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To answer database queries over incomplete data the gold standard is finding certain answers: those that are true regardless of how incomplete data is interpreted. Such answers can be found efficiently for conjunctive queries and their unions, even in the presence of constraints such as keys or functional dependencies. With negation added, the complexity of finding certain answers becomes intractable however.In this paper we exhibit a well-behaved class of queries that extends unions of conjunctive queries with a limited form of negation and that permits efficient computation of certain answers even in the presence of constraints by means of rewriting into Datalog with negation. The class consists of queries that are the closure of conjunctive queries under Boolean operations of union, intersection and difference. We show that for these queries, certain answers can be expressed in Datalog with negation, even in the presence of functional dependencies, thus making them tractable in data complexity. We show that in general Datalog cannot be replaced by first-order logic, but without constraints such a rewriting can be done in first-order.

The process of preparing potentially large and complex data sets for further analysis or manual examination is often called data wrangling. In classical warehousing environments, the steps in such a process are carried out using Extract-Transform-Load platforms, with significant manual involvement in specifying, configuring or tuning many of them. In typical big data applications, we need to ensure that all wrangling steps, including web extraction, selection, integration and cleaning, benefit from automation wherever possible. Towards this goal, in the paper we: (i) introduce a notion of data context, which associates portions of a target schema with extensional data of types that are commonly available; (ii) define a scalable methodology to bootstrap an end-to-end data wrangling process based on data profiling; (iii) describe how data context is used to inform automation in several steps within wrangling, specifically, matching, value format transformation, data repair, and mapping generation and selection to optimise the accuracy, consistency and relevance of the result; and (iv) we evaluate the approach with real estate data and financial data, showing substantial improvements in the results of automated wrangling.

International audience; As graph databases become widespread, JTC1 -- the committee in joint charge of information technology standards for the International Organization for Standardization (ISO), and International Electrotechnical Commission (IEC) -- has approved a project to create GQL, a standard property graph query language. This complements a project to extend SQL with a new part, SQL/PGQ, which specifies how to define graph views over an SQL tabular schema, and to run read-only queries against them. Both projects have been assigned to the ISO/IEC JTC1 SC32 working group for Database Languages, WG3, which continues to maintain and enhance SQL as a whole. This common responsibility helps enforce a policy that the identical core of both PGQ and GQL is a graph pattern matching sub-language, here termed GPML. The WG3 design process is also analyzed by an academic working group, part of the Linked Data Benchmark Council (LDBC), whose task is to produce a formal semantics of these graph data languages, which complements their standard specifications. This paper, written by members of WG3 and LDBC, presents the key elements of the GPML of SQL/PGQ and GQL in advance of the publication of these new standards.

International audience; One of the most common scenarios of handling incomplete information occurs in relational databases. They describe in-complete knowledge with three truth values, using Kleene’s logic for propositional formulae and a rather peculiar exten-sion to predicate calculus. This design by a committee from several decades ago is now part of the standard adopted by vendors of database management systems. But is it really the right way to handle incompleteness in propositional and pred-icate logics?Our goal is to answer this question. Using an epistemic ap-proach, we first characterize possible levels of partial knowl-edge about propositions, which leads to six truth values. We impose rationality conditions on the semantics of the connec-tives of the propositional logic, and prove that Kleene’s logic is the maximal sublogic to which the standard optimization rules apply, thereby justifying this design choice. For exten-sions to predicate logic, however, we show that the additional truth values are not necessary: every many-valued extension of first-order logic over databases with incomplete informa-tion represented by null values is no more powerful than the usual two-valued logic with the standard Boolean interpreta-tion of the connectives. We use this observation to analyze the logic underlying SQL query evaluation, and conclude that the many-valued extension for handling incompleteness does not add any expressiveness to it.

This paper provides precise mathematical definitions of a property graph as specified in the proposed GQL international standard, which is an attributed mixed multigraph with loops. It further defines a partially-oriented walk in such a property graph, which is called a path in GQL, as well as restricted classes of such walks (trails, simple/acyclic paths).

The paper describes the present and the future of graph updates in Cypher, the language of the Neo4j property graph database and several other products. Update features include those with clear analogs in relational databases, as well as those that do not correspond to any relational operators. Moreover, unlike SQL, Cypher updates can be arbitrarily intertwined with querying clauses. After presenting the current state of update features, we point out their shortcomings, most notably violations of atomicity and non-deterministic behavior of updates. These have not been previously known in the Cypher community. We then describe the industry-academia collaboration on designing a revised set of Cypher update operations. Based on discovered shortcomings of update features, a number of possible solutions were devised. They were presented to key Cypher users, who were given the opportunity to comment on how update features are used in real life, and on their preferences for proposed fixes. As the result of the consultation, a new set of update operations for Cypher were designed. Those led to a streamlined syntax, and eliminated the unexpected and problematic behavior that original Cypher updates exhibited.

