A New Well-Supported Semantics for Description Logic Programs

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.