Existential rules, a.k.a. dependencies in databases, and Datalog+/- in knowledge representation and reasoning recently, are a family of important logical languages widely used in computer science and artificial intelligence. Towards a deep understanding of these languages in model theory, we establish model-theoretic characterizations for a number of existential rule languages such as (disjunctive) embedded dependencies, tuple-generating dependencies (TGDs), (frontier-)guarded TGDs and linear TGDs. All these characterizations hold for arbitrary structures, and most of them also work on the class of finite structures. As a natural application of these characterizations, complexity bounds for the rewritability of above languages are also identified.
College of Intelligence and Computing, Tianjin University（天津大学智能与计算学部）
Existential rule languages are a family of ontology languages that have been widely used in ontology-mediated query answering (OMQA). However, for most of them, the expressive power of representing domain knowledge for OMQA, known as the program expressive power, is not well-understood yet. In this paper, we establish a number of novel characterizations for the program expressive power of several important existential rule languages, including tuple-generating dependencies (TGDs), linear TGDs, as well as disjunctive TGDs. The characterizations employ natural model-theoretic properties, and aut…
University of Oxford（牛津大学）；LIRMM（法国计算机科学、机器人学和微电子实验室）；Inria（法国国家信息与自动化研究所）；University of Montpellier（蒙彼利埃大学）；CNRS（法国国家科学研究中心）；DI ENS（巴黎高等师范学院信息学系）；ENS（巴黎高等师范学院）；PSL University（巴黎文理研究大学）
In this paper, we consider existential rules, an expressive formalism well suited to the representation of ontological knowledge and data-to-ontology mappings in the context of ontology-based data integration. The chase is a fundamental tool to do reasoning with existential rules as it computes all the facts entailed by the rules from a database instance. We introduce parallelisable sets of existential rules, for which the chase can be computed in a single breadth-first step from any instance. The question we investigate is the characterization of such rule sets. We show that parallelisable ru…
Western Sydney University（西悉尼大学）；Tianjin University（天津大学）；Huazhong University of Science & Technology（华中科技大学）
In ontology-based data access (OBDA), the classical database is enhanced with an ontology in the form of logical assertions generating new intensional knowledge. A powerful form of such logical assertions is the tuple-generating dependencies (TGDs), also called existential rules, where Horn rules are extended by allowing existential quantifiers to appear in the rule heads. In this paper we introduce a new language called loop restricted (LR) TGDs (existential rules), which are TGDs with certain restrictions on the loops embedded in the underlying rule set. We study the complexity of this new l…
Huazhong University of Technology & Science（华中科技大学）；Western Sydney University（西悉尼大学）；University of Alberta（阿尔伯塔大学）
Existential rules, also known as data dependencies in Databases, have been recently rediscovered as a promising family of languages for Ontology-based Query Answering. In this paper, we prove that disjunctive embedded dependencies exactly capture the class of recursively enumerable ontologies in Ontology-based Conjunctive Query Answering (OCQA). Our expressive completeness result does not rely on any built-in linear order on the database. To establish the expressive completeness, we introduce a novel semantic definition for OCQA ontologies. We also show that neither the class of disjunctive tu…
University Montpellier 2（蒙彼利埃第二大学）；TU Dresden（德累斯顿工业大学）
We address the issue of Ontology-Based Data Access, with ontologies represented in the framework of existential rules, also known as Datalog+/-. A well-known approach involves rewriting the query using ontological knowledge. We focus here on the basic rewriting technique which consists of rewriting the initial query into a union of conjunctive queries. First, we study a generic breadth-first rewriting algorithm, which takes as input any rewriting operator, and define properties of rewriting operators that ensure the correctness of the algorithm. Then, we focus on piece-unifiers, which provide …
Sun Yat-sen University（中山大学）；Huazhong University of Science and Technology（华中科技大学）；Fudan University（复旦大学）；Werstern Sydney University（西悉尼大学）
Traditional inconsistency-tolerent query answering in ontology-based data access relies on selecting maximal components of an ABox/database which are consistent with the ontology. However, some rules in ontologies might be unreliable if they are extracted from ontology learning or written by unskillful knowledge engineers. In this paper we present a framework of handling inconsistent existential rules under stable model semantics, which is defined by a notion called rule repairs to select maximal components of the existential rules. Surprisingly, for R-acyclic existential rules with R-stratifi…
The Sticky Path to Expressive Querying: Decidability of Navigational Queries under Existential Rules
TU Dresden（德累斯顿工业大学）；University of Wrocław（弗罗茨瓦夫大学）；Center for Scalable Data Analytics and Artificial Intelligence Dresden/Leipzig（德累斯顿/莱比锡可扩展数据分析与人工智能中心）
TU Dresden（德累斯顿工业大学）；Inria（法国国家信息与自动化研究所）；University Montpellier 2（蒙彼利埃第二大学）