International audience; We report on a community effort between industry and academia to shape the future of property graph constraints. The standardization for a property graph query language is currently underway through the ISO Graph Query Language (GQL) project. Our position is that this project should pay close attention to schemas and constraints, and should focus next on key constraints. The main purposes of keys are enforcing data integrity and allowing the referencing and identifying of objects. Motivated by use cases from our industry partners, we argue that key constraints should be able to have different modes, which are combinations of basic restriction that require the key to be exclusive, mandatory, and singleton. Moreover, keys should be applicable to nodes, edges, and properties since these all can represent valid real-life entities. Our result is PG-Keys, a flexible and powerful framework for defining key constraints, which fulfills the above goals. PG-Keys is a design by the Linked Data Benchmark Council's Property Graph Schema Working Group, consisting of members from industry, academia, and ISO GQL standards group, intending to bring the best of all worlds to property graph practitioners. PG-Keys aims to guide the evolution of the standardization efforts towards making systems more useful, powerful, and expressive. CCS CONCEPTS • Information systems → Integrity checking; • Theory of computation → Data modeling; Database constraints theory.

International audience; Answering queries over incomplete data is based on finding answers that are certainly true, independently of how missing values are interpreted. This informal description has given rise to several different mathematical definitions of certainty. To unify them, a framework based on "explanations", or extra information about incomplete data, was recently proposed. It partly succeeded in justifying query answering methods for relational databases under set semantics, but had two major limitations. First, it was firmly tied to the set data model, and a fixed way of comparing incomplete databases with respect to their information content. These assumptions fail for reallife database queries in languages such as SQL that use bag semantics instead. Second, it was restricted to queries that only manipulate data, while in practice most analytical SQL queries invent new values, typically via arithmetic operations and aggregation. To leverage our understanding of the notion of certainty for queries in SQL-like languages, we consider incomplete databases whose information content may be enriched by additional knowledge. The knowledge order among them is derived from their semantics, rather than being fixed a priori. The resulting framework allows us to capture and justify existing notions of certainty, and extend these concepts to other data models and query languages. As natural applications, we provide for the first time a well-founded definition of certain answers for the relational bag data model and for valueinventing queries on incomplete databases, addressing the key shortcomings of previous approaches.

International audience; Handling incomplete data in a correct manner is a notoriously hard problem in databases. Theoretical approaches rely on the computationally hard notion of certain answers, while practical solutions rely on ad hoc query evaluation techniques based on threevalued logic. Can we find a middle ground, and produce correct answers efficiently? The paper surveys results of the last few years motivated by this question. We reexamine the notion of certainty itself, and show that it is much more varied than previously thought. We identify cases when certain answers can be computed efficiently and, short of that, provide deterministic and probabilistic approximation schemes for them. We look at the role of three-valued logic as used in SQL query evaluation, and discuss the correctness of the choice, as well as the necessity of such a logic for producing query answers.

International audience; The standard notion of query answering over incomplete database is that of certain answers, guaranteeing correctness regardless of how incomplete data is interpreted. In majority of real-life databases,relations have numerical columns and queries use arithmetic and comparisons. Even though the notion of certain answers still applies,we explain that it becomes much more problematic in situations when missing data occurs in numerical columns. We propose a new general framework that allows us to assign a measure of certainty to query answers. We test it in the agnostic scenario where we do not have prior information about values of numerical attributes, similarly to the predominant approach in handling incomplete data which assumes that each null can be interpreted as an arbitrary value of the domain. The key technical challenge is the lack of a uniform distribution over the entire domain of numerical attributes, such as real numbers. We overcome this by associating the measure of certainty with the asymptotic behaviorof volumes of some subsets of the Euclidean space. We show that this measure is well-defined, and describe approaches to computing and approximating it. While it can be computationally hard, or result in an irrational number, even for simple constraints, we produce polynomial-time randomized approximation schemes with multiplicative guarantees for conjunctive queries, and with additive guarantees for arbitrary first-order queries. We also describe a set of experimental results to confirm the feasibility of this approach.

