When Can We Answer Queries Using Result-Bounded Data Interfaces?

We consider answering queries on data available through access methods, that provide lookup access to the tuples matching a given binding. Such interfaces are common on the Web; further, they often have bounds on how many results they can return, e.g., because of pagination or rate limits. We thus study result-bounded methods, which may return only a limited number of tuples. We study how to decide if a query is answerable using result-bounded methods, i.e., how to compute a plan that returns all answers to the query using the methods, assuming that the underlying data satisfies some integrity constraints. We first show how to reduce answerability to a query containment problem with constraints. Second, we show "schema simplification" theorems describing when and how result bounded services can be used. Finally, we use these theorems to give decidability and complexity results about answerability for common constraint classes.Comment: 65 pages; journal version of the PODS'18 paper arXiv:1706.0793

When Can We Answer Queries Using Result-Bounded Data Interfaces?

We consider answering queries where the underlying data is available only over limited interfaces which provide lookup access to the tuples matching a given binding, but possibly restricting the number of output tuples returned. Interfaces imposing such "result bounds" are common in accessing data via the web. Given a query over a set of relations as well as some integrity constraints that relate the queried relations to the data sources, we examine the problem of deciding if the query is answerable over the interfaces; that is, whether there exists a plan that returns all answers to the query, assuming the source data satisfies the integrity constraints. The first component of our analysis of answerability is a reduction to a query containment problem with constraints. The second component is a set of "schema simplification" theorems capturing limitations on how interfaces with result bounds can be useful to obtain complete answers to queries. These results also help to show decidability for the containment problem that captures answerability, for many classes of constraints. The final component in our analysis of answerability is a "linearization" method, showing that query containment with certain guarded dependencies -- including those that emerge from answerability problems -- can be reduced to query containment for a well-behaved class of linear dependencies. Putting these components together, we get a detailed picture of how to check answerability over result-bounded services.Comment: 45 pages, 2 tables, 43 references. Complete version with proofs of the PODS'18 paper. The main text of this paper is almost identical to the PODS'18 except that we have fixed some small mistakes. Relative to the earlier arXiv version, many errors were corrected, and some terminology has change

Queries with Guarded Negation (full version)

A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical algorithms in the case of unions of conjunctive queries, but become difficult or even undecidable when queries are allowed to contain negation. Inspired by recent results in finite model theory, we consider a restricted form of negation, guarded negation. We introduce a fragment of SQL, called GN-SQL, as well as a fragment of Datalog with stratified negation, called GN-Datalog, that allow only guarded negation, and we show that these query languages are computationally well behaved, in terms of testing query containment, query evaluation, open-world query answering, and boundedness. GN-SQL and GN-Datalog subsume a number of well known query languages and constraint languages, such as unions of conjunctive queries, monadic Datalog, and frontier-guarded tgds. In addition, an analysis of standard benchmark workloads shows that most usage of negation in SQL in practice is guarded negation

Querying Schemas With Access Restrictions

We study verification of systems whose transitions consist of accesses to a Web-based data-source. An access is a lookup on a relation within a relational database, fixing values for a set of positions in the relation. For example, a transition can represent access to a Web form, where the user is restricted to filling in values for a particular set of fields. We look at verifying properties of a schema describing the possible accesses of such a system. We present a language where one can describe the properties of an access path, and also specify additional restrictions on accesses that are enforced by the schema. Our main property language, AccLTL, is based on a first-order extension of linear-time temporal logic, interpreting access paths as sequences of relational structures. We also present a lower-level automaton model, Aautomata, which AccLTL specifications can compile into. We show that AccLTL and A-automata can express static analysis problems related to "querying with limited access patterns" that have been studied in the database literature in the past, such as whether an access is relevant to answering a query, and whether two queries are equivalent in the accessible data they can return. We prove decidability and complexity results for several restrictions and variants of AccLTL, and explain which properties of paths can be expressed in each restriction.Comment: VLDB201

