The DL-Lite Family and Relations (1401.3487v1)

Abstract: The recently introduced series of description logics under the common moniker DL-Lite has attracted attention of the description logic and semantic web communities due to the low computational complexity of inference, on the one hand, and the ability to represent conceptual modeling formalisms, on the other. The main aim of this article is to carry out a thorough and systematic investigation of inference in extensions of the original DL-Lite logics along five axes: by (i) adding the Boolean connectives and (ii) number restrictions to concept constructs, (iii) allowing role hierarchies, (iv) allowing role disjointness, symmetry, asymmetry, reflexivity, irreflexivity and transitivity constraints, and (v) adopting or dropping the unique same assumption. We analyze the combined complexity of satisfiability for the resulting logics, as well as the data complexity of instance checking and answering positive existential queries. Our approach is based on embedding DL-Lite logics in suitable fragments of the one-variable first-order logic, which provides useful insights into their properties and, in particular, computational behavior.

• The paper presents a detailed complexity analysis that demonstrates DL-Lite's efficient data handling through first-order rewritability despite increased combined complexity in some extensions.
• It classifies DL-Lite logics into distinct groups—core, Krom, Horn, and Bool—to delineate trade-offs between expressiveness and computational efficiency.
• The paper validates DL-Lite's practical applicability by highlighting its use in semantic web systems and its potential for scalable ontology management.

An Analysis of the DL-Lite Family of Description Logics

The DL-Lite family of Description Logics (DLs) stands out for its focus on managing ontologies with low computational cost, crucial for applications like ontology-based data access and semantic data integration. This paper provides an exhaustive exploration of the DL-Lite logics, emphasizing both their computational properties and conceptual coverage. The paper presents a systematic paper of the DL-Lite family along five axes, including various role constraints and the impact of the unique name assumption (UNA).

Key Contributions

The paper primarily investigates several description logics under the DL-Lite umbrella, analyzing their suitability for ontology management tasks while maintaining tractable reasoning. The core contributions are:

1. Complexity Analysis: The work provides a detailed analysis of the computational effects of extending DL-Lite with various logical constructs such as role hierarchies, number restrictions, and Boolean connectives. The complexity measures considered are both combined complexity and data complexity, with results showing that while DL-Lite maintains low data complexity due to its efficient query answering, the combined complexity may increase in certain extensions.
2. DL-Lite Variants: By classifying DL-Lite logics into distinct groups—core, Krom, Horn, and Bool—the paper delineates the boundaries between logics that are efficient and those that incur higher reasoning costs. The DL-Lite logics provide a logical basis for the OWL 2 QL profile, facilitating efficient query processing in large data settings.
3. Practical Implementations: Several semantic web inference systems, such as QuOnto and Owlgres, have implemented query rewriting techniques based on DL-Lite semantics, underscoring the practical viability of DL-Lite logics for real-world applications.

Numerical Results and Bold Claims

The paper supports its claims with robust theoretical and practical findings:

• AC Complexity: Many DL-Lite logics achieve low data complexity for instance checking, often reducible to AC complexity classes. The paper establishes that certain DL-Lite variants allow for first-order rewritable queries, making them highly suitable for integration with existing database technologies.
• NP and P Completeness: Some extensions, particularly those combining role inclusions and number restrictions, lead to NP or P completeness for combined complexity. This establishes the conceptual tradeoff between expressiveness and computational tractability.

Implications and Future Research

The DL-Lite family provides a crucial balance between expressive power for ontology representation and efficient reasoning support, a balance essential for scalable data applications. The results have significant implications:

• Ontology Management: By offering a tractable framework, DL-Lite aids in handling large ontologies crucial for semantic data systems, reducing the computational overhead for reasoning tasks.
• Expansion of DL Constructs: Future research could delve into integrating DL-Lite with constructs like role chains and nominals, examining how they impact computational boundaries.
• Query Rewriting and Efficiency: While query rewriting is a powerful tool, managing the size of rewritten queries to prevent performance bottlenecks in database systems is an ongoing challenge.

Overall, the paper's comprehensive analysis of DL-Lite logics provides a foundation for further exploration in knowledge representation, fostering advancements in both theoretical and application-driven domains of DLs. The formalism solidifies its place in the suite of description logics suitable for next-generation semantic web technologies.