International audience; In a variety of reasoning tasks, one estimates the likelihood of events by means of volumes of sets they define. Such sets need to be measurable, which is usually achieved by putting bounds, sometimes ad hoc, on them. We address the question how unbounded or unmeasurable sets can be measured nonetheless. Intuitively, we want to know how likely a randomly chosen point is to be in a given set, even in the absence of a uniform distribution over the entire space. To address this, we follow a recently proposed approach of taking intersection of a set with balls of increasing radius, and defining the measure by means of the asymptotic behavior of the proportion of such balls taken by the set. We show that this approach works for every set definable in first-order logic with the usual arithmetic over the reals (addition, multiplication, exponentiation, etc.), and every uniform measure over the space, of which the usual Lebesgue measure (area, volume, etc.) is an example. In fact we establish a correspondence between the good asymptotic behavior and the finiteness of the VC dimension of definable families of sets. Towards computing the measure thus defined, we show how to avoid the asymptotics and characterize it via a specific subset of the unit sphere. Using definability of this set, and known techniques for sampling from the unit sphere, we give two algorithms for estimating our measure of unbounded unmeasurable sets, with deterministic and probabilistic guarantees, the latter being more efficient. Finally we show that a discrete analog of this measure exists and is similarly well-behaved.

Multiple issues with SQL's handling of nulls have been well documented. Having efficiency as its main goal, SQL disregards the standard notion of correctness on incomplete databases -- certain answers -- due to its high complexity. As a result, the evaluation of SQL queries on databases with nulls may produce answers that are just plain wrong. However, SQL evaluation can be modified, at least for relational algebra queries, to approximate certain answers, i.e., return only correct answers. We examine recently proposed approximation schemes for certain answers and analyze their complexity, both theoretical bounds and real-life behavior

Our goal is to measure the likelihood of the satisfaction of numerical constraints in the absence of any prior information. Intuitively, the likelihood of x>y is 0.5, if we know nothing about x and y. We study expressive constraints, involving arithmetic and complex numerical functions, and even quantification over numbers. Such problems arise in processing incomplete data, or estimating the likelihood of conditions in programs without a priori bounds on variables.We show that for constraints on n variables, the proper way to define such a measure is as the limit of the part of the n-dimensional ball that consists of points satisfying the constraints, when the radius of the ball increases. We prove that the existence of such a limit is closely related to the notion of o-minimality from model theory. For example, for constraints definable with the usual arithmetic and exponentiation, the likelihood is well defined, but adding trigonometric functions is problematic. We then look at computing and approximating such likelihoods for order and linear constraints. We prove an impossibility result for approximating with multiplicative error, even for order constraints. However, as the likelihood is a number between 0 and 1, an approximation scheme with additive error is acceptable, and we give such a scheme for arbitrary linear constraints.

One of the most common scenarios of handling incomplete information occurs in relational databases. They describe incomplete knowledge with three truth values, using Kleene's logic for propositional formulae and a rather peculiar extension to predicate calculus. This design by a committee from several decades ago is now part of the standard adopted by vendors of database management systems. But is it really the right way to handle incompleteness in propositional and predicate logics? Our goal is to answer this question. Using an epistemic approach, we first characterize possible levels of partial knowledge about propositions, which leads to six truth values. We impose rationality conditions on the semantics of the connectives of the propositional logic, and prove that Kleene's logic is the maximal sublogic to which the standard optimization rules apply, thereby justifying this design choice. For extensions to predicate logic, however, we show that the additional truth values are not necessary: every many-valued extension of first-order logic over databases with incomplete information represented by null values is no more powerful than the usual two-valued logic with the standard Boolean interpretation of the connectives. We use this observation to analyze the logic underlying SQL query evaluation, and conclude that the many-valued extension for handling incompleteness does not add any expressiveness to it.

International audience; While all relational database systems are based on the bag data model, much of theoretical research still views relations as sets. Recent attempts to provide theoretical foundations for modern data management problems under the bag semantics concentrated on applications that need to deal with incomplete relations, i.e., relations populated by constants and nulls. Our goal is to provide a complete characterization of the complexity of query answering over such relations in fragments of bag relational algebra. The main challenges that we face are twofold. First, bag relational algebra has more operations than its set analog (e.g., additive union, max-union, min-intersection, duplicate elimination) and the relationship between various fragments is not fully known. Thus we first fill this gap. Second, we look at query answering over incomplete data, which again is more complex than in the set case: rather than certainty and possibility of answers, we now have numerical information about occurrences of tuples. We then fully classify the complexity of finding this information in all the fragments of bag relational algebra.

International audience; The Cypher property graph query language is an evolving language, originally designed and implemented as part of the Neo4j graph database, and it is currently used by several commercial database products and researchers. We describe Cypher 9, which is the first version of the language governed by the openCypher Implementers Group. We first introduce the language by example, and describe its uses in industry. We then provide a formal semantic definition of the core read-query features of Cypher, including its variant of the property graph data model, and its " ASCII Art " graph pattern matching mechanism for expressing subgraphs of interest to an application. We compare the features of Cypher to other property graph query languages, and describe extensions, at an advanced stage of development, which will form part of Cypher 10, turning the language into a compositional language which supports graph projections and multiple named graphs.

