Bounded Fitting for Expressive Description Logics

TL;DR

This paper extends the bounded fitting paradigm to more expressive description logics, demonstrating its theoretical viability and practical effectiveness through implementation and comparison with existing methods.

Contribution

It analyzes conditions under which bounded fitting retains its properties in expressive description logics and provides a practical SAT-based implementation.

Findings

Bounded fitting remains effective for expressive description logics with inverse roles and number restrictions.

The SAT-based implementation performs competitively against state-of-the-art learners.

The approach offers PAC-style guarantees for learning in complex 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.