz, 2024), so that the same formal machinery that simplifies the program also simplifies the justification presented to a person.

4. The first empirical validation of these ASP abstraction notions. A between-subjects online study with 99 analyzed participants tested whether the theoretically simpler traces produce measurable cognitive benefits, something the authors state the earlier formalisms lacked.

Main Findings

• Clustering improved accuracy. A one-factor ANOVA showed a significant effect of abstraction on mean accuracy (F = 2.72, p = 0.049). Post-hoc pairwise comparisons were significant for cluster vs. default (T = 2.75, p = 0.009) and for cluster-and-removal vs. default (T = 2.52, p = 0.016).

• Removal reduced answer time. A one-factor Welch ANOVA showed a significant effect of abstraction on mean answer time (F = 6.41, p = 0.001). Post-hoc tests were significant for cluster vs. cluster-and-removal (T = 3.25, p = 0.017) and for cluster-and-removal vs. default (T = −3.23, p = 0.018). The cluster-and-removal group was significantly faster than both other groups, which the authors describe as a synergetic effect.

• Removal alone did not improve accuracy. The authors offer two possible explanations: the default explanations may already have been below the participants' complexity threshold, or the formal notion of χ-irrelevance for removal may be capturing specificity, since it strips details common across instances and leaves the distinctive ones.

• Clustering did not hurt speed, and removal did not hurt accuracy. The authors frame this as the double benefit of abstraction: structural organization supports understanding, while discarding irrelevant detail supports speed.

• No significant effect on confidence. A one-factor ANOVA on mean reported confidence found no significant effect of abstraction (F = 1.58, p = 0.19). Marginal, non-significant trends appeared for default vs. removal (T = −1.71, p = 0.096) and cluster vs. default (T = 1.84, p = 0.072). Participants reported higher confidence on correct answers (mean 80 ± 1.56) than on incorrect ones (mean 69 ± 2.31), indicating a reliable sense of their own accuracy regardless of explanation type.

• Positive stimuli were easier than negative stimuli. An exploratory ANOVA found a main effect of stimulus valence (F = 9.89, p = 0.002), with accuracy for positive stimuli (M = 0.82 ± 0.02) significantly higher than for negative stimuli (M = 0.70 ± 0.02). No significant interaction with abstraction was observed.

• No difference in perceived usefulness. Subjective assessments of explanation usefulness did not differ between conditions, and no effect of domain on the dependent variables was observed, so results were aggregated across all domains.

Methodology in Plain English

The authors first set up a formal framework. They take an Answer Set Programming program P and a set χ of possible problem instances, then ask whether a mapping m exists that compresses the program while keeping the answer sets in correspondence with the original ones for every instance in χ. The mapping can delete atoms that never discriminate between outcomes and merge atoms that always lead to the same conclusion. Applying m to P and to an instance F yields a smaller program whose xclingo output is a shorter justification.

For the experiment, the authors built three concept-learning domains drawn from biology: flowers, mushrooms, and cacti. Each domain has six domain-specific decision attributes and one binary target label (for example, whether a flower has a scent, or whether a cactus has slow growth). Each domain contributed 8 instances: 2 positive instances for learning and 3 positive plus 3 negative instances for testing. Participants saw the two learning instances together with a textual explanation derived from an answer set program, then classified six unseen instances without explanations and rated their confidence on a slider from 0 to 100, with an "I don't know" option.

