Maria Vanina Martinez

Inconsistency handling in Datalog+/- ontologies

The advent of the Semantic Web has made the problem of inconsistency management especially relevant. Datalog+/- is a family of ontology languages that is in particular useful for representing and reasoning over lightweight ontologies in the Semantic Web. In this paper, we study different semantics for query answering in inconsistent Datalog+/- ontologies. We develop a general framework for inconsistency management in Datalog+/- ontologies based on incision functions from belief revision, in which we can characterize several query answering semantics as special cases: (i) consistent answers, originally developed for relational databases and recently adopted for some classes of description logics (DLs), (ii) intersection semantics, a sound approximation of consistent answers, and (iii) lazy consistent answers, a novel alternative semantics that offers a good compromise between quality of answers and computation time. We also provide complexity results for query answering under the different semantics, including data tractability results.

How Dirty Is Your Relational Database? An Axiomatic Approach

There has been a significant amount of interest in recent years on how to reason about inconsistent knowledge bases. However, with the exception of three papers by Lozinskii, Hunter and Konieczny and by Grant and Hunter, there has been almost no work on characterizing the degree of dirtiness of a database. One can conceive of many reasonable ways of characterizing how dirty a database is. Rather than choose one of many possible measures, we present a set of axioms that any dirtiness measure must satisfy. We then present several plausible candidate dirtiness measures from the literature (including those of Hunter-Konieczny and Grant-Hunter) and identify which of these satisfy our axioms and which do not. Moreover, we define a new dirtiness measure which satisfies all of our axioms.

Aggregate Query Answering under Uncertain Schema Mappings

Recent interest in managing uncertainty in data integration has led to the introduction of probabilistic schema mappings and the use of probabilistic methods to answer queries across multiple databases using two semantics: by-table and by-tuple. In this paper, we develop three possible semantics for aggregate queries: the range, distribution, and expected value semantics, and show that these three semantics combine with the by-table and by-tuple semantics in six ways. We present algorithms to process COUNT, AVG, SUM, MIN, and MAX queries under all six semantics and develop results on the complexity of processing such queries under all six semantics. We show that computing COUNT is in PTIME for all six semantics and computing SUM is in PTIME for all but the by-tuple/distribution semantics. Finally, we show that AVG, MIN, and MAX are PTIME computable for all by-table semantics and for the by-tuple/range semantics.We developed a prototype implementation and experimented with both real-world traces and simulated data. We show that, as expected, naive processing of aggregates does not scale beyond small databases with a small number of mappings. The results also show that the polynomial time algorithms are scalable up to several million tuples as well as with a large number of mappings.

Complexity of Inconsistency-Tolerant Query Answering in Datalog+/–

The study of inconsistency-tolerant semantics for query answering in ontological languages has recently gained much attention. In this work, we consider three inconsistency-tolerant semantics recently proposed in the literature, namely: consistent query answering, the intersection (also called IAR) semantics, and the intersection of closed repairs (ICR) semantics. We study the data complexity of conjunctive query answering under these semantics for a wide set of tractable fragments of Datalog+/–. The Datalog+/– family of ontology languages covers several important description logics (DLs), bridging the gap in expressive power between database query languages and DLs as ontology languages, and extending the well-known Datalog language in order to embed DLs. Its properties of decidability of query answering and of tractability of query answering in the (data) complexity make Datalog+/– very useful in modeling real-world applications in which inconsistency-tolerant reasoning is essential.

Probabilistic preference logic networks

Reasoning about an entitys preferences (be it a user of an application, an individual targeted for marketing, or a group of people whose choices are of interest) has a long history in different areas of study. In this paper, we adopt the point of view that grows out of the intersection of databases and knowledge representation, where preferences are usually represented as strict partial orders over the set of tuples in a database or the consequences of a knowledge base. We introduce probabilistic preference logic networks (PPLNs), which flexibly combine such preferences with probabilistic uncertainty. Their applications are clear in domains such as the Social Semantic Web, where users often express preferences in an incomplete manner and through different means, many times in contradiction with each other. We show that the basic problems associated with reasoning with PPLNs (computing the probability of a world or a given query) are #P-hard, and then explore ways to make these computations tractable by: (i) leveraging results from order theory to obtain a polynomial-time randomized approximation scheme (FPRAS) under fixed-parameter assumptions; and (ii) studying a fragment of the language of PPLNs for which exact computations can be performed in fixed-parameter polynomial time.

