Organisation

Usually every Friday 10 - 12 AM

Contact: Maximilian Pensel

Participants

• Pavlos Marantidis
• Antoine Mottet
• Maximilian Pensel
• Caterina Viola

Papers

Non-Uniform Data Complexity of Query Answering in Description Logics

C. Lutz, F. Wolter (2012)

In ontology-based data access (OBDA), ontologies are used as an interface for querying instance data. Since in typical applications the size of the data is much larger than the size of the ontology and query, data complexity is the most important complexity measure. In this paper, we propose a new method for investigating data complexity in OBDA: instead of classifying whole logics according to their complexity, we aim at classifying each individual ontology within a given master language. Our results include a P/coNP-dichotomy theorem for ontologies of depth one in the description logic ALCFI, the equivalence of a P/coNP-dichotomy theorem for ALC/ALCI-ontologies of unrestricted depth to the famous dichotomy conjecture for CSPs by Feder and Vardi, and a non-P/coNP-dichotomy theorem for ALCF-ontologies.

Ontology-Based Data Access: A Study through Disjunctive Datalog, CSP, and MMSNP

C. Lutz et al. (2014) with Appendix

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 article, 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 article are threefold. First, we show that popular ontology-mediated query languages have the same expressive power as natural fragments of disjunctive datalog, and we study the relative succinctness of ontology-mediated queries and disjunctive datalog queries. 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.

On the Relationship between Consistent Query Answering and Constraint Satisfaction Problems

C. Lutz, F. Wolter (2015)

Recently, Fontaine has pointed out a connection between consistent query answering (CQA) and constraint satisfaction problems (CSP) [Fontaine, LICS 2013]. We investigate this connection more closely, identifying classes of CQA problems based on denial constraints and GAV constraints that correspond exactly to CSPs in the sense that a complexity classification of the CQA problems in each class is equivalent (up to FO-reductions) to classifying the complexity of all CSPs. We obtain these classes by admitting only monadic relations and only a single variable in denial constraints/GAVs and restricting queries to hypertree UCQs. We also observe that dropping the requirement of UCQs to be hypertrees corresponds to transitioning from CSP to its logical generalization MMSNP and identify a further relaxation that corresponds to transitioning from MMSNP to GMSNP (also know as MMSNP_2). Moreover, we use the CSP connection to carry over decidability of FO-rewritability and Datalog-rewritability to some of the identified classes of CQA problems.

Containment in Monadic Disjunctive Datalog, MMSNP, and Expressive Description Logics

P. Bourhis, C. Lutz (2016)

We study query containment in three closely related formalisms: monadic disjunctive Datalog (MDDLog), MMSNP (a logical generalization of constraint satisfaction problems), and ontology-mediated queries (OMQs) based on expressive description logics and unions of conjunctive queries. Containment in MMSNP was known to be decidable due to a result by Feder and Vardi, but its exact complexity has remained open. We prove 2NExpTime-completeness and extend this result to monadic disjunctive Datalog and to OMQs.

Rewritability in Monadic Disjunctive Datalog, MMSNP, and Expressive Description Logics

C. Feier, A. Kuusisto, C. Lutz (2017)

We study rewritability of monadic disjunctive Datalog programs, (the complements of) MMSNP sentences, and ontology-mediated queries (OMQs) based on expressive description logics of the ALC family and on conjunctive queries. We show that rewritability into FO and into monadic Datalog (MDLog) are decidable, and that rewritability into Datalog is decidable when the original query satisfies a certain condition related to equality. We establish 2NExpTime-completeness for all studied problems except rewritability into MDLog for which there remains a gap between 2NExpTime and 3ExpTime. We also analyze the shape of rewritings, which in the MMSNP case correspond to obstructions, and give a new construction of canonical Datalog programs that is more elementary than existing ones and also applies to non-Boolean queries.