The need for an ontological layer on top of data, associated with advanced reasoning mechanisms able to exploit the semantics encoded in ontologies, has been acknowledged both in the database and knowledge representation communities. We focus in this paper on the ontological query answering problem, which consists of querying data while taking ontological knowledge into account. More specifically, we establish complexities of the conjunctive query entailment problem for classes of existential rules (also called tuple-generating dependencies, Datalog+/- rules, or forall-exists-rules. Our contri…
Institute for Theoretical Computer Science（理论计算机科学研究所）；Technische Universität Dresden（德累斯顿工业大学）；Department of Computer Science（计算机科学系）；Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）
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 precise…
INRIA（法国国家信息与自动化研究所）；University of Angers（昂热大学）；University of Montpellier（蒙彼利埃大学）
Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology-Based Query Answering. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure the termination of a breadth-first forward chaining algorithm known as the chase. First, we propose a new tool that allows to extend existing acyclicity conditions ensuring chase termination, while keeping good complexity properties. Second, we consider the extension to existential rules with nonmonotonic negation under stable model semantics and further exte…
INRIA（法国国家信息与自动化研究所）；University of Angers（昂热大学）；University of Montpellier（蒙彼利埃大学）
Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology- Based Data Access. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure the termination of a breadth-first forward chaining algorithm known as the chase. Several variants of the chase have been proposed. In the first part of this paper, we propose a new tool that allows to extend existing acyclicity conditions ensuring chase termination, while keeping good complexity properties. In the second part, we study the extension to existent…
We consider existential rules (aka Datalog+) as a formalism for specifying ontologies. In recent years, many classes of existential rules have been exhibited for which conjunctive query (CQ) entailment is decidable. However, most of these classes cannot express transitivity of binary relations, a frequently used modelling construct. In this paper, we address the issue of whether transitivity can be safely combined with decidable classes of existential rules. First, we prove that transitivity is incompatible with one of the simplest decidable classes, namely aGRD (acyclic graph of rule dependen…
In our pursuit of generic criteria for decidable ontology-based querying, we introduce 'finite-cliquewidth sets' (FCS) of existential rules, a model-theoretically defined class of rule sets, inspired by the cliquewidth measure from graph theory. By a generic argument, we show that FCS ensures decidability of entailment for a sizable class of queries (dubbed 'DaMSOQs') subsuming conjunctive queries (CQs). The FCS class properly generalizes the class of finite-expansion sets (FES), and for signatures of arity at most 2, the class of bounded-treewidth sets (BTS). For higher arities, BTS is only i…
LIRMM（蒙彼利埃计算机科学、机器人与微电子实验室）；Inria（法国国家信息与自动化研究所）；University of Montpellier（蒙彼利埃大学）；CNRS（法国国家科学研究中心）；DI ENS（巴黎高等师范学院计算机系）；ENS（巴黎高等师范学院）；PSL University（巴黎文理研究大学）
Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common assumption is that rule heads are atomic, i.e., restricted to a single atom. Such assumptions are considered to be made without loss of generality as long as all sets of rules can be normalised while preserving entailment. However, an important question is whether the properties that ensure the decidability of reasoning are preserved as well. We provide a systemat…
Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a prominent problem in knowledge representation and databases. This problem can be solved using the chase algorithm, which extends the given set of facts with fresh facts in order to satisfy the rules. If the chase terminates, then CQs can be evaluated directly in the resulting set of facts. The chase, however, does not terminate necessarily, and checking whether the chase terminates on a given set of rules and facts is undecidable. Numerous acyclicity notions were proposed as sufficient conditions for c…
University of Montpellier（蒙彼利埃大学）；LIRMM（蒙彼利埃计算机信息、机器人与微电子实验室）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）
Existential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in the context of ontology-mediated query answering. Forward chaining, also known as the chase, is a fundamental tool for computing universal models of knowledge bases, which consist of existential rules and facts. Several chase variants have been defined, which differ on the way they handle redundancies. A set of existential rules is bounded if it ensures the e…
Datalog is one of the best-known rule-based languages, and extensions of it are used in a wide context of applications. An important Datalog extension is Disjunctive Datalog, which significantly increases the expressivity of the basic language. Disjunctive Datalog is useful in a wide range of applications, ranging from Databases (e.g., Data Integration) to Artificial Intelligence (e.g., diagnosis and planning under incomplete knowledge). However, in recent years an important shortcoming of Datalog-based languages became evident, e.g. in the context of data-integration (consistent query-answeri…
