🤖 AI Summary
This work proposes a novel well-founded semantics for description logic programs that addresses two key limitations of existing approaches: high consistency-checking complexity (located at the second level of the polynomial hierarchy) and the absence of a characterization via reduct transformations. By imposing a stricter evaluation mechanism on ontology atoms, the proposed semantics retains well-foundedness while reducing the consistency problem to NP-completeness. It admits precise characterizations through both a fixed-point operator and a reduct transformation, constitutes a strict subset of the prevailing semantics, and coincides with it on certain syntactic classes. To the best of our knowledge, this is the first well-founded semantics for description logic programs that simultaneously offers a reduct-based characterization, lower computational complexity, and closer alignment with logic programming principles.
📝 Abstract
Description logic programs are a powerful formalism for combining rules with ontologies. The well-supported semantics for description logic programs ensures that no answer sets rely on cyclic dependencies. Most popular semantics for logic programming have this property of well-supportedness. We recognize two limitations of the current well-supported semantics for DL programs: its increased computational complexity for the consistency problem and its lack of a reduct transformation characterization. In this work, we present a new semantics which evaluates ontological atoms more strictly than the current semantics. This keeps the complexity of its consistency problem NP-complete, rather than increasing it to the second level of the polynomial hierarchy. Additionally, we identify a syntactic class of description logic programs for which our new semantics is equivalent to the current semantics. We characterize our semantics using a fixpoint operator and a reduct-based transformation. Our new semantics is a strict subset of the current well-supported semantics, so it maintains the prior notion of well-supportedness while inducing its own stricter notion. We prefer our new notion of well-supportedness due to its similarities with logic programming.