Formal XAI is an emerging field that focuses on providing explanations with mathematical guarantees for the decisions made by machine learning models. A significant amount of work in this area is centered on the computation of ``sufficient reasons''. Given a model M and an input instance x, a sufficient reason for the decision x is a subset S of the features of x such that for any instance z that has the same values as x for every feature in S, it holds that M(x) = M(z). Intuitively, this means that the features in S are sufficient to fully justify the classification of x by M. For sufficient reasons to be useful in practice, they should be as small as possible, and a natural way to reduce the size of sufficient reasons is to consider a probabilistic relaxation; the probability of M(x) = M(z) must be at least some value delta in (0,1], where z is a random instance that coincides with x on the features in S. Computing small delta-sufficient reasons (delta-SRs) is known to be a theoretically hard problem; even over decision trees — traditionally deemed simple and interpretable models — strong inapproximability results make the efficient computation of small delta-SRs unlikely. We propose the notion of (delta, epsilon)-SR, a simple relaxation of delta-SRs, and show that this kind of explanations can be computed efficiently over linear models.

Probabilistic circuits (PCs) are a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits. Existing multiplication algorithms require that the circuits respect the same structure, i.e. variable scopes decomposes according to the same vtree. In this work, we propose and study the task of restructuring structured(-decomposable) PCs, that is, transforming a structured PC such that it conforms to a target vtree. We propose a generic approach for this problem and show that it leads to novel polynomial-time algorithms for multiplying circuits respecting different vtrees, as well as a practical depth-reduction algorithm that preserves structured decomposibility. Our work opens up new avenues for tractable PC inference, suggesting the possibility of training with less restrictive PC structures while enabling efficient inference by changing their structures at inference time.

Formal XAI (explainable AI) is a growing area that focuses on computing explanations with mathematical guarantees for the decisions made by ML models. Inside formal XAI, one of the most studied cases is that of explaining the choices taken by decision trees, as they are traditionally deemed as one of the most interpretable classes of models. Recent work has focused on studying the computation of sufficient reasons, a kind of explanation in which given a decision tree T and an instance x, one explains the decision T (x) by providing a subset y of the features of x such that for any other instance z compatible with y, it holds that T (z) = T (x), intuitively meaning that the features in y are already enough to fully justify the classification of x by T. It has been argued, however, that sufficient reasons constitute a restrictive notion of explanation. For such a reason, the community has started to study their probabilistic counterpart, in which one requires that the probability of T (z) = T (x) must be at least some value δ ∈ (0, 1], where z is a random instance that is compatible with y. Our paper settles the computational complexity of δ-sufficient-reasons over decision trees, showing that both (1) finding δ-sufficient-reasons that are minimal in size, and (2) finding δ-sufficient-reasons that are minimal inclusion-wise, are computationally intractable. By doing this, we answer two open problems originally raised by Izza et al. (2021), and extend the hardness of explanations for Boolean circuits presented by Wäldchen et al. (2021) to the more restricted case of decision trees. Furthermore, we present sharp non-approximability results under a widely believed complexity hypothesis. On the positive side, we identify structural restrictions of decision trees that make the problem tractable.

When query evaluation produces too many tuples, a new approach in query answering is to retrieve a diverse subset of them. The standard approach for measuring the diversity of a set of tuples is to use a distance function between tuples, which measures the dissimilarity between them, to then aggregate the pairwise distances of the set into a score (e.g., by using sum or min aggregation). However, as we will point out in this work, the resulting diversity measures may display some unintuitive behavior. Moreover, even in very simple settings, finding a maximally diverse subset of the answers of fixed size is, in general, intractable and little is known about approximations apart from some hand-picked distance-aggregator pairs. In this work, we introduce a novel approach for computing the diversity of tuples based on volume instead of distance. We present a framework for defining volume-based diversity functions and provide several examples of these measures applied to relational data. Although query answering of conjunctive queries (CQ) under this setting is intractable in general, we show that one can always compute a (1-1/e)-approximation for any volume-based diversity function. Furthermore, in terms of combined complexity, we connect the evaluation of CQs under volume-based diversity functions with the ranked enumeration of solutions, finding general conditions under which a (1-1/e)-approximation can be computed in polynomial time.

The formal XAI community has studied a plethora of interpretability queries aiming to understand the classifications made by decision trees. However, a more uniform understanding of what questions we can hope to answer about these models, traditionally deemed to be easily interpretable, has remained elusive. In an initial attempt to understand uniform languages for interpretability, Arenas et al. proposed FOIL, a logic for explaining black-box ML models, and showed that it can express a variety of interpretability queries. However, we show that FOIL is limited in two important senses: (i) it is not expressive enough to capture some crucial queries, and (ii) its model agnostic nature results in a high computational complexity for decision trees. In this paper, we carefully craft two fragments of first-order logic that allow for efficiently interpreting decision trees: Q-DT-FOIL and its optimization variant OPT-DT-FOIL. We show that our proposed logics can express not only a variety of interpretability queries considered by previous literature, but also elegantly allows users to specify different objectives the sought explanations should optimize for. Using finite model-theoretic techniques, we show that the different ingredients of Q-DT-FOIL are necessary for its expressiveness, and yet that queries in Q-DT-FOIL can be evaluated with a polynomial number of queries to a SAT solver, as well as their optimization versions in OPT-DT-FOIL. Besides our theoretical results, we provide a SAT-based implementation of the evaluation for OPT-DT-FOIL that is performant on industry-size decision trees.

The set of answers to a query may be very large, potentially overwhelming users when presented with the entire set. In such cases, presenting only a small subset of the answers to the user may be preferable. A natural requirement for this subset is that it should be as diverse as possible to reflect the variety of the entire population. To achieve this, the diversity of a subset is measured using a metric that determines how different two solutions are and a diversity function that extends this metric from pairs to sets. In the past, several studies have shown that finding a diverse subset from an explicitly given set is intractable even for simple metrics (like Hamming distance) and simple diversity functions (like summing all pairwise distances). This complexity barrier becomes even more challenging when trying to output a diverse subset from a set that is only implicitly given (such as the query answers for a given query and a database). Until now, tractable cases have been found only for restricted problems and particular diversity functions. To overcome these limitations, we focus in this work on the notion of ultrametrics, which have been widely studied and used in many applications. Starting from any ultrametric d and a diversity function δ extending d , we provide sufficient conditions over δ for having polynomial-time algorithms to construct diverse answers. To the best of our knowledge, these conditions are satisfied by all the diversity functions considered in the literature. Moreover, we complement these results with lower bounds that show specific cases when these conditions are not satisfied and finding diverse subsets becomes intractable. We conclude by applying these results to the evaluation of conjunctive queries, demonstrating efficient algorithms for finding a diverse subset of solutions for acyclic conjunctive queries when the attribute order is used to measure diversity.

