Complexity of Approximate Query Answering under Inconsistency in Datalog+/-

This is the author accepted manuscript. The final version is freely available from IJCAI via the link in this recordSeveral semantics have been proposed to query inconsistent ontological knowledge bases, including the intersection of repairs and the intersection of closed repairs as two approximate inconsistencytolerant semantics. In this paper, we analyze the complexity of conjunctive query answering under these two semantics for a wide range of Datalog± languages. We consider both the standard setting, where errors may only be in the database, and the generalized setting, where also the rules of a Datalog± knowledge base may be erroneous.This work was supported by The Alan Turing Institute under the UK EPSRC grant EP/N510129/1, and by the EPSRC grants EP/R013667/1, EP/L012138/1, and EP/M025268/1

Complexity of Inconsistency-Tolerant Query Answering in Datalog+/- under Cardinality-Based Repairs

This is the author accepted manuscript. The final version is available from Association for the Advancement of Artificial Intelligence (AAAI) via the link in this recordQuerying inconsistent ontological knowledge bases is an important problem in practice, for which several inconsistencytolerant query answering semantics have been proposed, including query answering relative to all repairs, relative to the intersection of repairs, and relative to the intersection of closed repairs. In these semantics, one assumes that the input database is erroneous, and the notion of repair describes a maximally consistent subset of the input database, where different notions of maximality (such as subset and cardinality maximality) are considered. In this paper, we give a precise picture of the computational complexity of inconsistencytolerant (Boolean conjunctive) query answering in a wide range of Datalog± languages under the cardinality-based versions of the above three repair semantics.This work was supported by the Alan Turing Institute under the UK EPSRC grant EP/N510129/1, and by the EPSRC grants EP/R013667/1, EP/L012138/1, and EP/M025268/1

Datalog± Ontology Consolidation

Knowledge bases in the form of ontologies are receiving increasing attention as they allow to clearly represent both the available knowledge, which includes the knowledge in itself and the constraints imposed to it by the domain or the users. In particular, Datalog ± ontologies are attractive because of their property of decidability and the possibility of dealing with the massive amounts of data in real world environments; however, as it is the case with many other ontological languages, their application in collaborative environments often lead to inconsistency related issues. In this paper we introduce the notion of incoherence regarding Datalog± ontologies, in terms of satisfiability of sets of constraints, and show how under specific conditions incoherence leads to inconsistent Datalog ± ontologies. The main contribution of this work is a novel approach to restore both consistency and coherence in Datalog± ontologies. The proposed approach is based on kernel contraction and restoration is performed by the application of incision functions that select formulas to delete. Nevertheless, instead of working over minimal incoherent/inconsistent sets encountered in the ontologies, our operators produce incisions over non-minimal structures called clusters. We present a construction for consolidation operators, along with the properties expected to be satisfied by them. Finally, we establish the relation between the construction and the properties by means of a representation theorem. Although this proposal is presented for Datalog± ontologies consolidation, these operators can be applied to other types of ontological languages, such as Description Logics, making them apt to be used in collaborative environments like the Semantic Web.Fil: Deagustini, Cristhian Ariel David. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Martinez, Maria Vanina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Falappa, Marcelo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Simari, Guillermo Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; Argentin

Functional Dependencies Unleashed for Scalable Data Exchange

We address the problem of efficiently evaluating target functional dependencies (fds) in the Data Exchange (DE) process. Target fds naturally occur in many DE scenarios, including the ones in Life Sciences in which multiple source relations need to be structured under a constrained target schema. However, despite their wide use, target fds' evaluation is still a bottleneck in the state-of-the-art DE engines. Systems relying on an all-SQL approach typically do not support target fds unless additional information is provided. Alternatively, DE engines that do include these dependencies typically pay the price of a significant drop in performance and scalability. In this paper, we present a novel chase-based algorithm that can efficiently handle arbitrary fds on the target. Our approach essentially relies on exploiting the interactions between source-to-target (s-t) tuple-generating dependencies (tgds) and target fds. This allows us to tame the size of the intermediate chase results, by playing on a careful ordering of chase steps interleaving fds and (chosen) tgds. As a direct consequence, we importantly diminish the fd application scope, often a central cause of the dramatic overhead induced by target fds. Moreover, reasoning on dependency interaction further leads us to interesting parallelization opportunities, yielding additional scalability gains. We provide a proof-of-concept implementation of our chase-based algorithm and an experimental study aiming at gauging its scalability with respect to a number of parameters, among which the size of source instances and the number of dependencies of each tested scenario. Finally, we empirically compare with the latest DE engines, and show that our algorithm outperforms them

From Classical to Consistent Query Answering under Existential Rules

Querying inconsistent ontologies is an intriguing new problem that gave rise to a flourishing research activity in the description logic (DL) community. The computational complexity of consistent query answering under the main DLs is rather well understood; however, little is known about existential rules. The goal of the current work is to perform an in-depth analysis of the complexity of consistent query answering under the main decidable classes of existential rules enriched with negative constraints. Our investigation focuses on one of the most prominent inconsistency-tolerant semantics, namely, the AR semantics. We establish a generic complexity result, which demonstrates the tight connection between classical and consistent query answering. This result allows us to obtain in a uniform way a relatively complete picture of the complexity of our problem