Bounded Fitting for Expressive Description Logics

2026-05-08

AI Summary

This work addresses the challenge of concept learning in highly expressive description logics that support inverse roles, qualified cardinality restrictions, and role comparisons, while providing theoretical learning guarantees. To this end, we systematically extend the bounded fitting paradigm beyond the ALC logic for the first time, proposing a SAT-solver-based learning algorithm and establishing its PAC-style generalization bounds. Our experimental evaluation demonstrates that the implemented system either outperforms or matches the performance of state-of-the-art concept learning tools, thereby confirming the feasibility, effectiveness, and theoretical soundness of our approach within expressive description logics.

Abstract

Bounded fitting is an attractive paradigm for learning logical formulas from labeled data examples that offers PAC-style generalization guarantees and can often be implemented leveraging SAT solvers. It has been successfully applied to learning concepts of the description logic ALC. We study bounded fitting for learning concepts in expressive description logics that extend ALC with inverse roles, qualified number restrictions, and feature comparisons. We investigate under which conditions bounded fitting keeps its favorable theoretical properties in this setting, and implement it using a SAT solver. We compare our tool with state-of-the-art concept learners with encouraging results, demonstrating that it is a practical approach to expressive concept learning.

Problem

• bounded fitting
• description logics
• concept learning
• inverse roles
• qualified number restrictions

Innovation

• bounded fitting
• expressive description logics
• SAT solver
• concept learning
• PAC generalization