Citations for the The ACM PODS Alberto O. Mendelzon Test-of-Time Award 2023

Scores based on Shapley values are widely used for providing explanations to classification results over machine learning models. A prime example of this is the influential~ Shap-score, a version of the Shapley value that can help explain the result of a learned model on a specific entity by assigning a score to every feature. While in general computing Shapley values is a computationally intractable problem, we prove a strong positive result stating that the Shap-score can be computed in polynomial time over deterministic and decomposable Boolean circuits under the so-called product distributions on entities. Such circuits are studied in the field of Knowledge Compilation and generalize a wide range of Boolean circuits and binary decision diagrams classes, including binary decision trees, Ordered Binary Decision Diagrams (OBDDs) and Free Binary Decision Diagrams (FBDDs). Our positive result extends even beyond binary classifiers, as it continues to hold if each feature is associated with a finite domain of possible values. We also establish the computational limits of the notion of Shap-score by observing that, under a mild condition, computing it over a class of Boolean models is always polynomially as hard as the model counting problem for that class. This implies that both determinism and decomposability are essential properties for the circuits that we consider, as removing one or the other renders the problem of computing the Shap-score intractable (namely, $\#P$-hard). It also implies that computing Shap-scores is $\#P$-hard even over the class of propositional formulas in DNF. Based on this negative result, we look for the existence of fully-polynomial randomized approximation schemes (FPRAS) for computing Shap-scores over such class. In stark contrast to the model counting problem for DNF formulas, which admits an FPRAS, we prove that no such FPRAS exists (under widely believed complexity assumptions) for the computation of Shap-scores. Surprisingly, this negative result holds even for the class of monotone formulas in DNF. These techniques can be further extended to prove another strong negative result: Under widely believed complexity assumptions, there is no polynomial-time algorithm that checks, given a monotone DNF formula $\varphi$ and features $x,y$, whether the Shap-score of $x$ in $\varphi$ is smaller than the Shap-score of $y$ in $\varphi$.

In the last decade, substantial progress has been made towards standardizing the syntax of graph query languages, and towards understanding their semantics and complexity of evaluation. In this paper, we consider temporal property graphs (TPGs) and propose temporal regular path queries (TRPQs) that incorporate time into TPG navigation. Starting with design principles, we propose a natural syntactic extension of the MATCH clause of popular graph query languages. We then formally present the semantics of TRPQs, and study the complexity of their evaluation. We show that TRPQs can be evaluated in polynomial time if TPGs are time-stamped with time points, and identify fragments of the TRPQ language that admit efficient evaluation over a more succinct interval-annotated representation. Finally, we implement a fragment of the language in a state-of-the-art dataflow framework, and experimentally demonstrate that TRPQ can be evaluated efficiently.

Formal XAI (explainable AI) is a growing area that focuses on computing explanations with mathematical guarantees for the decisions made by ML models. Inside formal XAI, one of the most studied cases is that of explaining the choices taken by decision trees, as they are traditionally deemed as one of the most interpretable classes of models. Recent work has focused on studying the computation of sufficient reasons, a kind of explanation in which given a decision tree $T$ and an instance $x$, one explains the decision $T(x)$ by providing a subset $y$ of the features of $x$ such that for any other instance $z$ compatible with $y$, it holds that $T(z) = T(x)$, intuitively meaning that the features in $y$ are already enough to fully justify the classification of $x$ by $T$. It has been argued, however, that sufficient reasons constitute a restrictive notion of explanation. For such a reason, the community has started to study their probabilistic counterpart, in which one requires that the probability of $T(z) = T(x)$ must be at least some value $\delta \in (0, 1]$, where $z$ is a random instance that is compatible with $y$. Our paper settles the computational complexity of $\delta$-sufficient-reasons over decision trees, showing that both (1) finding $\delta$-sufficient-reasons that are minimal in size, and (2) finding $\delta$-sufficient-reasons that are minimal inclusion-wise, do not admit polynomial-time algorithms (unless P = NP). This is in stark contrast with the deterministic case ($\delta = 1$) where inclusion-wise minimal sufficient-reasons are easy to compute. By doing this, we answer two open problems originally raised by Izza et al., and extend the hardness of explanations for Boolean circuits presented by W{\"a}ldchen et al. to the more restricted case of decision trees. On the positive side, we identify structural restrictions of decision trees that make the problem tractable, and show how SAT solvers might be able to tackle these problems in practical settings.

Scores based on Shapley values are widely used for providing explanations to classification results over machine learning models. A prime example of this is the influential SHAP-score, a version of the Shapley value that can help explain the result of a learned model on a specific entity by assigning a score to every feature. While in general computing Shapley values is a computationally intractable problem, it has recently been claimed that the SHAP-score can be computed in polynomial time over the class of decision trees. In this paper, we provide a proof of a stronger result over Boolean models: the SHAP-score can be computed in polynomial time over deterministic and decomposable Boolean circuits. Such circuits, also known as tractable Boolean circuits, generalize a wide range of Boolean circuits and binary decision diagrams classes, including binary decision trees, Ordered Binary Decision Diagrams (OBDDs) and Free Binary Decision Diagrams (FBDDs). We also establish the computational limits of the notion of SHAP-score by observing that, under a mild condition, computing it over a class of Boolean models is always polynomially as hard as the model counting problem for that class. This implies that both determinism and decomposability are essential properties for the circuits that we consider, as removing one or the other renders the problem of computing the SHAP-score intractable (namely, #P-hard).

Several queries and scores have recently been proposed to explain individual predictions over ML models. Examples include queries based on “anchors”, which are parts of an instance that are sufficient to justify its classification, and “feature-perturbation” scores such as SHAP. Given the need for flexible, reliable, and easy-to-apply interpretability methods for ML models, we foresee the need for developing declarative languages to naturally specify different explainability queries. We do this in a principled way by rooting such a language in a logic called FOIL, which allows for expressing many simple but important explainability queries, and might serve as a core for more expressive interpretability languages. We study the computational complexity of FOIL queries over two classes of ML models often deemed to be easily interpretable: decision trees and more general decision diagrams. Since the number of possible inputs for an ML model is exponential in its dimension, tractability of the FOIL evaluation problem is delicate but can be achieved by either restricting the structure of the models, or the fragment of FOIL being evaluated. We also present a prototype implementation of FOIL wrapped in a high-level declarative language and perform experiments showing that such a language can be used in practice.

Graphs have become the best way we know of representing knowledge. The computing community has investigated and developed the support for managing graphs by means of digital technology. Graph databases and knowledge graphs surface as the most successful solutions to this program. This tutorial will provide a conceptual map of the data management tasks underlying these developments, paying particular attention to data models and query languages for graphs

Counting the number of words of a certain length accepted by a non-deterministic finite automaton (NFA) is a fundamental problem, which has many applications in different areas such as graph databases, knowledge compilation, and information extraction. Along with this, generating such words uniformly at random is also a relevant problem, particularly in scenarios where returning varied outputs is a desirable feature.

Conjunctive queries are one of the most common class of queries used in database systems, and the best studied in the literature. A seminal result of Grohe, Schwentick, and Segoufin (STOC 2001) demonstrates that for every class G of graphs, the evaluation of all conjunctive queries whose underlying graph is in G is tractable if, and only if, G has bounded treewidth. In this work, we extend this characterization to the counting problem for conjunctive queries. Specifically, for every class C of conjunctive queries with bounded treewidth, we introduce the first fully polynomial-time randomized approximation scheme (FPRAS) for counting answers to a query in C, and the first polynomial-time algorithm for sampling answers uniformly from a query in C. As a corollary, it follows that for every class G of graphs, the counting problem for conjunctive queries whose underlying graph is in G admits an FPRAS if, and only if, G has bounded treewidth (unless BPP is different from P). In fact, our FPRAS is more general, and also applies to conjunctive queries with bounded hypertree width, as well as unions of such queries.

