Statistical EL is ExpTime-complete

TL;DR

This paper proves that the consistency problem for Statistical EL ontologies is ExpTime-complete, establishing its computational complexity by matching lower and upper bounds.

Contribution

It demonstrates the ExpTime-completeness of Statistical EL's consistency problem, resolving an open question in description logic complexity.

Findings

The consistency problem for Statistical EL is ExpTime-hard.

Combined with existing upper bounds, the problem is shown to be ExpTime-complete.

The proof involves a reduction from EL with negation of atomic concepts.

Abstract

We show that the consistency problem for Statistical EL ontologies, defined by Pe{\~{n}}aloza and Potyka, is ExpTime-hard. Together with existing ExpTime upper bounds, we conclude ExpTime-completeness of the logic. Our proof goes via a reduction from the consistency problem for EL extended with negation of atomic concepts.