Description Logics with Two Types of Definite Descriptions: Complexity, Expressiveness, and Automated Deduction
This work addresses the limited referential expressivity of ontologies in description logic $mathcal{ALC}$ by formally distinguishing and introducing *local* and *global* definite descriptions—two novel classes of deterministic descriptions. Semantically, both extensions are grounded in bisimulation-based interpretations; we rigorously prove that the global extension is strictly more expressive than the local one, yet both retain ExpTime decidability. We devise a unified tableau-based decision procedure and implement a prototype satisfiability reasoner supporting both logics. Empirical evaluation confirms the method’s effectiveness and exposes how syntactic formula structure impacts reasoning performance. Key contributions include: (i) the first formal semantic distinction between local and global definite descriptions in $mathcal{ALC}$; (ii) tight complexity bounds establishing ExpTime-completeness for both extensions; and (iii) a theoretically sound and practically implementable reasoning framework integrating semantics, decision procedure, and empirical validation.