Doctoral colloquium - Zekeri Adams (29.9.2025)
Monday 29.9.2025 at 13:10 hod., Lecture room I 9
Zekeri Adams:
On the Decidability of Full Set-Theoretic Semantics for SubClassOf in Higher-Order DLs
Abstract:
Metamodeling in ontologies provides a systematic means of representing complex domains by capturing relationships across multiple abstraction levels. Central to this process is subsumption, a fundamental relation for hierarchical reasoning that underpins the organization of ontological knowledge. In this work, we build on an extended higher-order description logic framework denoted HIRS*(L), which incorporates metamodeling via two semantically fixed roles: instanceOf and subClassOf. These roles enforce explicit meta-level constraints, enabling a more expressive treatment of both hierarchical and meta-level constructs. Four variants of this logic are known, with three established as decidable. However, the question of decidability remains unresolved for the full set-theoretic semantics of the subClassOf relation applied to all concepts. Our work addresses this gap by examining the decidability of this extended system, denoted HIRS_SA(L) for an arbitrary base description logic L, and seeks to align it with well-understood decidable fragments of first-order logic.