Download PDFOpen PDF in browserSubsumption in FL_⊥reg with TBox Is in ExpTime.17 pages•Published: October 23, 2026AbstractDescription Logics (DLs) are a family of formal languages used for representing and reasoning about structured knowledge in terms of concepts and their relationships. The expressive power of a DL depends on the constructors available for building complex concepts.In this work, we investigate subsumption in the restricted description logic FL_⊥reg and the related fragments FL_reg, FL_⊥, and FL_0. These formalisms support value restrictions over role names, where the subscript reg indicates the use of regular expressions over roles. Subsumption between two concept descriptions in FL_⊥reg and FL_reg is PSpace-complete. When subsumption is considered with respect to a TBox (i.e., a set of axioms), the complexity increases to ExpTime-complete. These results can be derived either from complexity bounds established for more expressive logics or from algorithms designed for harder reasoning problems. We reprove the PSpace-completeness result and provide a new proof of ExpTime-completeness for FL_reg and FL_⊥reg with TBoxes via a novel reduction to parity pushdown games. Our algorithm relies only on the constructs available in these logics and may therefore be implemented more easily. Keyphrases: computational complexity, description logic, pushdown games In: Erika Ábrahám, Nikolaj Bjørner and Michael Rawson (editors). Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning, vol 112, pages 200-216.
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