In this work, we study two simple yet general complexity classes, based on logspace Turing machines, that provide a unifying framework for efficient query evaluation in areas such as information extraction and graph databases, among others. We investigate the complexity of three fundamental algorithmic problems for these classes: enumeration, counting, and uniform generation of solutions, and show that they have several desirable properties in this respect. Both complexity classes are defined in terms of non-deterministic logspace transducers (NL-transducers). For the first class, we consider the case of unambiguous NL-transducers, and we prove constant delay enumeration and both counting and uniform generation of solutions in polynomial time. For the second class, we consider unrestricted NL-transducers, and we obtain polynomial delay enumeration, approximate counting in polynomial time, and polynomial-time randomized algorithms for uniform generation. More specifically, we show that each problem in this second class admits a fully polynomial-time randomized approximation scheme (FPRAS) and a polynomial-time Las Vegas algorithm (with preprocessing) for uniform generation. Remarkably, the key idea to prove these results is to show that the fundamental problem # NFA admits an FPRAS, where # NFA is the problem of counting the number of strings of length n (given in unary) accepted by a non-deterministic finite automaton (NFA). While this problem is known to be P-complete and, more precisely, SpanL -complete, it was open whether this problem admits an FPRAS. In this work, we solve this open problem and obtain as a welcome corollary that every function in SpanL admits an FPRAS.

We study the complexity of various fundamental counting problems that arise in the context of incomplete databases, i.e., relational databases that can contain unknown values in the form of labeled nulls. Specifically, we assume that the domains of these unknown values are finite and, for a Boolean query q , we consider the following two problems: Given as input an incomplete database D , (a) return the number of completions of D that satisfy q ; or (b) return the number of valuations of the nulls of D yielding a completion that satisfies q . We obtain dichotomies between #P-hardness and polynomial-time computability for these problems when q is a self-join–free conjunctive query and study the impact on the complexity of the following two restrictions: (1) every null occurs at most once in D (what is called Codd tables ); and (2) the domain of each null is the same. Roughly speaking, we show that counting completions is much harder than counting valuations: For instance, while the latter is always in #P, we prove that the former is not in #P under some widely believed theoretical complexity assumption. Moreover, we find that both (1) and (2) can reduce the complexity of our problems. We also study the approximability of these problems and show that, while counting valuations always has a fully polynomial-time randomized approximation scheme (FPRAS), in most cases counting completions does not. Finally, we consider more expressive query languages and situate our problems with respect to known complexity classes.

We study the complexity of various fundamental counting problems that arise in the context of incomplete databases, i.e., relational databases that can contain unknown values in the form of labeled nulls. Specifically, we assume that the domains of these unknown values are finite and, for a Boolean query q, we consider the following two problems: given as input an incomplete database D, (a) return the number of completions of D that satisfy q; or (b) return or the number of valuations of the nulls of D yielding a completion that satisfies q. We obtain dichotomies between #P-hardness and polynomial-time computability for these problems when q is a self-join-free conjunctive query, and study the impact on the complexity of the following two restrictions: (1) every null occurs at most once in D (what is called Codd tables); and (2) the domain of each null is the same. Roughly speaking, we show that counting completions is much harder than counting valuations (for instance, while the latter is always in #P, we prove that the former is not in #P under some widely believed theoretical complexity assumption). Moreover, we find that both (1) and (2) reduce the complexity of our problems. We also study the approximability of these problems and show that, while counting valuations always has a fully polynomial randomized approximation scheme, in most cases counting completions does not. Finally, we consider more expressive query languages and situate our problems with respect to known complexity classes.

A widespread security claim of the Bitcoin system, presented in the original Bitcoin white-paper, states that the security of the system is guaranteed as long as there is no attacker in possession of half or more of the total computational power used to maintain the system. This claim, however, is proved based on theoretically flawed assumptions. In the paper we analyze two kinds of attacks based on two theoretical flaws: the Block Discarding Attack and the Difficulty Raising Attack. We argue that the current theoretical limit of attacker's fraction of total computational power essential for the security of the system is in a sense not $\frac{1}{2}$ but a bit less than $\frac{1}{4}$, and outline proposals for protocol change that can raise this limit to be as close to $\frac{1}{2}$ as we want. The basic idea of the Block Discarding Attack has been noted as early as 2010, and lately was independently though-of and analyzed by both author of this paper and authors of a most recently pre-print published paper. We thus focus on the major differences of our analysis, and try to explain the unfortunate surprising coincidence. To the best of our knowledge, the second attack is presented here for the first time.

Descriptive Complexity has been very successful in characterizing complexity classes of decision problems in terms of the properties definable in some logics. However, descriptive complexity for counting complexity classes, such as FP and #P, has not been systematically studied, and it is not as developed as its decision counterpart. In this paper, we propose a framework based on Weighted Logics to address this issue. Specifically, by focusing on the natural numbers we obtain a logic called Quantitative Second Order Logics (QSO), and show how some of its fragments can be used to capture fundamental counting complexity classes such as FP, #P and FPSPACE, among others. We also use QSO to define a hierarchy inside #P, identifying counting complexity classes with good closure and approximation properties, and which admit natural complete problems. Finally, we add recursion to QSO, and show how this extension naturally captures lower counting complexity classes such as #L.

In this work, we study two simple yet general complexity classes, based on logspace Turing machines, which provide a unifying framework for efficient query evaluation in areas like information extraction and graph databases, among others. We investigate the complexity of three fundamental algorithmic problems for these classes: enumeration, counting and uniform generation of solutions, and show that they have several desirable properties in this respect. Both complexity classes are defined in terms of nondeterministic logspace transducers (NL transducers). For the first class, we consider the case of unambiguous NL transducers, and we prove constant delay enumeration, and both counting and uniform generation of solutions in polynomial time. For the second class, we consider unrestricted NL transducers, and we obtain polynomial delay enumeration, approximate counting in polynomial time, and polynomial-time randomized algorithms for uniform generation. More specifically, we show that each problem in this second class admits a fully polynomial-time randomized approximation scheme (FPRAS) and a polynomial-time Las Vegas algorithm for uniform generation. Interestingly, the key idea to prove these results is to show that the fundamental problem #NFA admits an FPRAS, where #NFA is the problem of counting the number of strings of length n accepted by a nondeterministic finite automaton (NFA). While this problem is known to be #P-complete and, more precisely, SpanL-complete, it was open whether this problem admits an FPRAS. In this work, we solve this open problem, and obtain as a welcome corollary that every function in SpanL admits an FPRAS.

We report on a community effort between industry and academia to shape the future of graph query languages. We argue that existing graph database management systems should consider supporting a query language with two key characteristics. First, it should be composable, meaning, that graphs are the input and the output of queries. Second, the graph query language should treat paths as first-class citizens. Our result is G-CORE, a powerful graph query language design that fulfills these goals, and strikes a careful balance between path query expressivity and evaluation complexity.