Warded Datalog+- extends the logic-based language Datalog with existential quantifiers in rule heads. Existential rules are needed for advanced reasoning tasks, e.g., ontological reasoning. The theoretical efficiency guarantees of Warded Datalog+- do not cover extensions crucial for data analytics, such as arithmetic. Moreover, despite the significance of arithmetic for common data analytic scenarios, no decidable fragment of any Datalog+- language extended with arithmetic has been identified. We close this gap by defining a new language that extends Warded Datalog+- with arithmetic and prove …
Several types of dependencies have been proposed for the static analysis of existential rule ontologies, promising insights about computational properties and possible practical uses of a given set of rules, e.g., in ontology-based query answering. Unfortunately, these dependencies are rarely implemented, so their potential is hardly realised in practice. We focus on two kinds of rule dependencies -- positive reliances and restraints -- and design and implement optimised algorithms for their efficient computation. Experiments on real-world ontologies of up to more than 100,000 rules show the s…
University of Hildesheim（希尔德斯海姆大学）；University of Bremen（不来梅大学）；University of Wrocław（弗罗茨瓦夫大学）
We study the problem to decide, given sets T1,T2 of tuple-generating dependencies (TGDs), also called existential rules, whether T2 is a conservative extension of T1. We consider two natural notions of conservative extension, one pertaining to answers to conjunctive queries over databases and one to homomorphisms between chased databases. Our main results are that these problems are undecidable for linear TGDs, undecidable for guarded TGDs even when T1 is empty, and decidable for frontier-one TGDs.
Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；Technische Universität Dresden（德累斯顿工业大学）；Technische Universität Wien（维也纳工业大学）
We study reasoning with existential rules to perform query answering over streams of data. On static databases, this problem has been widely studied, but its extension to rapidly changing data has not yet been considered. To bridge this gap, we extend LARS, a well-known framework for rule-based stream reasoning, to support existential rules. For that, we show how to translate LARS with existentials into a semantics-preserving set of existential rules. As query answering with such rules is undecidable in general, we describe how to leverage the temporal nature of streams and present suitable no…
Recent years have witnessed the successful application of low-dimensional vector space representations of knowledge graphs to predict missing facts or find erroneous ones. However, it is not yet well-understood to what extent ontological knowledge, e.g. given as a set of (existential) rules, can be embedded in a principled way. To address this shortcoming, in this paper we introduce a general framework based on a view of relations as regions, which allows us to study the compatibility between ontological knowledge and different types of vector space embeddings. Our technical contribution is tw…
Center for Semantic Web Research（语义网研究中心）；University of Chile（智利大学）；TU Wien（维也纳工业大学）；University of Edinburgh（爱丁堡大学）
Many efforts have been dedicated to identifying restrictions on ontologies expressed as tuple-generating dependencies (tgds), a.k.a. existential rules, that lead to the decidability for the problem of answering ontology-mediated queries (OMQs). This has given rise to three families of formalisms: guarded, non-recursive, and sticky sets of tgds. In this work, we study the containment problem for OMQs expressed in such formalisms, which is a key ingredient for solving static analysis tasks associated with them. Our main contribution is the development of specially tailored techniques for OMQ con…
University of Western Sydney（西悉尼大学）；University of Alberta（阿尔伯塔大学）
Finite chase, or alternatively chase termination, is an important condition to ensure the decidability of existential rule languages. In the past few years, a number of rule languages with finite chase have been studied. In this work, we propose a novel approach for classifying the rule languages with finite chase. Using this approach, a family of decidable rule languages, which extend the existing languages with the finite chase property, are naturally defined. We then study the complexity of these languages. Although all of them are tractable for data complexity, we show that their combined …
Banca d’Italia（意大利银行）；TU Wien（维也纳工业大学）；University of Oxford（牛津大学）
We provide a framework for probabilistic reasoning in Vadalog-based Knowledge Graphs (KGs), satisfying the requirements of ontological reasoning: full recursion, powerful existential quantification, expression of inductive definitions. Vadalog is a Knowledge Representation and Reasoning (KRR) language based on Warded Datalog+/-, a logical core language of existential rules, with a good balance between computational complexity and expressive power. Handling uncertainty is essential for reasoning with KGs. Yet Vadalog and Warded Datalog+/- are not covered by the existing probabilistic logic prog…
University of Montpellier（蒙彼利埃大学）；LIRMM（蒙彼利埃计算机信息、机器人与微电子实验室）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）
