Existential Rules Research Articles

Dyadic Existential Rules

Abstract Existential rules form an expressive ${{\textsf{Datalog}}}$ -based language to specify ontological knowledge. The presence of existential quantification in rule-heads, however, makes the main reasoning tasks undecidable. To overcome this limitation, in the last two decades, a number of classes of existential rules guaranteeing the decidability of query answering have been proposed. Unfortunately, only some of these classes fully encompass ${{\textsf{Datalog}}}$ and, often, this comes at the price of higher computational complexity. Moreover, expressive classes are typically unable to exploit tools developed for classes exhibiting lower expressiveness. To mitigate these shortcomings, this paper introduces a novel general syntactic condition that allows us to define, systematically and in a uniform way, from any decidable class $\mathcal{C}$ of existential rules, a new class called ${{\textsf{Dyadic-}\mathcal{C}}}$ enjoying the following properties: (i) it is decidable; (ii) it generalizes ${{\textsf{Datalog}}}$ ; (iii) it generalizes $\mathcal{C}$ ; (iv) it can effectively exploit any reasoner for query answering over $\mathcal{C}$ ; and (v) its computational complexity does not exceed the highest between the one of $\mathcal{C}$ and the one of ${{\textsf{Datalog}}}$ .

Semi-Oblivious Chase Termination for Linear Existential Rules: An Experimental Study

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 existential rules, a central class of constraints with several applications. In this setting, there is a mature body of theoretical work that provides syntactic characterizations of when the chase terminates, algorithms for checking chase termination, and precise complexity results. Our main objective is to experimentally evaluate the existing chase termination algorithms with the aim of understanding which input parameters affect their performance, clarifying whether they can be used in practice, and revealing their performance limitations.

General Acyclicity and Cyclicity Notions for the Disjunctive Skolem Chase

The disjunctive skolem chase is a sound, complete, and potentially non-terminating procedure for solving boolean conjunctive query entailment over knowledge bases of disjunctive existential rules. We develop novel acyclicity and cyclicity notions for this procedure; that is, we develop sufficient conditions to determine chase termination and non-termination. Our empirical evaluation shows that our novel notions are significantly more general than existing criteria.

Polynomial combined first-order rewritings for linear and guarded existential rules

We consider the problem of ontological query answering, that is, the problem of answering a database query (typically a conjunctive query) in the presence of an ontology. This means that during the query answering process we also need to take into account the knowledge that can be inferred from the given database and ontology. Building, however, ontology-aware database systems from scratch, with sophisticated optimization techniques, is a highly non-trivial task that requires a great engineering effort. Therefore, exploiting conventional database systems is an important route towards efficient ontological query answering. Nevertheless, standard database systems are unaware of ontologies. An approach to ontological query answering that enables the use of standard database systems is the so-called polynomial combined query rewriting, originally introduced in the context of description logics: the conjunctive query q and the ontology Σ are rewritten in polynomial time into a first-order query qΣ (in a database-independent way), while the database D and the ontology Σ are rewritten in polynomial time into a new database DΣ (in a query-independent way), such that the answer to q in the presence of Σ over D coincides with the answer to qΣ over DΣ. The latter can then be computed by exploiting a conventional database system.In this work, we focus on linear and guarded existential rules, which form robust rule-based languages for modeling ontologies, and investigate the limits of polynomial combined query rewriting. In particular, we show that this type of rewriting can be successfully applied to (i) linear existential rules when the rewritten query can use the full power of first-order queries, (ii) linear existential rules when the arity of the underlying schema is fixed and the rewritten query is positive existential, namely it uses only existential quantification, conjunction, and disjunction, and (iii) guarded existential rules when the underlying schema is fixed and the rewritten query is positive existential. We can show that the above results reach the limits (under standard complexity-theoretic assumptions such as ▪) of polynomial combined query rewriting in the case of linear and guarded existential rules.

Scalable Query Answering Under Uncertainty to Neuroscientific Ontological Knowledge: The NeuroLang Approach.

Researchers in neuroscience have a growing number of datasets available to study the brain, which is made possible by recent technological advances. Given the extent to which the brain has been studied, there is also available ontological knowledge encoding the current state of the art regarding its different areas, activation patterns, keywords associated with studies, etc. Furthermore, there is inherent uncertainty associated with brain scans arising from the mapping between voxels-3D pixels-and actual points in different individual brains. Unfortunately, there is currently no unifying framework for accessing such collections of rich heterogeneous data under uncertainty, making it necessary for researchers to rely on ad hoc tools. In particular, one major weakness of current tools that attempt to address this task is that only very limited propositional query languages have been developed. In this paper we present NeuroLang, a probabilistic language based on first-order logic with existential rules, probabilistic uncertainty, ontologies integration under the open world assumption, and built-in mechanisms to guarantee tractable query answering over very large datasets. NeuroLang's primary objective is to provide a unified framework to seamlessly integrate heterogeneous data, such as ontologies, and map fine-grained cognitive domains to brain regions through a set of formal criteria, promoting shareable and highly reproducible research. After presenting the language and its general query answering architecture, we discuss real-world use cases showing how NeuroLang can be applied to practical scenarios.

