- The paper establishes an expressive equivalence between ontology-mediated queries and fragments of disjunctive datalog, such as monadic disjunctive datalog.
- The paper connects ontology queries to CSPs and MMSNP, revealing core computational dichotomies and conditions for rewritability.
- The study classifies the complexity of ontology-mediated queries and provides decidability results for query containment and logical rewritability.
An Analysis of Ontology-based Data Access: Disjunctive Datalog, CSP, and MMSNP
This paper investigates the landscape of Ontology-Based Data Access (OBDA), with a focus on how ontology-mediated queries relate to disjunctive datalog, constraint satisfaction problems (CSPs), and monotone monadic second-order logic without inequality (MMSNP). OBDA enhances the querying of incomplete data sources by incorporating domain-specific ontological knowledge. The core aim of the paper is to explore the expressive power, rewritability, and computational complexity of various classes of ontology-mediated queries, formulating these in terms of logical fragments and computational paradigms such as disjunctive datalog and CSPs.
Main Contributions
- Expressive Equivalence:
- The paper establishes a mapping from ontology-mediated queries, specifically with conjunctive queries, to fragments of disjunctive datalog. For instance, (ALC, UCQ) is shown to be expressively equivalent to monadic disjunctive datalog (MDDlog). The paper also demonstrates how specific fragments of disjunctive datalog can capture ontology-mediated queries framed in various description logics (DLs).
- Relating OBDA to CSPs and MMSNP:
- The authors draw connections between ontology-mediated queries and CSPs, extending these to their logical generalization MMSNP. This covers bases like first-order rewritability, distribution of P/NP dichotomies, and ultimately the containment problem in ontology-mediated queries. These equivalences help in categorizing different ontology languages based on their computational properties.
- Complexity Classifications:
- The research furnishes a deep dive into the complexity classes of these logic-based query languages. By leveraging CSP analogies, it maps the computational problems to standard complexity categories (such as PTime and NP). The paper reinforces these classifications with a discussion on the Feder-Vardi conjecture, which proposes a dichotomy between tractable and intractable CSPs.
- Query Containment and Rewritability:
- Decidability results are provided for query containment within the identified logical hierarchies. Furthermore, the paper evaluates conditions under which queries can be rewritten into datalog or first-order logic, supporting the use of traditional database systems for efficient query processing.
Theoretical and Practical Implications
The findings have significant theoretical implications, offering a comprehensive framework for characterizing the expressive limits and computational feasibility of ontology-mediated queries. Practically, this enhances data integration and query answering in domains such as the semantic web and bioinformatics by optimizing how ontological knowledge is used to fill data gaps and reframe queries.
Future Directions
One of the directions for future work lies in addressing extensions beyond the guarded fragment and exploring more expressive ontology languages like those involving transitive roles or inverse roles while keeping in check their computational narrative. Additionally, an examination of the practical applicability in real-world datasets, as well as refining the algorithms for query rewriting, can lead to advancements in effective data processing and retrieval systems.
In conclusion, this paper contributes to the body of knowledge by systematically bridging logical paradigms with computational queries, all under the umbrella of ontological data access. It charts a path for future studies to expand and apply these theoretical models in complex, data-rich environments.