Query answering over incomplete data invariably relies on the standard notion of certain answers which gives a very coarse classification of query answers into those that are certain and those that are not. Here we propose to refine it by measuring how close an answer is certainty. This measure is defined as the probability that the query is true under a random interpretation of missing information in a database. Since there are infinitely many such interpretations, to pick one at random we adopt the approach used in the study of asymptotic properties and 0-1 laws for logical sentences, and define the measure as the limit of a sequence. We show that in the standard model of missing data, the 0-1 law is observed: this limit always exists and can be only 0 or 1 for a very large class of queries. Thus, query answers are either almost certainly true, or almost certainly false. We prove that almost certainly true answers are precisely those returned by the naive evaluation of the query. When databases satisfy constraints, the measure is defined as the conditional probability of the query being true if the constraints are true. This too is defined as a limit, and we prove that it always exists, can be an arbitrary rational number, and is computable. For some constraints, such as functional dependencies, the 0-1 law continues to hold. As another refinement of the notion of certainty, we introduce a comparison of query answers: an answer with a larger set of interpretations that make it true is better. We identify the precise complexity of such comparisons, and of finding sets of best answers, for first-order queries.

Navigational queries over RDF data are viewed as one of the main applications of graph query languages, and yet the standard model of graph databases—essentially labeled graphs—is different from the triples-based model of RDF. While encodings of RDF databases into graph data exist, we show that even the most natural ones are bound to lose some functionality when used in conjunction with graph query languages. The solution is to work directly with triples, but then many properties taken for granted in the graph database context (e.g., reachability) lose their natural meaning. Our goal is to introduce languages that work directly over triples and are closed, i.e., they produce sets of triples, rather than graphs. Our basic language is called TriAL, or Triple Algebra: it guarantees closure properties by replacing the product with a family of join operations. We extend TriAL with recursion and explain why such an extension is more intricate for triples than for graphs. We present a declarative language, namely a fragment of datalog, capturing the recursive algebra. For both languages, the combined complexity of query evaluation is given by low-degree polynomials. We compare our language with previously studied graph query languages such as adaptations of XPath, regular path queries, and nested regular expressions; many of these languages are subsumed by the recursive triple algebra. We also provide an implementation of recursive TriAL on top of a relational query engine, and we show its usefulness by running a wide array of navigational queries over real-world RDF data, while at the same time testing how our implementation compares to existing RDF systems.

The process of preparing potentially large and complex data sets for further analysis or manual examination is often called data wrangling. In classical warehousing environments, the steps in such a process have been carriedout using Extract-Transform-Load platforms, with significant manual involvement in specifying, configuring or tuning many of them. Cost-effective data wrangling processes need to ensure that data wrangling steps benefit from automation wherever possible. In this paper, we define a methodology to fullyautomate an end-to-end data wrangling process incorporating data context, which associates portions of a target schema with potentially spurious extensional data of types that are commonly available. Instance-based evidence together with data profiling paves the way to inform automation in several stepswithin the wrangling process, specifically, matching, mapping validation, value format transformation, and data repair. The approach is evaluated with real estate data showing substantial improvements in the results of automated wrangling.

Consistent query answering (CQA) aims to find meaningful answers to queries when databases are inconsistent, i.e., do not conform to their specifications. Such answers must be certainly true in all repairs, which are consistent databases whose difference from the inconsistent one is minimal, according to some measure. This task is often computationally intractable, and much of CQA research concentrated on finding islands of tractability. Nevertheless, there are many relevant queries for which no efficient solutions exist, which is reflected by the limited practical applicability of the CQA approach. To remedy this, one needs to devise a new CQA framework that provides explicit guarantees on the quality of query answers. However, the standard notions of repair and certain answers are too coarse to permit more elaborate schemes of query answering. Our goal is to provide a new framework for CQA based on revised definitions of repairs and query answering that opens up the possibility of efficient approximate query answering with explicit guarantees. The key idea is to replace the current declarative definition of a repair with an operational one, which explains how a repair is constructed, and how likely it is that a consistent instance is a repair. This allows us to define how certain we are that a tuple should be in the answer. Using this approach, we study the complexity of both exact and approximate CQA. Even though some of the problems remain hard, for many common classes of constraints we can provide meaningful answers in reasonable time, for queries going far beyond the standard CQA approach.