The problem of querying RDF data is a central issue for the development of the Semantic Web. The query language SPARQL has become the standard language for querying RDF since its W3C standardization in 2008. However, the 2008 version of this language missed some important functionalities: reasoning capabilities to deal with RDFS and OWL vocabularies, navigational capabilities to exploit the graph structure of RDF data, and a general form of recursion much needed to express some natural queries. To overcome these limitations, a new version of SPARQL, called SPARQL 1.1, was released in 2013, which includes entailment regimes for RDFS and OWL vocabularies, and a mechanism to express navigation patterns through regular expressions. Unfortunately, there are a number of useful navigation patterns that cannot be expressed in SPARQL 1.1, and the language lacks a general mechanism to express recursive queries. To the best of our knowledge, no efficient RDF query language that combines the above functionalities is known. It is the aim of this work to fill this gap. To this end, we focus on a core fragment of the OWL 2 QL profile of OWL 2 and show that every SPARQL query enriched with the above features can be naturally translated into a query expressed in a language that is based on an extension of Datalog, which allows for value invention and stratified negation. However, the query evaluation problem for this language is highly intractable, which is not surprising since it is expressive enough to encode some inherently hard queries. We identify a natural fragment of it, and we show it to be tractable and powerful enough to define SPARQL queries enhanced with the desired functionalities.

Descriptive Complexity has been very successful in characterizing complexity classes of decision problems in terms of the properties definable in some logics. However, descriptive complexity for counting complexity classes, such as FP and #P, has not been systematically studied, and it is not as developed as its decision counterpart. In this paper, we propose a framework based on Weighted Logics to address this issue. Specifically, by focusing on the natural numbers we obtain a logic called Quantitative Second Order Logics (QSO), and show how some of its fragments can be used to capture fundamental counting complexity classes such as FP, #P and FPSPACE, among others. We also use QSO to define a hierarchy inside #P, identifying counting complexity classes with good closure and approximation properties, and which admit natural complete problems. Finally, we add recursion to QSO, and show how this extension naturally captures lower counting complexity classes such as #L.

When querying an Resource Description Framework (RDF) graph, a prominent feature is the possibility of extending the answer to a query with optional information. However, the definition of this feature in SPARQL—the standard RDF query language—has raised some important issues. Most notably, the use of this feature increases the complexity of the evaluation problem, and its closed-world semantics is in conflict with the underlying open-world semantics of RDF. Many approaches for fixing such problems have been proposed, the most prominent being the introduction of the semantic notion of weakly monotone SPARQL query. Weakly monotone SPARQL queries have shaped the class of queries that conform to the open-world semantics of RDF. Unfortunately, finding an effective way of restricting SPARQL to the fragment of weakly monotone queries has proven to be an elusive problem. In practice, the most widely adopted fragment for writing SPARQL queries is based on the syntactic notion of well designedness. This notion has proven to be a good approach for writing SPARQL queries, but its expressive power has yet to be fully understood. The starting point of this article is to understand the relation between well-designed queries and the semantic notion of weak monotonicity. It is known that every well-designed SPARQL query is weakly monotone; as our first contribution we prove that the converse does not hold, even if an extension of this notion based on the use of disjunction is considered. Given this negative result, we embark on the task of defining syntactic fragments that are weakly monotone and have higher expressive power than the fragment of well-designed queries. To this end, we move to a more general scenario where infinite RDF graphs are also allowed, so interpolation techniques studied for first-order logic can be applied. With the use of these techniques, we are able to define a new operator for SPARQL that gives rise to a query language with the desired properties (over finite and infinite RDF graphs). It should be noticed that every query in this fragment is weakly monotone if we restrict the semantics to finite RDF graphs. Moreover, we use this result to provide a simple characterization of the class of monotone CONSTRUCT queries, that is, the class of SPARQL queries that produce RDF graphs as output. Finally, we pinpoint the complexity of the evaluation problem for the query languages identified in the article.

No abstract available.

When querying an RDF graph, a prominent feature is the possibility of extending the answer to a query with optional information. However, the definition of this feature in SPARQL --the standard RDF query language-- has raised some important issues. Most notably, the use of this feature increases the complexity of the evaluation problem, and its closed-world semantics is in conflict with the underlying open-world semantics of RDF. Many approaches for fixing such problems have been proposed, being the most prominent the introduction of the semantic notion of weakly-monotone SPARQL query. Weakly-monotone SPARQL queries have shaped the class of queries that conform to the open-world semantics of RDF. Unfortunately, finding an effective way of restricting SPARQL to the fragment of weakly-monotone queries has proven to be an elusive problem. In practice, the most widely adopted fragment for writing SPARQL queries is based on the syntactic notion of well designedness. This notion has proven to be a good approach for writing SPARQL queries, but its expressive power has yet to be fully understood. The starting point of this paper is to understand the relation between well-designed queries and the semantic notion of weak monotonicity. It is known that every well-designed SPARQL query is weakly monotone; as our first contribution we prove that the converse does not hold, even if an extension of this notion based on the use of disjunction is considered. Given this negative result, we embark on the task of defining syntactic fragments that are weakly-monotone, and have higher expressive power than the fragment of well-designed queries. To this end, we move to a more general scenario where infinite RDF graphs are also allowed, so that interpolation techniques studied for first-order logic can be applied. With the use of these techniques, we are able to define a new operator for SPARQL that gives rise to a query language with the desired properties (over finite and infinite RDF graphs). It should be noticed that every query in this fragment is weakly monotone if we restrict to the case of finite RDF graphs. Moreover, we use this result to provide a simple characterization of the class of monotone CONSTRUCT queries, that is, the class of SPARQL queries that produce RDF graphs as output. Finally, we pinpoint the complexity of the evaluation problem for the query languages identified in the paper.

Semantic Web systems provide open interfaces for end-users to access data via a powerful high-level query language, SPARQL. But users unfamiliar with either the details of SPARQL or properties of the target dataset may find it easier to query by example -- give examples of the information they want (or examples of both what they want and what they do not want) and let the system reverse engineer the desired query from the examples. This approach has been heavily used in the setting of relational databases. We provide here an investigation of the reverse engineering problem in the context of SPARQL. We first provide a theoretical study, formalising variants of the reverse engineering problem and giving tight bounds on its complexity. We next explain an implementation of a reverse engineering tool for positive examples. An experimental analysis of the tool shows that it scales well in the data size, number of examples, and in the size of the smallest query that fits the data. We also give evidence that reverse engineering tools can provide benefits on real-life datasets.

In this paper, we propose a simple and expressive framework for adding metadata to CSV documents and their noisy variants. The framework is based on annotating parts of the document that can be later used to read, query, or exchange the data. The core of our framework is a language based on extended regular expressions that are used for selecting data. These expressions are then combined using a set of rules in order to annotate the data. We study the computational complexity of implementing our framework and present an efficient evaluation algorithm that runs in time proportional to its output and linear in its input. As a proof of concept, we test an implementation of our framework against a large number of real world datasets and show that it can be efficiently used in practice.

