[Paper Review] Ontology-based Data Access: A Study through Disjunctive Datalog, CSP, and MMSNP

Meghyn Bienvenu, Balder ten Cate+2 more|arXiv (Cornell University)|Jan 28, 2013

Semantic Web and Ontologies30 references55 citations

TL;DR

This paper establishes deep connections between ontology-mediated queries (OMQs) and formalisms in logic and constraint satisfaction, showing that OMQs based on disjunctive Datalog, CSPs, and MMSNP formulas are interdefinable. It proves key undecidability results: FO-rewritability and datalog-rewritability of OMQs are undecidable for certain ontology languages, even when restricted to unions of conjunctive queries and unary atomic queries.

ABSTRACT

Ontology-based data access is concerned with querying incomplete data sources in the presence of domain-specific knowledge provided by an ontology. A central notion in this setting is that of an ontology-mediated query, which is a database query coupled with an ontology. In this paper, we study several classes of ontology-mediated queries, where the database queries are given as some form of conjunctive query and the ontologies are formulated in description logics or other relevant fragments of first-order logic, such as the guarded fragment and the unary-negation fragment. The contributions of the paper are three-fold. First, we characterize the expressive power of ontology-mediated queries in terms of fragments of disjunctive datalog. Second, we establish intimate connections between ontology-mediated queries and constraint satisfaction problems (CSPs) and their logical generalization, MMSNP formulas. Third, we exploit these connections to obtain new results regarding (i) first-order rewritability and datalog-rewritability of ontology-mediated queries, (ii) P/NP dichotomies for ontology-mediated queries, and (iii) the query containment problem for ontology-mediated queries.

Motivation & Objective

• To characterize the expressive power of ontology-mediated queries (OMQs) using fragments of disjunctive Datalog.
• To establish formal connections between OMQs and constraint satisfaction problems (CSPs), and their logical generalization, MMSNP formulas.
• To determine the decidability and complexity of fundamental problems in OMQs, including first-order and datalog rewritability, data complexity, and query containment.
• To provide a unified framework for classifying OMQs based on logical and computational properties, especially in the context of description logics and guarded fragments.

Proposed method

• Reduces the problem of OMQ rewritability to the satisfiability of MMSNP formulas and CSP instances.
• Uses tiling problems as a reduction target to prove undecidability of FO-rewritability and datalog-rewritability.
• Constructs specific ontologies and data instances that simulate tiling and 3-colorability problems to demonstrate undecidability.
• Employs logical translations between OMQs, disjunctive Datalog, and MMSNP to establish expressive equivalence across formalisms.
• Leverages the guarded fragment (GF), unary negation fragment (UNFO), and guarded negation fragment (GNFO) as core ontology languages.
• Applies model-theoretic techniques to show that the absence of finite obstruction sets implies non-FO-rewritability.

Experimental results

Research questions

• RQ1 What is the expressive power of ontology-mediated queries in terms of disjunctive Datalog fragments?
• RQ2 How are ontology-mediated queries related to constraint satisfaction problems (CSPs) and MMSNP formulas?
• RQ3 Is first-order rewritability decidable for ontology-mediated queries over standard description logics and guarded fragments?
• RQ4 Is datalog-rewritability decidable for ontology-mediated queries, and what are the complexity bounds?
• RQ5 What is the data complexity of ontology-mediated queries, and do P/NP dichotomies hold in this setting?

Key findings

• FO-rewritability of ontology-mediated queries is undecidable for ontology languages including the guarded fragment and unary negation fragment.
• Datalog-rewritability of ontology-mediated queries is also undecidable, even for unions of conjunctive queries and unary atomic queries.
• The paper establishes a tight correspondence between OMQs and MMSNP formulas, showing that OMQs can express exactly the class of MMSNP-definable queries.
• A P/NP dichotomy holds for data complexity of OMQs when the ontology is fixed and the query is a union of conjunctive queries.
• Query containment for ontology-mediated queries is undecidable, even when restricted to unary atomic queries and simple ontology languages.
• The existence of a finite obstruction set for an OMQ is undecidable, which directly implies non-FO-rewritability in such cases.