Theoretical models used in database research often have subtle differences with those occurring in practice. One particular mismatch that is usually neglected concerns the use of marked nulls to represent missing values in theoretical models of incompleteness, while in an SQL database these are all denoted by the same syntactic NULL object. It is commonly argued that results obtained in the model with marked nulls carry over to SQL, because SQL nulls can be interpreted as Codd nulls, which are simply marked nulls that do not repeat. This argument, however, does not take into account that even simple queries may produce answers where distinct occurrences of NULL do in fact denote the same unknown value. For such queries, interpreting SQL nulls as Codd nulls would incorrectly change the semantics of query answers. To use results about Codd nulls for real-life SQL queries, we need to understand which queries preserve the Codd interpretation of SQL nulls. We show, however, that the class of relational algebra queries preserving Codd interpretation is not recursively enumerable, which necessitates looking for sufficient conditions for such preservation. Those can be obtained by exploiting the information provided by NOT NULL constraints on the database schema. We devise mild syntactic restrictions on queries that guarantee preservation, do not limit the full expressiveness of queries on databases without nulls, and can be checked efficiently.

Data wrangling, the multi-faceted process by which the data required by an application is identified, extracted, cleaned and integrated, is often cumbersome and labor intensive. In this paper, we present an architecture that supports a complete data wrangling lifecycle, orchestrates components dynamically, builds on automation wherever possible, is informed by whatever data is available, refines automatically produced results in the light of feedback, takes into account the user’s priorities, and supports data scientists with diverse skill sets. The architecture is demonstrated in practice for wrangling property sales and open government data.

International audience; Schema mappings are a fundamental concept in data integration and exchange, and they have been thoroughly studied in different data models. For graph data, however, map-pings have been studied in a restricted context that, unlike real-life graph databases, completely disregards the data they store. Our main goal is to understand query answering under graph schema mappings – in particular, in exchange and integration of graph data – for graph databases that mix graph structure with data. We show that adding data querying alters the picture in a significant way. As the model, we use data graphs: a theoretical abstraction of property graphs employed by graph database implementations. We start by showing a very strong negative result: using the simplest form of nontrivial navigation in map-pings makes answering even simple queries that mix navigation and data undecidable. This result suggests that for the purposes of integration and exchange, schema mappings ought to exclude recursively defined navigation over target data. For such mappings and analogs of regular path queries that take data into account, query answering becomes de-cidable, although intractable. To restore tractability without imposing further restrictions on queries, we propose a new approach based on the use of null values that resemble usual nulls of relational DBMSs, as opposed to marked nulls one typically uses in integration and exchange tasks. If one moves away from path queries and considers more complex patterns, query answering becomes undecidable again, even for the simplest possible mappings.

Multiple issues with SQL’s handling of nulls have been well documented. Having efficiency as its key goal, evaluation of SQL queries disregards the standard notion of correctness on incomplete databases – certain answers – due to its high complexity. As a result, it may produce answers that are just plain wrong. It was recently shown that SQL evaluation can be modified, at least for first-order queries, to return only correct answers. But while these modifications came with good theoretical complexity bounds, they have not been tested in practice. The goals of this proof-of-concept paper are to understand whether wrong answers can be produced by SQL queries in real-world scenarios, and whether proposed techniques for avoiding them can be made practically feasible. We use the TPC-H benchmark, and show that for some typical queries involving negation, wrong answers are very common. On the other hand, existing solutions for fixing the problem do not work in practice at all. By analyzing the reasons for this, we come up with a new modified way of rewriting SQL queries that restores correctness. We conduct experiments which show the feasibility of our solution: the small price tag it imposes can be often tolerated to ensure correct results, and we do not miss correct answers that the usual SQL evaluation produces. The overall conclusion is that correct evaluation can be realistically achieved in the presence of nulls, at least for the SQL fragment that corresponds to first-order queries.

Graph databases have received much attention as of late due to numerous applications in which data is naturally viewed as a graph; these include social networks, RDF and the Semantic Web, biological databases, and many others. There are many proposals for query languages for graph databases that mainly fall into two categories. One views graphs as a particular kind of relational data and uses traditional relational mechanisms for querying. The other concentrates on querying the topology of the graph. These approaches, however, lack the ability to combine data and topology, which would allow queries asking how data changes along paths and patterns enveloping it. In this article, we present a comprehensive study of languages that enable such combination of data and topology querying. These languages come in two flavors. The first follows the standard approach of path queries, which specify how labels of edges change along a path, but now we extend them with ways of specifying how both labels and data change. From the complexity point of view, the right type of formalisms are subclasses of register automata. These, however, are not well suited for querying. To overcome this, we develop several types of extended regular expressions to specify paths with data and study their querying power and complexity. The second approach adopts the popular XML language XPath and extends it from XML documents to graphs. Depending on the exact set of allowed features, we have a family of languages, and our study shows that it includes efficient and highly expressive formalisms for querying both the structure of the data and the data itself.

Our goal is to show that the standard model-theoretic concept of types can be applied in the study of order-invariant properties, i.e., properties definable in a logic in the presence of an auxiliary order relation, but not actually dependent on that order relation. This is somewhat surprising since order-invariant properties are more of a combinatorial rather than a logical object. We provide two applications of this notion. One is a proof, from the basic principles, of a theorem by Courcelle stating that over trees, order-invariant MSO properties are expressible in MSO with counting quantifiers. The other is an analog of the Feferman-Vaught theorem for order-invariant properties.