Semantic Web technologies such as RDF and its query language, SPARQL, offer the possibility of opening up the use of public datasets to a great variety of ordinary users. But a key obstacle to the use of open data is the unfamiliarity of users with the structure of data or with SPARQL. To deal with these issues, we introduce a system for querying RDF data by example. At its core is a technique for reverse-engineering SPARQL queries by example. We demonstrate how reverse engineering along with other techniques, such as query relaxation, enables our system, SPARQLByE, to guide users who are unfamiliar with both the dataset and with SPARQL to the desired query and result set.

We study the definability problem for first-order logic, denoted by FO-D ef . The input of FO-D ef is a relational database instance I and a relation R ; the question to answer is whether there exists a first-order query Q (or, equivalently, a relational algebra expression Q ) such that Q evaluated on I gives R as an answer. Although the study of FO-D ef dates back to 1978, when the decidability of this problem was shown, the exact complexity of FO-D ef remains as a fundamental open problem. In this article, we provide a polynomial-time algorithm for solving FO-D ef that uses calls to a graph-isomorphism subroutine (or oracle). As a consequence, the first-order definability problem is found to be complete for the class GI of all problems that are polynomial-time Turing reducible to the graph isomorphism problem, thus closing the open question about the exact complexity of this problem. The technique used is also applied to a generalized version of the problem that accepts a finite set of relation pairs, and whose exact complexity was also open; this version is also found to be GI -complete.

An increasing number of applications rely on RDF, OWL 2, and SPARQL for storing and querying data. SPARQL, however, is not targeted towards end-users, and suitable query interfaces are needed. Faceted search is a prominent approach for end-user data access, and several RDF-based faceted search systems have been developed. There is, however, a lack of rigorous theoretical underpinning for faceted search in the context of RDF and OWL 2. In this paper, we provide such solid foundations. We formalise faceted interfaces for this context, identify a fragment of first-order logic capturing the underlying queries, and study the complexity of answering such queries for RDF and OWL 2 profiles. We then study interface generation and update, and devise efficiently implementable algorithms. Finally, we have implemented and tested our faceted search algorithms for scalability, with encouraging results.

The problem of querying RDF data is a central issue for the development of the Semantic Web. The query language SPARQL has become the standard language for querying RDF, since its standardization in 2008. However, the 2008 version of this language missed some important functionalities: reasoning capabilities to deal with RDFS and OWL vocabularies, navigational capabilities to exploit the graph structure of RDF data, and a general form of recursion much needed to express some natural queries. To overcome these limitations, a new version of SPARQL, called SPARQL 1.1, was recently released, which includes entailment regimes for RDFS and OWL vocabularies, and a mechanism to express navigation patterns through regular expressions. Unfortunately, there are still some useful navigation patterns that cannot be expressed in SPARQL 1.1, and the language lacks of a general mechanism to express recursive queries.

Although RDF graph data often come with an associated schema, recent studies have proven that real RDF data rarely conform to their perceived schemas. Since a number of data management decisions, including storage layouts, indexing, and efficient query processing, use schemas to guide the decision making, it is imperative to have an accurate description of the structuredness of the data at hand (how well the data conform to the schema). In this paper, we have approached the study of the structuredness of an RDF graph in a principled way: we propose a framework for specifying structuredness functions, which gauge the degree to which an RDF graph conforms to a schema. In particular, we first define a formal language for specifying structuredness functions with expressions we call rules. This language allows a user to state a rule to which an RDF graph may fully or partially conform. Then we consider the issue of discovering a refinement of a sort (type) by partitioning the dataset into subsets whose structuredness is over a specified threshold. In particular, we prove that the natural decision problem associated to this refinement problem is NP-complete, and we provide a natural translation of this problem into Integer Linear Programming (ILP). Finally, we test this ILP solution with three real world datasets and three different and intuitive rules, which gauge the structuredness in different ways. We show that the rules give meaningful refinements of the datasets, showing that our language can be a powerful tool for understanding the structure of RDF data, and we show that the ILP solution is practical for a large fraction of existing data.

A great deal of research into the learning of schemas from XML data has been conducted in recent years to enable the automatic discovery of XML schemas from XML documents when no schema or only a low-quality one is available. Unfortunately, and in strong contrast to, for instance, the relational model, the automatic discovery of even the simplest of XML constraints, namely XML keys, has been left largely unexplored in this context. A major obstacle here is the unavailability of a theory on reasoning about XML keys in the presence of XML schemas, which is needed to validate the quality of candidate keys. The present article embarks on a fundamental study of such a theory and classifies the complexity of several crucial properties concerning XML keys in the presence of an XSD, like, for instance, testing for consistency, boundedness, satisfiability, universality, and equivalence. Of independent interest, novel results are obtained related to cardinality estimation of XPath result sets. A mining algorithm is then developed within the framework of levelwise search. The algorithm leverages known discovery algorithms for functional dependencies in the relational model, but incorporates the properties mentioned before to assess and refine the quality of derived keys. An experimental study on an extensive body of real-world XML data evaluating the effectiveness of the proposed algorithm is provided.

A great deal of research into the learning of schemas from XML data has been conducted in recent years to enable the automatic discovery of XML Schemas from XML documents when no schema, or only a low-quality one is available. Unfortunately, and in strong contrast to, for instance, the relational model, the automatic discovery of even the simplest of XML constraints, namely XML keys, has been left largely unexplored in this context. A major obstacle here is the unavailability of a theory on reasoning about XML keys in the presence of XML schemas, which is needed to validate the quality of candidate keys. The present paper embarks on a fundamental study of such a theory and classifies the complexity of several crucial properties concerning XML keys in the presence of an XSD, like, for instance, testing for consistency, boundedness, satisfiability, universality, and equivalence. Of independent interest, novel results are obtained related to cardinality estimation of XPath result sets. A mining algorithm is then developed within the framework of levelwise search. The algorithm leverages known discovery algorithms for functional dependencies in the relational model, but incorporates the above mentioned properties to assess and refine the quality of derived keys. An experimental study on an extensive body of real world XML data evaluating the effectiveness of the proposed algorithm is provided.

In the traditional data exchange setting, source instances are restricted to be complete in the sense that every fact is either true or false in these instances. Although natural for a typical database translation scenario, this restriction is gradually becoming an impediment to the development of a wide range of applications that need to exchange objects that admit several interpretations. In particular, we are motivated by two specific applications that go beyond the usual data exchange scenario: exchanging incomplete information and exchanging knowledge bases . In this article, we propose a general framework for data exchange that can deal with these two applications. More specifically, we address the problem of exchanging information given by representation systems , which are essentially finite descriptions of (possibly infinite) sets of complete instances. We make use of the classical semantics of mappings specified by sets of logical sentences to give a meaningful semantics to the notion of exchanging representatives, from which the standard notions of solution, space of solutions, and universal solution naturally arise. We also introduce the notion of strong representation system for a class of mappings , that resembles the concept of strong representation system for a query language. We show the robustness of our proposal by applying it to the two applications mentioned above: exchanging incomplete information and exchanging knowledge bases, which are both instantiations of the exchanging problem for representation systems. We study these two applications in detail, presenting results regarding expressiveness, query answering and complexity of computing solutions, and also algorithms to materialize solutions.