The study used a complete between-subjects design with four randomly assigned groups: default (full logical trace), cluster, removal, and cluster-and-removal. Three domains were used deliberately to prevent proactive interference, where learning one rule hinders learning the next, and the order of domains and stimuli was randomized. Participants were recruited through Prolific and screened with comprehension and attention checks. Of 157 people who started, 103 completed the survey and questionnaire; 3 were excluded for restarting the survey and 2 for low answering times more than three standard deviations from their group mean, leaving 99 participants (age mean 35.9, sd 14.0; 64 female, 32 male, 1 other). Final group sizes were Default n = 19, Cluster n = 19, Removal n = 15, and Cluster-Removal n = 44. Levene's test confirmed homogeneity of variance (p > .05) for accuracy and confidence; because it was violated for answer time, the authors used a robust Welch ANOVA and Games-Howell post-hoc tests there. After the last domain, participants rated explanation usefulness (5 items based on a subset of Bahel et al., 2024), memorization effort (1 item), and familiarity with domain terminology (1 item) on Likert scales from 1 to 7, plus prior knowledge in computer science, logic, mathematics, programming, and the three domains (7 items) on a scale from 0 to 4.

Why This Matters

Impact on research. The paper connects formal work on ASP abstraction with empirical cognitive science, providing evidence that the formal notions do correspond to measurable human benefits. It also separates two abstraction effects that prior work treated together: clustering drives accuracy gains, while removal drives speed gains. This suggests that "simpler explanations" is not one intervention but several with distinct cognitive consequences.

Real-world applications. Healthcare decision support, where clinicians need concise justifications for recommendations. Autonomous aviation, cited by the authors as a high-stakes environment where black-box opacity is a barrier to trust. Law, also named as a domain requiring auditable decision processes. Neuro-symbolic systems more broadly, where ASP is already used as a reasoning layer for LLMs (Kareem et al., 2024; Rajasekharan et al., 2023) and where explanations must be conveyable to non-specialists.

Industry relevance. For developers building rule-based or neuro-symbolic systems, the paper offers a concrete recipe: apply a formal irrelevance mapping before rendering explanations. Clustering is the operation to reach for when users must generalize correctly to new cases; removal is the operation to reach for when they need to decide quickly. The finding that users do not feel more confident despite performing better and faster also matters for product design, since self-reported confidence cannot be used as a proxy for explanation quality.

Future Directions

1. Vary the complexity of the default explanation. The authors note that tasks must be of intermediate complexity for explanations to help (Ai et al., 2021), and they want to explore whether removal abstraction becomes significant for accuracy, and abstraction becomes significant for confidence, when the starting explanations are more complex.

2. Test whether χ-irrelevance captures specificity rather than abstraction. The removal operation strips details common across instances and leaves distinctive ones, which the authors compare to identifying a Siamese cat by eye color rather than by whiskers or paws. They plan to investigate this interpretation directly.

3. Explain the missing confidence effect. Understanding why objectively better and faster performance did not translate into higher reported confidence remains open.

4. Move toward cognitively aligned symbolic AI. The authors frame their broader program as tailoring symbolic explanations to human cognitive processes and positioning ASP as a system for studying how symbolic abstraction can foster cognitively aligned AI.

Target Audience

Researchers and practitioners working on explainable AI, particularly those using symbolic, rule-based, or neuro-symbolic methods such as Answer Set Programming, will find the formal contribution directly applicable. Cognitive scientists studying concept learning and explanation will find the experimental design and its separation of accuracy from effort informative. HCI and XAI designers who need to decide how much detail to show in a system's justification will benefit from the practical distinction between clustering and removal. A working knowledge of logic programming notation is helpful for the formal section, but the empirical results and the discussion are accessible without it.

Authors’ abstract

Explanations are central to human cognition, yet AI systems often produce outputs that are difficult to understand. While symbolic AI offers a transparent foundation for interpretability, raw logical traces often impose a high extraneous cognitive load. We investigate how formal abstractions, specifically removal and clustering, impact human reasoning performance and cognitive effort. Utilizing Answer Set Programming (ASP) as a formal framework, we define a notion of irrelevant details to be abstracted over to obtain simplified explanations. Our cognitive experiments, in which participants classified stimuli across domains with explanations derived from an answer set program, show that clustering details significantly improve participants' understanding, while removal of details significantly reduce cognitive effort, supporting the hypothesis that abstraction enhances human-centered symbolic explanations.