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We investigate the logical difference problem between general EL-TBoxes. The logical difference is the set of concept subsumptions that are logically entailed by a first TBox but not by a second one. We show how the logical difference between two EL-TBoxes can be reduced to fixpoint reasoning w.r.t. EL-TBoxes. Entailments of the first TBox can be represented by subsumptions of least fixpoint concepts by greatest fixpoint concepts, which can then be checked w.r.t. the second TBox. We present the foundations for a dedicated procedure based on a hypergraph representation of the fixpoint concepts without the use of automata-theoretic techniques, avoiding possible complexity issues of a reduction to modal μ-calculus reasoning. The subsumption checks are based on checking for the existence of simulations between the hypergraph representations of the fixpoint concepts and the TBoxes.

Foundations for the Logical Difference of EL-TBoxes