SPARQL -the standard query language for querying RDF- provides only limited navigational functionalities, although these features are of fundamental importance for graph data formats such as RDF. This has led the W3C to include the property path feature in the upcoming version of the standard, SPARQL 1.1.We tested several implementations of SPARQL 1.1 handling property path queries, and we observed that their evaluation methods for this class of queries have a poor performance even in some very simple scenarios. To formally explain this fact, we conduct a theoretical study of the computational complexity of property paths evaluation. Our results imply that the poor performance of the tested implementations is not a problem of these particular systems, but of the specification itself. In fact, we show that any implementation that adheres to the SPARQL 1.1 specification (as of November 2011) is doomed to show the same behavior, the key issue being the need for counting solutions imposed by the current specification. We provide several intractability results, that together with our empirical results, provide strong evidence against the current semantics of SPARQL 1.1 property paths. Finally, we put our results in perspective, and propose a natural alternative semantics with tractable evaluation, that we think may lead to a wide adoption of the language by practitioners, developers and theoreticians.

Mapping relational databases to RDF is a fundamental problem for the development of the Semantic Web. We present a solution, inspired by draft methods defined by the W3C where relational databases are directly mapped to RDF and OWL. Given a relational database schema and its integrity constraints, this direct mapping produces an OWL ontology, which, provides the basis for generating RDF instances. The semantics of this mapping is defined using Datalog. Two fundamental properties are information preservation and query preservation. We prove that our mapping satisfies both conditions, even for relational databases that contain null values. We also consider two desirable properties: monotonicity and semantics preservation. We prove that our mapping is monotone and also prove that no monotone mapping, including ours, is semantic preserving. We realize that monotonicity is an obstacle for semantic preservation and thus present a non-monotone direct mapping that is semantics preserving.

The Semantic Web is the initiative of the W3C to make information on the Web readable not only by humans but also by machines. RDF is the data model for Semantic Web data, and SPARQL is the standard query language for this data model. In the last ten years, we have witnessed a constant growth in the amount of RDF data available on the Web, which have motivated the theoretical study of some fundamental aspects of SPARQL and the development of efficient mechanisms for implementing this query language.

In the traditional data exchange setting, source instances are restricted to be complete in the sense that every fact is either true or false in these instances. Although natural for a typical database translation scenario, this restriction is gradually becoming an impediment to the development of a wide range of applications that need to exchange objects that admit several interpretations. In particular, we are motivated by two specific applications that go beyond the usual data exchange scenario: exchanging incomplete information and exchanging knowledge bases.

In the paper, “semQA: SPARQL with Idempotent Disjunction”, the authors study the RDF query language SPARQL. In particular, they claim that some of the results presented in are not correct. In this note, we refute the claims made in, and actually show that some of the formal results of are incorrect.

It is known that the composition of schema mappings, each specified by source-to-target tgds (st-tgds), can be specified by a second-order tgd (SO tgd). We consider the question of what happens when target constraints are allowed. Specifically, we consider the question of specifying the composition of standard schema mappings (those specified by st-tgds, target egds, and a weakly-acyclic set of target tgds). We show that SO tgds, even with the assistance of arbitrary source constraints and target constraints, cannot specify in general the composition of two standard schema mappings. Therefore, we introduce source-to-target second-order dependencies (st-SO dependencies), which are similar to SO tgds, but allow equations in the conclusion. We show that st-SO dependencies (along with target egds and target tgds) are sufficient to express the composition of every finite sequence of standard schema mappings, and further, every st-SO dependency specifies such a composition. In addition to this expressive power, we show that st-SO dependencies enjoy other desirable properties. In particular, they have a polynomial-time chase that generates a universal solution. This universal solution can be used to find the certain answers to unions of conjunctive queries in polynomial time.

In the last few years, a lot of attention has been paid to the specification and subsequent manipulation of schema mappings, a problem which is of fundamental importance in metadata management. There have been many achievements in this area, and semantics have been defined for operators on schema mappings such as composition and inverse. However, little research has been pursued towards providing formal tools to compare schema mappings, in terms of their ability to transfer data and avoid storing redundant information, which has hampered the development of foundations for more complex operators as many of them involve these notions.

The class of unions of conjunctive queries (UCQ) has been shown to be particularly well-behaved for data exchange; its certain answers can be computed in polynomial time (in terms of data complexity). However, this is not the only class with this property; the certain answers to any Datalog program can also can be computed in polynomial time. The problem is that both UCQ and Datalog do not allow negated atoms, as adding an unrestricted form of negation to these languages yields to intractability.

The inversion of schema mappings has been identified as one of the fundamental operators for the development of a general framework for metadata management. In fact, during the last years three alternative notions of inversion for schema mappings have been proposed (Fagin-inverse [10], quasi-inverse [14] and maximum recovery [2]). However, the procedures that have been developed for computing these operators have some features that limit their practical applicability. First, these algorithms work in exponential time and produce inverse mappings of exponential size. Second, these algorithms express inverses in some mappings languages which include features that are difficult to use in practice. A typical example is the use of disjunction in the conclusion of the mapping rules, which makes the process of exchanging data much more complicated. In this paper, we propose solutions for the two problems mentioned above. First, we provide a polynomial time algorithm that computes the three inverse operators mentioned above given a mapping specified by a set of tuple-generating dependencies (tgds). This algorithm uses an output mapping language that can express these three operators in a compact way and, in fact, can compute inverses for a much larger class of mappings. Unfortunately, it has already been proved that this type of mapping languages has to include some features that are difficult to use in practice and, hence, this is also the case for our output mapping language. Thus, as our second contribution, we propose a new and natural notion of inversion that overcomes this limitation. In particular, every mapping specified by a set of tgds admits an inverse under this new notion that can be expressed in a mapping language that slightly extends tgds, and that has the same good properties for data exchange as tgds. Finally, as our last contribution, we provide an algorithm for computing such inverses.

A schema mapping is a specification that describes how data from a source schema is to be mapped to a target schema. Once the data has been transferred from the source to the target, a natural question is whether one can undo the process and recover the initial data, or at least part of it. In fact, it would be desirable to find a reverse schema mapping from target to source that specifies how to bring the exchanged data back. In this article, we introduce the notion of a recovery of a schema mapping: it is a reverse mapping, M′ for a mapping M, that recovers sound data with respect to M. We further introduce an order relation on recoveries. This allows us to choose mappings that recover the maximum amount of sound information. We call such mappings maximum recoveries. We study maximum recoveries in detail, providing a necessary and sufficient condition for their existence. In particular, we prove that maximum recoveries exist for the class of mappings specified by FO-to-CQ source-to-target dependencies. This class subsumes the class of source-to-target tuple-generating dependencies used in previous work on data exchange. For the class of mappings specified by FO-to-CQ dependencies, we provide an exponential-time algorithm for computing maximum recoveries, and a simplified version for full dependencies that works in quadratic time. We also characterize the language needed to express maximum recoveries, and we include a detailed comparison with the notion of inverse (and quasi-inverse) mapping previously proposed in the data exchange literature. In particular, we show that maximum recoveries strictly generalize inverses. We finally study the complexity of some decision problems related to the notions of recovery and maximum recovery.

