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Germane Conflicts: Desirable Properties for Localising Inconsistency

AAAI 2025 · Learning theory and algorithms › Prediction and decision losses · approach: Adaptive testing and experiments · 1 citations (OpenAlex)

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Proposes a set of desirable properties for germane conflicts (localising inconsistency) and a new substitution-based conflict definition, analysing which properties it satisfies and its complexity (Σp2 membership).

Problem

Localising inconsistency in a knowledgebase to the subsets germane to it; minimal conflicts miss some problematic (iceberg) inconsistencies, and there is no principled way to assess candidate conflict definitions.

Approach

Introduces 14 desirable properties (e.g., inconsistency, inclusion, substitution-robustness, tautology-freeness) to assess germane-conflict definitions, and defines substitution conflicts as images of minimal conflicts under substitutions, which are robust to substitution and capture hidden iceberg conflicts.

Key results

• Substitution conflicts satisfy inconsistency, inclusion, atom-indifference, non-triviality, non-quasi-triviality, safe-set-freeness and substitution-robustness.
• Theorem 1: no conflict set satisfies inconsistency, inclusion, tautology-freeness and substitution-robustness together.
• Detecting substitution conflicts is in Σp2 (Proposition 18).

Surprising findings

• No star-conflict definition satisfies substitution-robustness, and no definition satisfying inconsistency, inclusion, tautology-freeness and substitution-robustness exists, so tautology-freeness must be given up for substitution robustness.

Limitations

• Substitution conflicts violate several semantic properties such as syntax-robustness, minimality and tautology-freeness.
• Detecting substitution conflicts is in Σp2, the same bound as star-conflicts, so no complexity gain.
• Evaluation is theoretical via properties and worked examples rather than empirical.

Experimental setup

Metrics: satisfaction of desirable properties computational complexity class

Baselines: minimal conflicts star-conflicts with Cn_id star-conflicts with Cn_dil star-conflicts with Cn_and star-conflicts with Cn_mod

Builds on: star-conflicts (De Bona and Hunter 2017) minimal conflicts inconsistency measures Reiter diagnosis

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