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

Inconsistency-tolerant semantics have been proposed to provide meaningful ontological query answers even in the presence of inconsistencies. Several such semantics rely on the notion of a repair, which is a "maximal" consistent subset of the database, where different maximality criteria might be adopted depending on the application at hand. Previous work in the context of Datalog+/- has considered only the subset and cardinality maximality criteria. We take here a step further and study inconsistency-tolerant semantics under maximality criteria based on weights and priority levels. We provide a thorough complexity analysis for a wide range of existential rule languages and for several complexity measures

Abduction in Annotated Probabilistic Temporal Logic

Annotated Probabilistic Temporal (APT) logic programs are a form of logic programs that allow users to state (or systems to automatically learn)rules of the form ``formula G becomes true K time units after formula F became true with L to U% probability.\u27\u27 In this paper, we develop a theory of abduction for APT logic programs. Specifically, given an APT logic program Pi, a set of formulas H that can be ``added\u27\u27 to Pi, and a goal G, is there a subset S of H such that Pi cup S is consistent and entails the goal G? In this paper, we study the complexity of the Basic APT Abduction Problem (BAAP). We then leverage a geometric characterization of BAAP to suggest a set of pruning strategies when solving BAAP and use these intuitions to develop a sound and complete algorithm

Querying Data Exchange Settings Beyond Positive Queries

Data exchange, the problem of transferring data from a source schema to a target schema, has been studied for several years. The semantics of answering positive queries over the target schema has been defined in early work, but little attention has been paid to more general queries. A few proposals of semantics for more general queries exist but they either do not properly extend the standard semantics under positive queries, giving rise to counterintuitive answers, or they make query answering undecidable even for the most important data exchange settings, e.g., with weakly-acyclic dependencies. The goal of this paper is to provide a new semantics for data exchange that is able to deal with general queries. At the same time, we want our semantics to coincide with the classical one when focusing on positive queries, and to not trade-off too much in terms of complexity of query answering. We show that query answering is undecidable in general under the new semantics, but it is \co\NP\complete when the dependencies are weakly-acyclic. Moreover, in the latter case, we show that exact answers under our semantics can be computed by means of logic programs with choice, thus exploiting existing efficient systems. For more efficient computations, we also show that our semantics allows for the construction of a representative target instance, similar in spirit to a universal solution, that can be exploited for computing approximate answers in polynomial time. Under consideration in Theory and Practice of Logic Programming (TPLP).Comment: Under consideration in Theory and Practice of Logic Programming (TPLP

Dimensional Inconsistency Measures and Postulates in Spatio-Temporal Databases

The problem of managing spatio-temporal data arises in many applications, such as location-based services, environmental monitoring, geographic information systems, and many others. Often spatio-temporal data arising from such applications turn out to be inconsistent, i.e., representing an impossible situation in the real world. Though several inconsistency measures have been proposed to quantify in a principled way inconsistency in propositional knowledge bases, little effort has been done so far on inconsistency measures tailored for the spatio-temporal setting.In this paper, we define and investigate new measures that are particularly suitable for dealing with inconsistent spatio-temporal information, because they explicitly take into account the spatial and temporal dimensions, as well as the dimension concerning the identifiers of the monitored objects. Specifically, we first define natural measures that look at individual dimensions (time, space, and objects), and then propose measures based on the notion of a repair. We then analyze their behavior w.r.t. common postulates defined for classical propositional knowledge bases, and find that the latter are not suitable for spatio-temporal databases, in that the proposed inconsistency measures do not often satisfy them. In light of this, we argue that also postulates should explicitly take into account the spatial, temporal, and object dimensions and thus define ?dimension-aware? counterparts of common postulates, which are indeed often satisfied by the new inconsistency measures. Finally, we study the complexity of the proposed inconsistency measures.Fil: Grant, John. Towson University; Estados UnidosFil: Martinez, Maria Vanina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Molinaro, Cristian. Università della Calabria; ItaliaFil: Parisi, Francesco. Università della Calabria; Itali