Conjunctive Queries Research Articles

Functorial Question Answering

Distributional compositional (DisCo) models are functors that compute the meaning of a sentence from the meaning of its words. We show that DisCo models in the category of sets and relations correspond precisely to relational databases. As a consequence, we get complexity-theoretic reductions from semantics and entailment of a fragment of natural language to evaluation and containment of conjunctive queries, respectively. Finally, we define question answering as an NP-complete problem.

Characterizing Tractability of Simple Well-Designed Pattern Trees with Projection

We study the complexity of evaluating well-designed pattern trees, a query language extending conjunctive queries with the possibility to define parts of the query to be optional. This possibility of optional parts is important for obtaining meaningful results over incomplete data sources as it is common in semantic web settings. Recently, a structural characterization of the classes of well-designed pattern trees that can be evaluated in polynomial time was shown. However, projection—a central feature of many query languages—was not considered in this study. We work towards closing this gap by giving a characterization of all tractable classes of simple well-designed pattern trees with projection (under some common complexity theoretic assumptions). Since well-designed pattern trees correspond to the fragment of well-designed {AND, OPTIONAL}-SPARQL queries this gives a complete description of the tractable classes of queries with projections in this fragment that can be characterized by the underlying graph structures of the queries. For non-simple pattern trees the tractability criteria for simple pattern trees do not capture all tractable classes. We thus extend the characterization for the non-simple case in order to capture some additional tractable cases.

The parameterized complexity and kernelization of resilience for database queries

Given a database instance and a query on it whose result is initially non-empty, the resilience decision problem is to decide if there exist a small enough number of facts in the database instance such that the deletion of these facts empties the result of the given query. In this paper, we revisit the resilience decision problem. We investigate the parameterized complexity for various classes of database queries. We consider the factors including the query size and the number of variables, and present several intractable cases even from the perspective of parameterized complexity. Meanwhile, we refine the characteristics of resilience for self-join-free conjunctive queries containing triads, and show that it is still NP-hard even if the structure of the input database instance is simple. This result implies the hardness essentially comes from the parity of triangle sequence instead of the complicate (non-planar) intersections of cycles. On the other hand, we also obtain some positive results showing that the resilience decision problem is still fixed parameter tractable for an important case through kernelization. Our work demonstrates a new insight for employing resilience computation in database operations.

Using Feature-Based Description Logics to avoid Duplicate Elimination in Object-Relational Query Languages

A sound inference procedure is presented for removing operations that eliminate duplicates in queries formulated in a bag-algebra. The procedure is shown complete for positive queries over finite databases, and operates by appeal to logical consequence problems for feature-based description logics in which a TBox embeds an object-relational schema. For unions of conjunctive queries in which an embedded schema excludes cover constraints, the procedure runs in PTIME, and in EXPTIME otherwise.

Data Access With Horn Ontologies: Where Description Logics Meet Existential Rules

Two main families of ontology languages are considered in the context of data access, namely Horn description logics and existential rules. In this paper, we review the semantic relationships between these families in the light of the ontology-mediated query answering problem. To this end, we rely on the standard translation of description logics in first-order logic and on the notion of semantic emulation. We focus on description logics and classes of existential rules for which the con-junctive query answering problem has polynomial data complexity.

Consistent Query Answering for Primary Keys in Datalog

We study the complexity of consistent query answering on databases that may violate primary key constraints. A repair of such a database is any consistent database that can be obtained by deleting a minimal set of tuples. For every Boolean query q, CERTAINTY(q) is the problem that takes a database as input and asks whether q evaluates to true on every repair. In Koutris and Wijsen (ACM Trans. Database Syst. 42(2), 9:1–9:45, 2017), the authors show that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either in P or coNP-complete, and it is decidable which of the two cases applies. In this article, we sharpen this result by showing that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either expressible in symmetric stratified Datalog (with some aggregation operator) or coNP-complete. Since symmetric stratified Datalog is in L, we thus obtain a complexity-theoretic dichotomy between L and coNP-complete. Another new finding of practical importance is that CERTAINTY(q) is on the logspace side of the dichotomy for queries q where all join conditions express foreign-to-primary key matches, which is undoubtedly the most common type of join condition.