Semantic Optimization of Conjunctive Queries

This work deals with the problem of semantic optimization of the central class of conjunctive queries (CQs). Since CQ evaluation is NP-complete, a long line of research has focussed on identifying fragments of CQs that can be efficiently evaluated. One of the most general restrictions corresponds to generalized hypetreewidth bounded by a fixed constant k ≥ 1; the associated fragment is denoted GHWk. A CQ is semantically in GHWk if it is equivalent to a CQ in GHWk. The problem of checking whether a CQ is semantically in GHWk has been studied in the constraint-free case, and it has been shown to be NP-complete. However, in case the database is subject to constraints such as tuple-generating dependencies (TGDs) that can express, e.g., inclusion dependencies, or equality-generating dependencies (EGDs) that capture, e.g., key dependencies, a CQ may turn out to be semantically in GHWk under the constraints, while not being semantically in GHWk without the constraints. This opens avenues to new query optimization techniques. In this article, we initiate and develop the theory of semantic optimization of CQs under constraints. More precisely, we study the following natural problem: Given a CQ and a set of constraints, is the query semantically in GHWk, for a fixed k ≥ 1, under the constraints, or, in other words, is the query equivalent to one that belongs to GHWk over all those databases that satisfy the constraints? We show that, contrary to what one might expect, decidability of CQ containment is a necessary but not a sufficient condition for the decidability of the problem in question. In particular, we show that checking whether a CQ is semantically in GHW1 is undecidable in the presence of full TGDs (i.e., Datalog rules) or EGDs. In view of the above negative results, we focus on the main classes of TGDs for which CQ containment is decidable and that do not capture the class of full TGDs, i.e., guarded, non-recursive, and sticky sets of TGDs, and show that the problem in question is decidable, while its complexity coincides with the complexity of CQ containment. We also consider key dependencies over unary and binary relations, and we show that the problem in question is decidable in elementary time. Furthermore, we investigate whether being semantically in GHWk alleviates the cost of query evaluation. Finally, in case a CQ is not semantically in GHWk, we discuss how it can be approximated via a CQ that falls in GHWk in an optimal way. Such approximations might help finding “quick” answers to the input query when exact evaluation is intractable

Inductive Logic Programming in Databases: from Datalog to DL+log

In this paper we address an issue that has been brought to the attention of the database community with the advent of the Semantic Web, i.e. the issue of how ontologies (and semantics conveyed by them) can help solving typical database problems, through a better understanding of KR aspects related to databases. In particular, we investigate this issue from the ILP perspective by considering two database problems, (i) the definition of views and (ii) the definition of constraints, for a database whose schema is represented also by means of an ontology. Both can be reformulated as ILP problems and can benefit from the expressive and deductive power of the KR framework DL+log. We illustrate the application scenarios by means of examples. Keywords: Inductive Logic Programming, Relational Databases, Ontologies, Description Logics, Hybrid Knowledge Representation and Reasoning Systems. Note: To appear in Theory and Practice of Logic Programming (TPLP).Comment: 30 pages, 3 figures, 2 tables

Semantic Acyclicity Under Constraints

A conjunctive query (CQ) is semantically acyclic if it is equivalent to an acyclic one. Semantic acyclicity has been studied in the constraint-free case, and deciding whether a query enjoys this property is NP-complete. However, in case the database is subject to constraints such as tuple-generating dependencies (tgds) that can express, e.g., inclusion dependencies, or equality-generating dependencies (egds) that capture, e.g., functional dependencies, a CQ may turn out to be semantically acyclic under the constraints while not semantically acyclic in general. This opens avenues to new query optimization techniques. In this paper we initiate and develop the theory of semantic acyclicity under constraints. More precisely, we study the following natural problem: Given a CQ and a set of constraints, is the query semantically acyclic under the constraints, or, in other words, is the query equivalent to an acyclic one over all those databases that satisfy the set of constraints? We show that, contrary to what one might expect, decidability of CQ containment is a necessary but not sufficient condition for the decidability of semantic acyclicity. In particular, we show that semantic acyclicity is undecidable in presence of full tgds (i.e., Datalog rules). In view of this fact, we focus on the main classes of tgds for which CQ containment is decidable, and do not capture the class of full tgds, namely guarded, non-recursive and sticky tgds. For these classes we show that semantic acyclicity is decidable, and its complexity coincides with the complexity of CQ containment. In the case of egds, we show that semantic acyclicity is undecidable even over unary and binary predicates. When restricted to keys the problem becomes decidable (NP-complete) over such schemas. We finally consider the problem of evaluating a semantically acyclic query over a database that satisfies a set of constraints. For guarded tgds the evaluation problem is tractable. © Association Computing for Machiner

Global Numerical Constraints on Trees

We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of a given node. By contrast, the logic introduced in the present work can concisely express numerical bounds on any region, descendants or ancestors for instance. We prove that the logic is decidable in single exponential time even if the numerical constraints are in binary form. We also illustrate the usage of the logic in the description of numerical constraints on multi-directional path queries on XML documents. Furthermore, numerical restrictions on regular languages (XML schemas) can also be concisely described by the logic. This implies a characterization of decidable counting extensions of XPath queries and XML schemas. Moreover, as the logic is closed under negation, it can thus be used as an optimal reasoning framework for testing emptiness, containment and equivalence