The More the Merrier: Combining Properties for ABox Abduction under Repair Semantics for ELbot

2026-06-17

AI Summary

This work investigates the generation of abductive explanations for missing ABox entailments in the description logic EL⊥, aiming to simultaneously satisfy multiple desirable properties—such as signature restrictions and minimal conflict—while adhering to optimization criteria. Under a repair-based semantics, it systematically explores, for the first time, abductive reasoning that integrates multiple properties with optimization constraints, considering both brave and AR (answer set-based) inference mechanisms. The main contributions lie in establishing the existence and computability of such multi-property combined explanations and demonstrating that their computational complexity remains on par with that of single-property scenarios. Consequently, this approach offers a more practical and flexible explanatory framework for knowledge bases without incurring additional theoretical overhead.

Abstract

Abduction is a central approach to explain missing entailments from a knowledge base by providing a hypothesis, that would, if added to the knowledge base, make the missing entailment become true. Abduction under repair semantics has recently been investigated in detail, where several desirable properties and optimality criteria were considered, such as signature-restrictions and minimality in size and of introduced conflicts. Naturally, hypotheses that satisfy more than one of these properties or combine a property with an optimality criterion would be even more desirable for applications. So far, such hypotheses have not been investigated in the literature. In the present paper, we consider the ABox abduction problem for hypotheses satisfying more than one property or additional optimality criteria, for EL_bot under brave and AR semantics. Our main observation is that often requiring additional properties for hypotheses does not lead to an increase of complexity.

Problem

• ABox abduction
• repair semantics
• EL_bot
• optimality criteria
• signature-restriction

Innovation

• ABox abduction
• repair semantics
• EL_bot
• optimality criteria
• signature restriction