The chase is a fundamental tool for existential rules. Several chase variants are known, which differ on how they handle redundancies possibly caused by the introduction of nulls. Given a chase variant, the halting problem takes as input a set of existential rules and asks if this set of rules ensures the termination of the chase for any factbase. It is well-known that this problem is undecidable for all known chase variants. The related problem of boundedness asks if a given set of existential rules is bounded, i.e., whether there is a predefined upper bound on the number of (breadth-first) s…
FBK-IRST（布鲁诺·凯斯勒基金会研究院）；University Of Trento（特伦托大学）；Otto-von-Guericke University of Magdeburg（马格德堡奥托·冯·格里克大学）
The proliferation of contextualized knowledge in the Semantic Web (SW) has led to the popularity of knowledge formats such as \emph{quads} in the SW community. A quad is an extension of an RDF triple with contextual information of the triple. In this paper, we study the problem of query answering over quads augmented with forall-existential bridge rules that enable interoperability of reasoning between triples in various contexts. We call a set of quads together with such expressive bridge rules, a quad-system. Query answering over quad-systems is undecidable, in general. We derive decidable c…
We study the notion of boundedness in the context of positive existential rules, that is, whether there exists an upper bound to the depth of the chase procedure, that is independent from the initial instance. By focussing our attention on the oblivious and the semi-oblivious chase variants, we give a characterization of boundedness in terms of FO-rewritability and chase termination. We show that it is decidable to recognize if a set of rules is bounded for several classes and outline the complexity of the problem. This report contains the paper published at IJCAI 2019 and an appendix with ful…
University of Milan（米兰大学）；University of Western Ontario（西安大略大学）；University of Edinburgh（爱丁堡大学）；University of Cyprus（塞浦路斯大学）
The chase procedure is a fundamental algorithmic tool in databases that allows us to reason with constraints, such as existential rules, with a plethora of applications. It takes as input a database and a set of constraints, and iteratively completes the database as dictated by the constraints. A key challenge, though, is the fact that it may not terminate, which leads to the problem of checking whether it terminates given a database and a set of constraints. In this work, we focus on the semi-oblivious version of the chase, which is well-suited for practical implementations, and linear existe…
DKM, FBK-IRST（FBK-IRST 的 DKM 部门）；DISI, University Of Trento（特伦托大学 DISI 系）
The recent outburst of context-dependent knowledge on the Semantic Web (SW) has led to the realization of the importance of the quads in the SW community. Quads, which extend a standard RDF triple, by adding a new parameter of the `context' of an RDF triple, thus informs a reasoner to distinguish between the knowledge in various contexts. Although this distinction separates the triples in an RDF graph into various contexts, and allows the reasoning to be decoupled across various contexts, bridge rules need to be provided for inter-operating the knowledge across these contexts. We call a set of…
Simple conceptual graphs are considered as the kernel of most knowledge representation formalisms built upon Sowa's model. Reasoning in this model can be expressed by a graph homomorphism called projection, whose semantics is usually given in terms of positive, conjunctive, existential FOL. We present here a family of extensions of this model, based on rules and constraints, keeping graph homomorphism as the basic operation. We focus on the formal definitions of the different models obtained, including their operational semantics and relationships with FOL, and we analyze the decidability and …
University of Oxford（牛津大学）；Alan Turing Institute（艾伦·图灵研究所）
Inspired by the magic sets for Datalog, we present a novel goal-driven approach for answering queries over terminating existential rules with equality (aka TGDs and EGDs). Our technique improves the performance of query answering by pruning the consequences that are not relevant for the query. This is challenging in our setting because equalities can potentially affect all predicates in a dataset. We address this problem by combining the existing singularization technique with two new ingredients: an algorithm for identifying the rules relevant to a query and a new magic sets algorithm. We sho…
In ontology-based data access, databases are connected to an ontology via mappings from queries over the database to queries over the ontology. In this paper, we consider mappings from relational databases to first-order ontologies, and define an ASP-based framework for GLAV mappings with queries over the ontology in the mapping rule bodies. We show that this type of mappings can be used to express constraints and exceptions, as well as being a powerful mechanism for succinctly representing OBDA mappings. We give an algorithm for brave reasoning in this setting, and show that this problem has …
A large body of research is currently investigating on the connection between machine learning and game theory. In this work, game theory notions are injected into a preference learning framework. Specifically, a preference learning problem is seen as a two-players zero-sum game. An algorithm is proposed to incrementally include new useful features into the hypothesis. This can be particularly important when dealing with a very large number of potential features like, for instance, in relational learning and rule extraction. A game theoretical analysis is used to demonstrate the convergence of…