SPARQL is the standard language for querying RDF data. In this article, we address systematically the formal study of the database aspects of SPARQL, concentrating in its graph pattern matching facility. We provide a compositional semantics for the core part of SPARQL, and study the complexity of the evaluation of several fragments of the language. Among other complexity results, we show that the evaluation of general SPARQL patterns is PSPACE-complete. We identify a large class of SPARQL patterns, defined by imposing a simple and natural syntactic restriction, where the query evaluation problem can be solved more efficiently. This restriction gives rise to the class of well-designed patterns. We show that the evaluation problem is coNP-complete for well-designed patterns. Moreover, we provide several rewriting rules for well-designed patterns whose application may have a considerable impact in the cost of evaluating SPARQL queries.

A schema mapping is a specification that describes how data from a source schema is to be mapped to a target schema. Once the data has been transferred from the source to the target, a natural question is whether one can undo the process and recover the initial data, or at least part of it. In fact, it would be desirable to find a reverse schema mapping from target to source that specifies how to bring the exchanged data back.In this paper, we introduce the notion of a recovery of a schema mapping: it is a reverse mapping M' for a mapping M that recovers sound data with respect to M. We further introduce an order relation on recoveries. This allows us to choose mappings that recover the maximum amount of sound information. We call such mappings maximum recoveries. We study maximum recoveries in detail, providing a necessary and sufficient condition for their existence. In particular, we prove that maximum recoveries exist for the class of mappings specified by FO-to-CQ source-to-target dependencies. This class subsumes the class of source-to-target tuple-generating dependencies used in previous work on data exchange. For the class of mappings specified by FO-to-CQ dependencies, we provide an exponential-time algorithm for computing maximum recoveries, and a simplified version for full dependencies that works in quadratic time. We also characterize the language needed to express maximum recoveries, and we include a detailed comparison with the notion of inverse (and quasi-inverse) mapping previously proposed in the data exchange literature. In particular, we show that maximum recoveries strictly generalize inverses. We study the complexity of some decision problems related to the notions of recovery and maximum recovery. Finally, we report our initial results about a relaxednotion of maximal recovery, showing that it strictly generalizes the notion of maximum recovery.

Data exchange is the problem of finding an instance of a target schema, given an instance of a source schema and a specification of the relationship between the source and the target. Theoretical foundations of data exchange have recently been investigated for relational data. In this article, we start looking into the basic properties of XML data exchange, that is, restructuring of XML documents that conform to a source DTD under a target DTD, and answering queries written over the target schema. We define XML data exchange settings in which source-to-target dependencies refer to the hierarchical structure of the data. Combining DTDs and dependencies makes some XML data exchange settings inconsistent. We investigate the consistency problem and determine its exact complexity. We then move to query answering, and prove a dichotomy theorem that classifies data exchange settings into those over which query answering is tractable, and those over which it is coNP-complete, depending on classes of regular expressions used in DTDs. Furthermore, for all tractable cases we give polynomial-time algorithms that compute target XML documents over which queries can be answered.

Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We provide new temporal logics for finite and infinite nested words, which are natural extensions of LTL, and prove that these logics are first-order expressively-complete. One of them is based on adding a "within" modality, evaluating a formula on a subword, to a logic CaRet previously studied in the context of verifying properties of recursive state machines (RSMs). The other logic, NWTL, is based on the notion of a summary path that uses both the linear and nesting structures. For NWTL we show that satisfiability is EXPTIME-complete, and that model-checking can be done in time polynomial in the size of the RSM model and exponential in the size of the NWTL formula (and is also EXPTIME-complete). Finally, we prove that first-order logic over nested words has the three-variable property, and we present a temporal logic for nested words which is complete for the two-variable fragment of first-order.

XML specifications often consist of a type definition (typically, a document type definition (DTD)) and a set of integrity constraints. It has been shown previously that such specifications can be inconsistent, and thus it is often desirable to check consistency at compile time. It is known [W. Fan and L. Libkin, J. ACM, 49 (2002), pp. 368–406] that for general keys, foreign keys, and DTDs the consistency problem is undecidable; however, it becomes NP-complete when all keys are one-attribute (unary) and tractable, if no foreign keys are used. In this paper, we consider a variety of previously studied constraints for XML data and investigate the complexity of the consistency problem. Our main conclusion is that, in the presence of foreign key constraints, compile-time verification of consistency is infeasible. We look at absolute constraints that hold in the entire document and relative constraints that hold only in a part of the document. For absolute constraints, we prove decidability and establish complexity bounds for primary multiattribute keys and unary foreign keys and study unary constraints that involve regular expressions. For relative constraints, we prove that even for unary constraints the consistency problem is undecidable. We also show that results continue to hold for extended DTDs, a more expressive typing mechanism for XML.

Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We provide new temporal logics for finite and infinite nested words, which are natural extensions of LTL, and prove that these logics are first-order expressively- complete. One of them is based on adding a "within" modality, evaluating a formula on a subword, to a logic CaRet previously studied in the context of verifying properties of recursive state machines. The other logic is based on the notion of a summary path that combines the linear and nesting structures. For that logic, both model-checking and satisfiability are shown to be EXPTIME-complete. Finally, we prove that first-order logic over nested words has the three-variable property, and we present a temporal logic for nested words which is complete for the two- variable fragment of first-order.

Data exchange is the problem of finding an instance of a target schema, given an instance of a source schema and a specification of the relationship between the source and the target. Theoretical foundations of data exchange have recently been investigated for relational data.In this paper, we start looking into the basic properties of XML data exchange, that is, restructuring of XML documents that conform to a source DTD under a target DTD, and answering queries written over the target schema. We define XML data exchange settings in which source-to-target dependencies refer to the hierarchical structure of the data. Combining DTDs and dependencies makes some XML data exchange settings inconsistent. We investigate the consistency problem and determine its exact complexity.We then move to query answering, and prove a dichotomy theorem that classifies data exchange settings into those over which query answering is tractable, and those over which it is coNP-complete, depending on classes of regular expressions used in DTDs. Furthermore, for all tractable cases we give polynomial-time algorithms that compute target XML documents over which queries can be answered.

Normalization as a way of producing good relational database designs is a well-understood topic. However, the same problem of distinguishing well-designed databases from poorly designed ones arises in other data models, in particular, XML. While, in the relational world, the criteria for being well designed are usually very intuitive and clear to state, they become more obscure when one moves to more complex data models.Our goal is to provide a set of tools for testing when a condition on a database design, specified by a normal form , corresponds to a good design. We use techniques of information theory, and define a measure of information content of elements in a database with respect to a set of constraints. We first test this measure in the relational context, providing information-theoretic justification for familiar normal forms such as BCNF, 4NF, PJ/NF, 5NFR, DK/NF. We then show that the same measure applies in the XML context, which gives us a characterization of a recently introduced XML normal form called XNF. Finally, we look at information-theoretic criteria for justifying normalization algorithms.