Ontology-Mediated Querying with Horn Description Logics

An ontology-mediated query (OMQ) consists of a database query paired with an ontology. When evaluated on a database, an OMQ returns not only the answers that are already in the database, but also those answers that can be obtained via logical reasoning using rules from ontology. There are many open questions regarding the complexities of problems related to OMQs. Motivated by the use of ontologies in practice, new reasoning problems which have never been considered in the context of ontologies become relevant, since they can improve the usability of ontology enriched systems. This thesis deals with various reasoning problems that emerge from ontology-mediated querying and it investigates the computational complexity of these problems. We focus on ontologies formulated in Horn description logics, which are a popular choice for ontologies in practice. In particular, the thesis gives results regarding the data complexity of OMQ evaluation by completely classifying complexity and rewritability questions for OMQs based on an EL ontology and a conjunctive query. Furthermore, the query-by-example problem, and the expressibility and verification problem in ontology-based data access are introduced and investigated.

The uniform measure of simple regular sets of infinite trees

We consider the problem of computing the measure of a regular set of infinite binary trees. While the general case remains unsolved, we show that the measure of a language can be computed when the set is given in one of the following three formalisms: a first-order formula with no descendant relation; a Boolean combination of conjunctive queries (with descendant relation); or by a non-deterministic safety tree automaton. Additionally, in the first two cases the measure of the set is always rational, while in the third it is an algebraic number. Moreover, we provide an example of a first-order formula that uses descendant relation and defines a language of infinite trees having an irrational (but algebraic) measure.

Onto2problog: A Probabilistic Ontology-Mediated Querying System using Probabilistic Logic Programming

We present onto2problog, a tool that supports ontology-mediated querying of probabilistic data via probabilistic logic programming engines. Our tool supports conjunctive queries on probabilistic data under ontologies encoded in the description logic mathcal{ELH}^{dr}, thus capturing a large part of the OWL 2 EL profile.

Lifted Successor Generation Using Query Optimization Techniques

The standard PDDL language for classical planning uses several first-order features, such as schematic actions. Yet, most classical planners ground this first-order representation into a propositional one as a preprocessing step. While this simplifies the design of other parts of the planner, in several benchmarks the grounding process causes an exponential blowup that puts otherwise solvable tasks out of reach of the planners. In this work, we take a step towards planning with lifted representations. We tackle the successor generation task, a key operation in forward-search planning, directly on the lifted representation using well-known techniques from database theory. We show how computing the variable substitutions that make an action schema applicable in a given state is essentially a query evaluation problem. Interestingly, a large number of the action schemas in the standard benchmarks result in acyclic conjunctive queries, for which query evaluation is tractable. Our empirical results show that our approach is competitive with the standard (grounded) successor generation techniques in a few domains and outperforms them on benchmarks where grounding is challenging or infeasible.

Conservative Extensions in Horn Description Logics with Inverse Roles

We investigate the decidability and computational complexity of conservative extensions and the related notions of inseparability and entailment in Horn description logics (DLs) with inverse roles. We consider both query conservative extensions, defined by requiring that the answers to all conjunctive queries are left unchanged, and deductive conservative extensions, which require that the entailed concept inclusions, role inclusions, and functionality assertions do not change. Upper bounds for query conservative extensions are particularly challenging because characterizations in terms of unbounded homomorphisms between universal models, which are the foundation of the standard approach to establishing decidability, fail in the presence of inverse roles. We resort to a characterization that carefully mixes unbounded and bounded homomorphisms and enables a decision procedure that combines tree automata and a mosaic technique. Our main results are that query conservative extensions are 2ExpTime-complete in all DLs between ELI and Horn-ALCHIF and between Horn-ALC and Horn-ALCHIF, and that deductive conservative extensions are 2ExpTime-complete in all DLs between ELI and ELHIF_bot. The same results hold for inseparability and entailment.

Optimal Algorithms for Ranked Enumeration of Answers to Full Conjunctive Queries.

