A New Well-Supported Semantics for Description Logic Programs

Description logic programs are a powerful tool for combining rule-based logic with ontologies. A key feature of these programs is "well-supportedness," which ensures that answer sets do not rely on circular reasoning. This paper introduces a new semantics for these programs that addresses two major drawbacks of the current approach: high computational complexity and the lack of a clear way to characterize the system through a "reduct" transformation. By evaluating ontological atoms more strictly, the authors provide a more efficient and theoretically grounded framework that aligns more closely with standard logic programming.

Addressing Computational Complexity

The current well-supported semantics for description logic programs suffers from high computational costs, with the consistency problem reaching the second level of the polynomial hierarchy. The authors' new approach mitigates this by applying a stricter evaluation to ontological atoms. This adjustment successfully lowers the complexity of the consistency problem to NP-complete, making it more computationally manageable while still maintaining the essential property of well-supportedness.

A New Theoretical Foundation

Beyond improving efficiency, the authors provide a robust formal characterization of their new semantics. They define the system using a fixpoint operator and a reduct-based transformation. These tools allow researchers to better understand how the program arrives at its conclusions. By establishing these formal mechanisms, the authors align their semantics with traditional logic programming, providing a more intuitive and consistent way to model knowledge.

Relationship to Existing Semantics

The new semantics acts as a strict subset of the existing well-supported semantics. This means that while it introduces a more rigorous standard for what constitutes a "well-supported" result, it remains compatible with the core principles of the original framework. Furthermore, the authors identify a specific syntactic class of description logic programs where the new semantics and the current semantics are equivalent, ensuring that the new method can be applied reliably across different types of program structures.