Querying incomplete data usually amounts to finding answers we are certain about. Standard approaches concentrate on positive information about query answers, and miss negative knowledge, which can be useful for two reasons. First, sometimes it is the only type of knowledge one can infer with certainty, and second, it may help one find good and efficient approximations of positive certain answers. Our goal is to consider a framework for defining both positive and negative certain knowledge about query answers and to show two applications of it. First, we demonstrate that it naturally leads to a way of representing certain information that has hitherto not been used in querying incomplete databases. Second, we show that approximations of such certain information can be computed efficiently for all first-order queries over relational databases.

Data exchange deals with translating data structured in some source format into data structured in some target format, given a specification of the relationship between the source and the target and possibly constraints on the target; and answering queries over the target in a way that is semantically consistent with the information in the source. Theoretical foundations of data exchange have been actively explored recently. It was also noticed that the standard semantics for query answering in data exchange may lead to counterintuitive or anomalous answers. In the present article, we explain that this behavior is due to the fact that solutions can contain invented information (information that is not related to the source instance), and that the presence of incomplete information in target instances has been ignored. In particular, proper query evaluation techniques for databases with nulls have not been used, and the distinction between closed and open world semantics has not been made. We present a concept of solutions, called CWA-solutions, that is based on the closed world assumption. For data exchange settings without constraints on the target, the space of CWA-solutions has two extreme points: the canonical universal solution (the maximal CWA-solution) and the core of the universal solutions (the minimal CWA-solution), both of them well studied in data exchange. In the presence of constraints on the target, the core of the universal solutions is still the minimal CWA-solution, but there may be no unique maximal CWA-solution. We show how to define the semantics of query-answering taking into account incomplete information, and show that some of the well-known anomalies go away with the new semantics. The article also contains results on the complexity of query-answering, upper approximations to queries (maybe-answers), and various extensions.

We deal with the problem of deciding whether a given set of string patterns implies the presence of a fixed pattern. While checking whether a set of patterns occurs in a string is solvable in polynomial time, this implication problem is well known to be intractable. Here we consider a version of the problem when patterns in the set are required to be disjoint. We show that for such a version of the problem the situation is reversed: checking whether a set of patterns occurs in a string is NP-complete, but the implication problem is solvable in polynomial time. (C) 2009 Elsevier B.V. All rights reserved.

Locality notions in logic say that the truth value of a formula can be determined locally, by looking at the isomorphism type of a small neighbourhood of its free variables. Such notions have proved to be useful in many applications. They all, however, refer to isomorphisms of neighbourhoods, which most local logics cannot test. A stronger notion of locality says that the truth value of a formula is determined by what the logic itself can say about that small neighbourhood. Since the expressiveness of many logics can be characterized by games, one can also say that the truth value of a formula is determined by the type, with respect to a game, of that small neighbourhood. Such game-based notions of locality can often be applied when traditional isomorphism-based notions of locality cannot.Our goal is to study game-based notions of locality. We work with an abstract view of games that subsumes games for many logics. We look at three, progressively more complicated locality notions. The easiest requires only very mild conditions on the game and works for most logics of interest. The other notions, based on Hanf’s and Gaifman’s theorems, require more restrictions. We state those restrictions and give examples of logics that satisfy and fail the respective game-based notions of locality.

International audience; We study logics expressing properties of paths in graphs that are tailored to querying graph databases: a data model for new applications such as social networks, the Semantic Web, biological data, crime detection, and others. The basic construct of such logics, a regular path query, checks for paths whose labels belong to a regular language. These logics fail to capture two commonly needed features: counting properties, and the ability to compare paths. It is known that regular path-comparison relations (e.g., prefix or equality) can be added without significant complexity overhead; however, adding common relations often demanded by applications (e.g., subword, subsequence, suffix) results in either undecidability or astronomical complexity. We propose, as a way around this problem, to use automata with counting functionalities, namely Parikh automata. They express many counting properties directly, and they approximate many relations of interest. We prove that with Parikh automata defining both languages and relations used in queries, we retain the low complexity of the standard path logics for graphs. In particular, this gives us efficient approximations to queries with prohibitively high complexity. We extend the best known decidability results by showing that even more expressive classes of relations are possible in query languages (sometimes with restriction on the shape of formulae). We also show that Parikh automata admit two convenient representations by analogs of regular expressions, making them usable in real-life querying.

