A New Well-Supported Semantics for Description Logic Programs

• URL: http://arxiv.org/abs/2607.21203v1
• Date: Thu, 23 Jul 2026 11:20:31 GMT
• Title: A New Well-Supported Semantics for Description Logic Programs
• Abstract summary: We present a new semantics which evaluates ontological atoms more strictly than the current semantics.<n>Our new semantics is a strict subset of the current well-supported semantics, so it maintains the prior notion of well-supportedness.
• Score: 2.990760778216954
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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