We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes seemingly different problems that had been studied in isolation. To this end, we extend classic algorithms that find the k-shortest paths in a weighted graph. For full conjunctive queries, including cyclic ones, our approach is optimal in terms of the time to return the top result and the delay between results. These optimality properties are derived for the widely used notion of data complexity, which treats query size as a constant. By performing a careful cost analysis, we are able to uncover a previously unknown trade-off between two incomparable enumeration approaches: one has lower complexity when the number of returned results is small, the other when the number is very large. We theoretically and empirically demonstrate the superiority of our techniques over batch algorithms, which produce the full result and then sort it. Our technique is not only faster for returning the first few results, but on some inputs beats the batch algorithm even when all results are produced.

Towards Universal Languages for Tractable Ontology Mediated Query Answering

An ontology language for ontology mediated query answering (OMQA-language) is universal for a family of OMQA-languages if it is the most expressive one among this family. In this paper, we focus on three families of tractable OMQA-languages, including first-order rewritable languages and languages whose data complexity of the query answering is in AC0 or PTIME. On the negative side, we prove that there is, in general, no universal language for each of these families of languages. On the positive side, we propose a novel property, the locality, to approximate the first-order rewritability, and show that there exists a language of disjunctive embedded dependencies that is universal for the family of OMQA-languages with locality. All of these results apply to OMQA with query languages such as conjunctive queries, unions of conjunctive queries and acyclic conjunctive queries.

Answering Conjunctive Queries with Inequalities in <em>DL-Lite</em><sub>ℛ</sub>

In the context of the Description Logic DL-Liteℛ≠, i.e., DL-Liteℛ without UNA and with inequality axioms, we address the problem of adding to unions of conjunctive queries (UCQs) one of the simplest forms of negation, namely, inequality. It is well known that answering conjunctive queries with unrestricted inequalities over DL-Liteℛ ontologies is in general undecidable. Therefore, we explore two strategies for recovering decidability, and, hopefully, tractability. Firstly, we weaken the ontology language, and consider the variant of DL-Liteℛ≠ corresponding to rdfs enriched with both inequality and disjointness axioms. Secondly, we weaken the query language, by preventing inequalities to be applied to existentially quantified variables, thus obtaining the class of queries named UCQ≠,bs. We prove that in the two cases, query answering is decidable, and we provide tight complexity bounds for the problem, both for data and combined complexity. Notably, the results show that answering UCQ≠,bs over DL-Liteℛ≠ ontologies is still in AC0 in data complexity.

Checking Chase Termination over Ontologies of Existential Rules with Equality

The chase is a sound and complete algorithm for conjunctive query answering over ontologies of existential rules with equality. To enable its effective use, we can apply acyclicity notions; that is, sufficient conditions that guarantee chase termination. Unfortunately, most of these notions have only been defined for existential rule sets without equality. A proposed solution to circumvent this issue is to treat equality as an ordinary predicate with an explicit axiomatisation. We empirically show that this solution is not efficient in practice and propose an alternative approach. More precisely, we show that, if the chase terminates for any equality axiomatisation of an ontology, then it terminates for the original ontology (which may contain equality). Therefore, one can apply existing acyclicity notions to check chase termination over an axiomatisation of an ontology and then use the original ontology for reasoning. We show that, in practice, doing so results in a more efficient reasoning procedure. Furthermore, we present equality model-faithful acyclicity, a general acyclicity notion that can be directly applied to ontologies with equality.

Deciding the Loosely Guarded Fragment and Querying Its Horn Fragment Using Resolution

We consider the following query answering problem: Given a Boolean conjunctive query and a theory in the Horn loosely guarded fragment, the aim is to determine whether the query is entailed by the theory. In this paper, we present a resolution decision procedure for the loosely guarded fragment, and use such a procedure to answer Boolean conjunctive queries against the Horn loosely guarded fragment. The Horn loosely guarded fragment subsumes classes of rules that are prevalent in ontology-based query answering, such as Horn ALCHOI and guarded existential rules. Additionally, we identify star queries and cloud queries, which using our procedure, can be answered against the loosely guarded fragment.