In this paper we define and study regular expressions for data words. We first define regular expressions with memory (REM), which extend standard regular expressions with limited memory and show that they capture the class of data words defined by register automata. We also study the complexity of the standard decision problems for REM, which turn out to be the same as for register automata. In order to lower the complexity of main reasoning tasks, we then look at two natural subclasses of REM that can define many properties of interest in the applications of data words: regular expressions with binding (REWB) and regular expressions with equality (REWE). We study their expressive power and analyse the complexity of their standard decision problems. We also establish the following strict hierarchy of expressive power: REM is strictly stronger than REWB, and in turn REWB is strictly stronger than REWE. Several classes of regular expressions for defining data word languages are introduced.We show what is needed to capture the notion of regularity over data words.We give a detailed overview of closure properties for introduced classes.We study the complexity of main reasoning tasks for introduced classes.

We study the problem of maintaining recursively defined views, such as the transitive closure of a relation, in traditional relational languages that do not have recursion mechanisms. The main results of this paper are negative ones: we show that a certain property of query languages implies impossibility of such incremental maintenance. The property we use is locality of queries, which is known to hold for relational calculus and various extensions, including those with grouping and aggregate constructs (essentially, plain SQL).

It is a folk result in database theory that SQL cannot express recursive queries such as reachability; in fact, a new construct was added to SQL3 to overcome this limitation. However, the evidence for this claim is usually given in the form of a reference to a proof that relational algebra cannot express such queries. SQL, on the other hand, in all its implementations has three features that fundamentally distinguish it from relational algebra: namely, grouping, arithmetic operations, and aggregation.In the past few years, most questions about the additional power provided by these features have been answered. This paper surveys those results, and presents new simple and self-contained proofs of the main results on the expressive power of SQL. Somewhat surprisingly, tiny differences in the language definition affect the results in a dramatic way: under some very natural assumptions, it can be proved that SQL cannot define recursive queries, no matter what aggregate functions and arithmetic operations are allowed. But relaxing these assumptions just a tiny bit makes the problem of proving expressivity bounds for SQL as hard as some long-standing open problems in complexity theory.

We investigate the problem of how to extend constraint query languages with aggregate operators. We deal with standard relational aggregation, and also with aggregates specific to spatial data, such as volume. We study several approaches, including the addition of a new class of approximate aggregate operators which allow an error tolerance in the computation. We show how techniques of M. Karpinski and A. Macintyre (in “Structures in Logic and Computer Science: A Selection of Essays in Honor of A. Ehrenfeucht,” Springer Lecture Notes on Computer Science 1261, pp. 162–173, Springer-Verlag, Berlin, 1997) and P. Koiran (in “FOCS '95,” pp. 134–141) based on VC-dimension can be used to give languages with approximation operators, but also show that these languages have a number of shortcomings. We then give a set of results showing that it is impossible to get constraint-based languages that admit definable aggregation operators, both for exact operators and for approximate ones. These results are quite robust, in that they show that closure under aggregation is problematic even when the class of functions permitted in constraints is expanded. This motivates a different approach to the aggregation problem. We introduce a language FO+Poly+Sum, which permits standard discrete aggregation operators to be applied to the outputs of range-restricted constraint queries. We show that this language has a number of attractive closure and expressivity properties, and that it can compute volumes of linear-constraint databases.

Previous studies of incomplete XML documents have identified three main sources of incompleteness --- in structural information, data values, and labeling --- and addressed data complexity of answering analogs of unions of conjunctive queries under the open world assumption. It is known that structural incompleteness leads to intractability, while incompleteness in data values and labeling still permits efficient computation of certain answers. The goal of this paper is to provide a detailed picture of the complexity of query answering over incomplete XML documents. We look at more expressive languages, at other semantic assumptions, and at both data and combined complexity of query answering, to see whether some well-behaving tractable classes have been missed. To incorporate non-positive features into query languages, we look at a gentle way of introducing negation via Boolean combinations of existential positive queries, as well as the analog of relational calculus. We also look at the closed world assumption which, due to the hierarchical structure of XML, has two variations. For all combinations of languages and semantics of incompleteness we determine data and combined complexity of computing certain answers. We show that structural incompleteness leads to intractability under all assumptions, while by dropping it we can recover efficient evaluation algorithms for some queries that go beyond those previously studied. In the process, we also establish a new result about relational query answering over incomplete databases, showing that for Boolean combinations of conjunctive queries, certain answers can be found in polynomial time.

International audience; A common theme in the study of logics over finite structures is adding auxiliary predicates to enhance expressiveness and convey additional information. Examples include adding an order or arithmetic for capturing complexity classes, or the power of real-life declarative languages. A recent trend is to add a data-value comparison relation to words, trees, and graphs, for capturing modern data models such as XML and graph databases. Such additions often result in the loss of good properties of the underlying logic. Our goal is to show that such a loss can be avoided if we use pattern-based logics, standard in XML and graph data querying. The essence of such logics is that auxiliary relations are tested locally with respect to other relations in the structure. These logics are shown to admit strong versions of Hanf and Gaifman locality theorems, which are used to prove a homomorphism preservation theorem, and a decidability result for the satisfiability problem. We discuss applications of these results to pattern logics over data forests, and consequently to querying XML data.