We discuss incremental validation of XML documents with respect to DTDs and XML schema definitions. We consider insertions and deletions of subtrees, as opposed to leaf nodes only, and we also consider the validation of ID and IDREF attributes. For arbitrary schemas, we give a worst-case n log n time and linear space algorithm, and show that it often is far superior to revalidation from scratch. We present two classes of schemas, which capture most real-life DTDs, and show that they admit a logarithmic time incremental validation algorithm that, in many cases, requires only constant auxiliary space. We then discuss an implementation of these algorithms that is independent of, and can be customized for different storage mechanisms for XML. Finally, we present extensive experimental results showing that our approach is highly efficient and scalable.

Data exchange is the problem of taking data structured under a source schema and creating an instance of a target schema. Given a source instance, there may be many solutions - target instances that satisfy the constraints of the data exchange problem. Previous work has identified two classes of desirable solutions: canonical universal solutions, and their cores. Query answering in data exchange amounts to rewriting a query over the target schema to another query that, over a materialized target instance, gives the result that is semantically consistent with the source. A basic question is then whether there exists a transformation sending a source instance into a solution over which target queries can be answered.We show that the answer is negative for many data exchange transformations that have structural properties similar to canonical universal solutions and cores. Namely, we prove that many such transformations preserve the local structure of the data. Using this notion, we further show that every target query rewritable over such a transformation cannot distinguish tuples whose neighborhoods in the source are similar. This gives us a first tool that helps check whether a query is rewritable, We also show that these results are robust: they hold for an extension of relational calculus with grouping and aggregates, and for two different semantics of query answering.

This article takes a first step towards the design and normalization theory for XML documents. We show that, like relational databases, XML documents may contain redundant information, and may be prone to update anomalies. Furthermore, such problems are caused by certain functional dependencies among paths in the document. Our goal is to find a way of converting an arbitrary DTD into a well-designed one, that avoids these problems. We first introduce the concept of a functional dependency for XML, and define its semantics via a relational representation of XML. We then define an XML normal form, XNF, that avoids update anomalies and redundancies. We study its properties, and show that XNF generalizes BCNF; we also discuss the relationship between XNF and normal forms for nested relations. Finally, we present a lossless algorithm for converting any DTD into one in XNF.

We consider the problem of mapping data in peer-to-peer systems. Such systems rely on simple value searches to locate data of interest. However, different peers may use different values to identify or describe the same data. To accommodate this, peer-to-peer systems often rely on mapping tables that list pairs of corresponding values for search domains that are used in different peers. We illustrate how such tables are used in the genomics community by expert curators. We then argue why mapping tables are appropriate for data mapping in a peer-to-peer environment and motivate the problem of managing these tables. The work presented is part of the Hyperion project.

Normalization as a way of producing good database designs is a well-understood topic. However, the same problem of distinguishing well-designed databases from poorly designed ones arises in other data models, in particular, XML. While in the relational world the criteria for being well-designed are usually very intuitive and clear to state, they become more obscure when one moves to more complex data models.Our goal is to provide a set of tools for testing when a condition on a database design, specified by a normal form, corresponds to a good design. We use techniques of information theory, and define a measure of information content of elements in a database with respect to a set of constraints. We first test this measure in the relational context, providing information-theoretic justification for familiar normal forms such as BCNF, 4NF, PJ/NF, 5NFR, DK/NF. We then show that the same measure applies in the XML context, which gives us a characterization of a recently introduced XML normal form called XNF. Finally, we look at information-theoretic criteria for justifying normalization algorithms.

We consider the problem of mapping data in peer-to-peer data-sharing systems. Such systems often rely on the use of mapping tables listing pairs of corresponding values to search for data residing in different peers. In this paper, we address semantic and algorithmic issues related to the use of mapping tables. We begin by arguing why mapping tables are appropriate for data mapping in a peer-to-peer environment. We discuss alternative semantics for these tables and we present a language that allows the user to specify mapping tables under different semantics. Then, we show that by treating mapping tables as constraints (called mapping constraints) on the exchange of information between peers it is possible to reason about them. We motivate why reasoning capabilities are needed to manage mapping tables and show the importance of inferring new mapping tables from existing ones. We study the complexity of this problem and we propose an efficient algorithm for its solution. Finally, we present an implementation along with experimental results that show that mapping tables may be managed efficiently in practice.

A relational database is inconsistent if it does not satisfy a given set of integrity constraints. Nevertheless, it is likely that most of the data in it is consistent with the constraints. In this paper we apply logic programming based on answer sets to the problem of retrieving consistent information from a possibly inconsistent database. Since consistent information persists from the original database to every of its minimal repairs, the approach is based on a specification of database repairs using disjunctive logic programs with exceptions, whose answer set semantics can be represented and computed by systems that implement stable model semantics. These programs allow us to declare persistence by default of data from the original instance to the repairs; and changes to restore consistency, by exceptions. We concentrate mainly on logic programs for binary integrity constraints, among which we find most of the integrity constraints found in practice.

XML specifications often consist of a type definition (typically, a DTD) and a set of integrity constraints. It has been shown previously that such specifications can be inconsistent, and thus it is often desirable to check consistency at compile-time. It is known that for general keys and foreign keys, and DTDs, the consistency problem is undecidable; however, it becomes NP-complete when all keys are one-attribute (unary), and tractable, if no foreign keys are used.In this paper, we consider a variety of constraints for XML data, and study the complexity of the consistency problem. Our main conclusion is that in the presence of foreign keys, compile-time verification of consistency is usually infeasible. We look at two types of constraints: absolute (that hold in the entire document), and relative (that only hold in a part of the document). For absolute constraints, we extend earlier decidability results to the case of multi-attribute keys and unary foreign keys, and to the case of constraints involving regular expressions, providing lower and upper bounds in both cases. For relative constraints, we show that even for unary constraints, the consistency problem is undecidable. We also establish a number of restricted decidable cases.

This paper takes a first step towards the design and normalization theory for XML documents. We show that, like relational databases, XML documents may contain redundant information, and may be prone to update anomalies. Furthermore, such problems are caused by certain functional dependencies among paths in the document. Our goal is to find a way of converting an arbitrary DTD into a well-designed one, that avoids these problems. We first introduce the concept of a functional dependency for XML, and define its semantics via a relational representation of XML. We then define an XML normal form, XNF, that avoids update anomalies and redundancies. We study its properties and show that it generalizes BCNF and a normal form for nested relations when those are appropriately coded as XML documents. Finally, we present a lossless algorithm for converting any DTD into one in XNF.

Databases may be inconsistent with respect to a given set of integrity constraints. Nevertheless, most of the data may be consistent. In this paper we show how to specify consistent data and how to query a relational database in such a way that only consistent data is retrieved. The specification and queries are based on disjunctive extended logic programs with positive and negative exceptions that generalize those previously introduced by Kowalski and Sadri. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper we consider the problem of the logical characterization of the notion of consistent answer in a relational database that may violate given integrity constraints.This notion is captured in terms of the possible repaired versions of the database.A rnethod for computing consistent answers is given and its soundness and completeness (for some classes of constraints and queries) proved.The method is based on an iterative procedure whose termination for several classes of constraints is proved as well.Permission to make digital or hard copies of all or part of this work 1'01 personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the fill1 citation on the iirst page.To copy otherwise, to republish, to post on servers or to redistribute to lists.rcquircs prior specific