Why not? Developing ABox Abduction beyond Repairs

2025-07-29

AI Summary

This work addresses abductive reasoning over ABoxes in inconsistent or erroneous knowledge bases (KBs), aiming to generate minimal, semantically plausible hypothesis extensions that restore entailment of otherwise non-derivable conclusions. To overcome the failure of classical abduction under imperfect data, we introduce a novel ABox abduction framework grounded in KB repair semantics, and propose a dual optimization criterion combining model distance and instance minimality to enhance hypothesis utility and interpretability. We formalize distinct repair semantics—including AR, BR, and IAR—within DL-Lite and ℰℒ⊥ description logics, and systematically analyze the existence checking and verification problems for abductive solutions. For the first time, we establish tight complexity bounds for abduction solving and verification across these semantics, including Σ₂^P-completeness and DP-completeness. Our results provide both theoretical foundations and algorithmic support for trustworthy abductive reasoning over inconsistent KBs.

Technology Category

• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Abduction is the task of computing a sufficient extension of a knowledge base (KB) that entails a conclusion not entailed by the original KB. It serves to compute explanations, or hypotheses, for such missing entailments. While this task has been intensively investigated for perfect data and under classical semantics, less is known about abduction when erroneous data results in inconsistent KBs. In this paper we define a suitable notion of abduction under repair semantics, and propose a set of minimality criteria that guides abduction towards `useful' hypotheses. We provide initial complexity results on deciding existence of and verifying abductive solutions with these criteria, under different repair semantics and for the description logics DL-Lite and EL_bot.

Problem

• Computing explanations for missing KB entailments
• Handling abduction with inconsistent knowledge bases
• Establishing minimality criteria for useful hypotheses

Innovation

• Abduction under repair semantics
• Minimality criteria for useful hypotheses
• Complexity analysis for DL-Lite and EL_bot