Focused most probable world computations in probabilistic logic programs

The “Most Probable World” (MPW) problem in probabilistic logic programming (PLPs) is that of finding a possible world with the highest probability. Past work has shown that this problem is computationally intractable and involves solving exponentially many linear programs, each of which is of exponential size. In this paper, we study what happens when the user focuses his interest on a set of atoms in such a PLP. We show that we can significantly reduce the number of worlds to be considered by defining a “reduced” linear program whose solution is in one-one correspondence with the exact solution to the MPW problem. However, the problem is still intractable. We develop a Monte Carlo sampling approach that enables us to build a quick approximation of the reduced linear program that allows us to estimate (inexactly) the solution to the MPW problem. We show experimentally that our approach works well in practice, scaling well to problems where the exact solution is intractable to compute.

Preference-Based Query Answering in Probabilistic Datalog+/– Ontologies

The incorporation of preferences into information systems, such as databases, has recently seen a surge in interest, mainly fueled by the revolution in Web data availability. Modeling the preferences of a user on the Web has also increasingly become appealing to many companies since the explosion of popularity of social media. The other surge in interest is in modeling uncertainty in these domains, since uncertainty can arise due to many uncontrollable factors. In this paper, we propose an extension of the Datalog+/– family of ontology languages with two models: one representing user preferences and one representing the (probabilistic) uncertainty with which inferences are made. Assuming that more probable answers are in general more preferable, one asks how to rank answers to a user’s queries, since the preference model may be in conflict with the preferences induced by the probabilistic model—the need thus arises for preference combination operators. We propose four specific operators and study their semantic and computational properties. We also provide an algorithm for ranking answers based on the iteration of the well-known skyline answers to a query and show that, under certain conditions, it runs in polynomial time in the data complexity. Furthermore, we report on an implementation and experimental results.

Inconsistency-Tolerant Reasoning in Datalog ± Ontologies via an Argumentative Semantics

The Semantic Web provides an effective infrastructure that allows data to be easily shared and reused across applications. At its core is the description of ontological knowledge using ontological languages which are powerful knowledge representation tools with good decidability and tractability properties; Datalog\(^{\pm }\) is one of these tools.The problem of inconsistency has been acknowledged in both the Semantic Web and Database Theory communities. Here we introduce elements of defeasible argumentative reasoning in Datalog\(^{\pm }\), consequences to represent statements whose truth can be challenged leading to a better handling of inconsistency in ontological languages.

Inconsistency-Tolerant query rewriting for linear datalog+/-

Inconsistency management in knowledge bases is an important problem that has been studied for a long time. During the recent years, additional interest in this topic has been sparked with the advent of the Semantic Web, which has made this problem even more relevant, since inconsistencies are very likely to occur in open environments such as the Web. Inconsistency-tolerant semantics to query answering have therefore become of special interest for representation and reasoning formalisms for the Semantic Web. Datalog+/--- is a family of ontology languages that is in particular useful for representing and reasoning over lightweight ontologies in the Semantic Web. In this paper, we focus on inconsistency-tolerant query answering under the intersection semantics in linear Datalog+/---, a sublanguage of Datalog+/--- that generalizes the DL-Lite family of tractable description logics (DLs). In particular, we show that query answering in linear Datalog+/--- is first-order rewritable under this inconsistency-tolerant semantics, and therefore very efficiently computable in the data complexity.

Improving Inconsistency Resolution by Considering Global Conflicts

Over the years, inconsistency management has caught the attention of researchers of different areas. Inconsistency is a problem that arises in many different scenarios, for instance, ontology development or knowledge integration. In such settings, it is important to have adequate automatic tools for handling potential conflicts. Here we propose a novel approach to belief base consolidation based on a refinement of kernel contraction that accounts for the relation among kernels using clusters. We define cluster contraction based consolidation operators as the contraction by falsum on a belief base using cluster incision functions, a refinement of smooth kernel incision functions. A cluster contraction-based approach to belief bases consolidation can successfully obtain a belief base satisfying the expected consistency requirement. Also, we show that the application of cluster contraction-based consolidation operators satisfy minimality regarding loss of information and are equivalent to operators based on maxichoice contraction.