Aggregate Searchable Encryption With Result Privacy

With searchable encryption (SE), the user is allowed to extract partial data from stored ciphertexts from the storage server, based on a chosen query of keywords. A majority of the existing SE schemes support SQL search query, i.e. 'Select * where (list of keywords).' However, applications for encrypted data analysis often need to count data matched with a query, instead of data extraction. For such applications, the execution of SQL aggregate query, i.e. 'Count * where (list of keywords)' at server is essential. Additionally, in case of semi-honest server, privacy of aggregate result is of primary concern. In this article, the authors propose an aggregate searchable encryption with result privacy (ASE-RP) that includes ASearch() algorithm. The proposed ASearch() performs aggregate operation (i.e. Count *) on the implicitly searched ciphertexts (for the conjunctive query) and outputs an encrypted result. The server, due to encrypted form of aggregate result, would not be able to get actual count unless having a decryption key and hence ASearch() offers result privacy.

Supporting hard queries over probabilistic preferences

Preference analysis is widely applied in various domains such as social choice and e-commerce. A recently proposed frame- work augments the relational database with a preference re- lation that represents uncertain preferences in the form of statistical ranking models, and provides methods to evaluate Conjunctive Queries (CQs) that express preferences among item attributes. In this paper, we explore the evaluation of queries that are more general and harder to compute. The main focus of this paper is on a class of CQs that cannot be evaluated by previous work. These queries are provably hard since relate variables that represent items be- ing compared. To overcome this hardness, we instantiate these variables with their domain values, rewrite hard CQs as unions of such instantiated queries, and develop several exact and approximate solvers to evaluate these unions of queries. We demonstrate that exact solvers that target specific common kinds of queries are far more efficient than gen- eral solvers. Further, we demonstrate that sophisticated ap- proximate solvers making use of importance sampling can be orders of magnitude more efficient than exact solvers, while showing good accuracy. In addition to supporting provably hard CQs, we also present methods to evaluate an important family of count queries, and of top-k queries.

Ontology-based Document Spanning Systems for Information Extraction

Information Extraction (IE) is the task of automatically organizing in a structured form data extracted from free text documents. In several contexts, it is often desirable that the extracted data are then organized according to an ontology, which provides a formal and conceptual representation of the domain of interest. Ontologies allow for a better data interpretation, as well as for their semantic integration with other information, as in Ontology-based Data Access (OBDA), a popular declarative framework for data management where an ontology is connected to a data layer through mappings. However, the data layer considered so far in OBDA has consisted essentially of relational databases, and how to declaratively couple an ontology with unstructured data sources is still unexplored. By leveraging the recent study on document spanners for rule-based IE by Fagin et al., in this paper, we propose a new framework that allows to map text documents to ontologies, in the spirit of OBDA. We investigate the problem of answering conjunctive queries in this framework. For ontologies specified in the Description Logics [Formula: see text] and [Formula: see text], we show that the problem is polynomial in the size of the underlying documents. We also provide algorithms to solve query answering by rewriting the input query on the basis of the ontology and its mapping toward the source documents. Through these techniques, we pursue a virtual approach, similar to that typically adopted in OBDA, which allows us to answer a query without having to first populate the entire ontology. Interestingly, for [Formula: see text], both the spanners used in the mapping and the one computed by the rewriting algorithm belong to the same class of expressiveness. This holds also for [Formula: see text], modulo some limitations on the form of the mapping. These results say that in these cases our framework can be easily implemented by decoupling ontology management and document access, which can be delegated to an external IE system able to process the extraction rules we use in the mapping.

Complexity column

This column concerns the complexity of evaluating database queries. In particular, for which conjunctive queries can we, after linear preprocessing, enumerate the query answer with only constant delay between entries? There is a beautiful answer, plus some lower bounds, extensions to dynamic databases and more. I thank Christoph Berkholz, Fabian Gerhardt and Nicole Schweikardt for their clearly written tutorial. It is a wonderful, self-contained introduction to this area.