A New Well-Supported Semantics for Description Logic Programs

Description logic programs are a powerful formalism for combining rules with ontologies.The wellsupported 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.