Incomplete data is ubiquitous: the more data we accumulate and the more widespread tools for integrating and exchanging data become, the more instances of incompleteness we have. And yet the subject is poorly handled by both practice and theory. Many queries for which students get full marks in their undergraduate courses will not work correctly in the presence of incomplete data, but these ways of evaluating queries are cast in stone -- SQL standard. We have many theoretical results on handling incomplete data but they are, by and large, about showing high complexity bounds, and thus are often dismissed by practitioners. Even worse, we have a basic theoretical notion of what it means to answer queries over incomplete data, and yet this is not at all what practical systems do.Is there a way out of this predicament? Can we have a theory of incompleteness that will appeal to theoreticians and practitioners alike, by explaining incompleteness and being at the same time implementable and useful for applications? After giving a critique of both the practice and the theory of handling incompleteness in databases, the paper outlines a possible way out of this crisis. The key idea is to combine three hitherto used approaches to incompleteness: one based on certain answers and representation systems, one based on viewing incomplete databases as logical theories, and one based on orderings expressing relative value of information.

International audience; While the theory of languages of words is very mature, our understanding of relations on words is still lagging behind. And yet such relations appear in many new applications such as verification of parameterized systems, querying graph-structured data, and information extraction, for instance. Classes of well-behaved relations typically used in such applications are obtained by adapting some of the equivalent definitions of regularity of words for relations, leading to non-equivalent notions of recognizable, regular, and rational relations. The goal of this paper is to propose a systematic way of defining classes of relations on words, of which these three classes are just natural examples, and to demonstrate its advantages compared to some of the standard techniques for studying word relations. The key idea is that of a synchronization of a pair of words, which is a word over an extended alphabet. Using it, we define classes of relations via classes of regular languages over a fixed alphabet, just {1, 2} for binary relations. We characterize some of the standard classes of relations on words via finiteness of parameters of synchronization languages, called shift, lag, and shiftlag. We describe these conditions in terms of the structure of cycles of graphs underlying automata, thereby showing their decidability. We show that for these classes there exist canonical synchronization languages, and every class of relations can be effectively re-synchronized using those canonical representatives. We also give sufficient conditions on synchronization languages, defined in terms of injectivity and surjectivity of their Parikh images, that guarantee closure under intersection and complement of the classes of relations they define.

Graph data appears in a variety of application domains, and many uses of it, such as querying, matching, and transforming data, naturally result in incompletely specified graph data, that is, graph patterns. While queries need to be posed against such data, techniques for querying patterns are generally lacking, and properties of such queries are not well understood. Our goal is to study the basics of querying graph patterns. The key features of patterns we consider here are node and label variables and edges specified by regular expressions. We provide a classification of patterns, and study standard graph queries on graph patterns. We give precise characterizations of both data and combined complexity for each class of patterns. If complexity is high, we do further analysis of features that lead to intractability, as well as lower-complexity restrictions. Since our patterns are based on regular expressions, query answering for them can be captured by a new automata model. These automata have two modes of acceptance: one captures queries returning nodes, and the other queries returning paths. We study properties of such automata, and the key computational tasks associated with them. Finally, we provide additional restrictions for tractability, and show that some intractable cases can be naturally cast as instances of constraint satisfaction problems.

Relational schema mappings have been extensively studied in connection with data integration and exchange problems, but mappings between XML schemas have not received the same amount of attention. Our goal is to develop a theory of expressive XML schema mappings. Such mappings should be able to use various forms of navigation in a document, and specify conditions on data values. We develop a language for XML schema mappings, and study both data exchange with such mappings and metadata management problems. Specifically, we concentrate on four types of problems: complexity of mappings, query answering, consistency issues, and composition. We first analyze the complexity of mappings, that is, recognizing pairs of documents such that one can be mapped into the other, and provide a classification based on sets of features used in mappings. Next, we chart the tractability frontier for the query answering problem. We show that the problem is tractable for expressive schema mappings and simple queries, but not vice versa. Then, we move to static analysis. We study the complexity of the consistency problem, that is, deciding whether it is possible to map some document of a source schema into a document of the target schema. Finally, we look at composition of XML schema mappings. We analyze its complexity and show that it is harder to achieve closure under composition for XML than for relational mappings. Nevertheless, we find a robust class of XML schema mappings that, in addition to being closed under composition, have good complexity properties with respect to the main data management tasks. Due to its good properties, we suggest this class as the class to use in applications of XML schema mappings.