Swift Markov Logic for Probabilistic Reasoning on Knowledge Graphs

AbstractWe 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 programming and statistical relational learning approaches for several reasons, including insufficient support for recursion with existential quantification and the impossibility to express inductive definitions. In this work, we introduce Soft Vadalog, a probabilistic extension to Vadalog, satisfying these desiderata. A Soft Vadalog program induces what we call a Probabilistic Knowledge Graph (PKG), which consists of a probability distribution on a network of chase instances, structures obtained by grounding the rules over a database using the chase procedure. We exploit PKGs for probabilistic marginal inference. We discuss the theory and present MCMC-chase, a Monte Carlo method to use Soft Vadalog in practice. We apply our framework to solve data management and industrial problems and experimentally evaluate it in the Vadalog system.

Preference-based inconsistency-tolerant query answering under existential rules

Ontology-mediated query answering (OMQA) emerged as a paradigm to enhance querying of data sources with an ontology that encodes background knowledge. In applications involving large amounts of data from multiple data sources, it might well be the case that inconsistency arises, making standard query answering useless, since everything is entailed by an inconsistent knowledge base. Being able to provide meaningful query answers in the presence of inconsistency is thus a critical issue to make OMQA systems successful in practice. The problem of querying inconsistent knowledge has attracted a great deal of interest over the years. Different inconsistency-tolerant semantics of query answering have been proposed, that is, approaches to answer queries in a meaningful way despite the knowledge at hand being inconsistent. Most of the semantics in the literature are based on the notion of repair, that is, a “maximal” consistent subset of the database. In general, there can be several repairs, so it is often natural and desirable to express preferences among them. In this paper, we propose a framework for querying inconsistent knowledge bases under user preferences for existential rule languages. Specifically, we introduce preference rules, a declarative formalism which enable users to express (i) preferences over both the database and the knowledge that can be derived from it via an ontology, and (ii) preconditions for preferences to hold. We then define two notions of preferred repairs which take preference rules into account. This naturally leads us to introducing preference-aware counterparts of popular inconsistency-tolerant semantics, where only preferred repairs are considered for query answering. We provide a thorough analysis of the data and combined complexity of different relevant problems for a wide range of existential rule languages.

Answering Queries with Negation over Existential Rules

Ontology-based query answering with existential rules is well understood and implemented for positive queries, in particular conjunctive queries. For queries with negation, however, there is no agreed-upon semantics or standard implementation. This problem is unknown for simpler rule languages, such as Datalog, where it is intuitive and practical to evaluate negative queries over the least model. This fails for existential rules, which instead of a single least model have multiple universal models that may not lead to the same results for negative queries. We therefore propose universal core models as a basis for a meaningful (non-monotonic) semantics for queries with negation. Since cores are hard to compute, we identify syntactic conditions (on rules and queries) under which our core-based semantics can equivalently be obtained for other universal models, such as those produced by practical chase algorithms. Finally, we use our findings to propose a semantics for a broad class of existential rules with negation.

Characterizing the Program Expressive Power of Existential Rule Languages

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 automata-theoretic properties sometimes, which thus provide powerful tools for identifying the definability of domain knowledge for OMQA in these languages.

Active knowledge graph completion

Enterprise and public Knowledge Graphs (KGs) are known to be incomplete. Methods for automatic completion, sometimes by rule learning, scale well. While previous rule-based methods learn closed (non-existential) rules, we introduce Open Path (OP) rules that are constrained existential rules. We present a novel algorithm, OPRL, for learning OP rules.Closed rules complete a KG by answering queries of unclear origin, usually derived from a holdback test set in experimental settings. However, OP rules can generate relevant queries for KG completion. OPRL generates queries even when there is no closed rule to answer the query, or when the correct answer is a missing entity that is not present in the KG.For OPRL to scale well, we propose a novel embedding-based fitness function to efficiently estimate rule quality. Additionally, we introduce a novel, efficient vector computation to formally assess rule quality.We evaluate OPRL using adaptations of Freebase, YAGO2, Wikidata, and a synthetic Poker KG. We find that OPRL mines hundreds of accurate rules from massive KGs with up to 8 M facts. The OP rules generate queries with precision as high as 98% and recall of 62% on a complete KG, demonstrating the first solution for active knowledge graph completion.

Inconsistency-tolerant query answering for existential rules

Querying inconsistent knowledge bases is an intriguing problem that gave rise to a flourishing research activity in the knowledge representation and reasoning community during the last years. It has been extensively studied in the context of description logics (DLs), and its computational complexity is rather well-understood. Although DLs are popular formalisms for modeling ontologies, it is generally agreed that rule-based ontologies are well-suited for data-intensive applications, since they allow us to conveniently deal with higher-arity relations, which naturally occur in standard relational databases. The goal of this work is to perform an in-depth complexity analysis of querying inconsistent knowledge bases in the case of the main decidable classes of existential rules, based on the notions of guardedness, linearity, acyclicity, and stickiness, enriched with negative (a.k.a. denial) constraints. Our investigation concentrates on three central inconsistency-tolerant semantics: the ABox repair (AR) semantics, considered as the standard one, and its main sound approximations, the intersection of repairs (IAR) semantics and the intersection of closed repairs (ICR) semantics.

Loop restricted existential rules and first-order rewritability for query answering

Abstract 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 language. We show that the conjunctive query answering (CQA) under the LR TGDs is decidable. In particular, we prove that this language satisfies the so-called bounded derivation-depth property (BDDP), which implies that the CQA is first-order rewritable, and its data complexity is in Ac$^{0}$. We also prove that the combined complexity of the CQA is 2-ExpTime complete, while the language membership is Pspace complete. Then we extend the LR TGDs language to the generalized loop restricted (GLR) TGDs language and prove that this class of TGDs still remains to be first-order rewritable and properly contains most of other first-order rewritable TGDs classes discovered in the literature so far.

Stable Model Semantics for Guarded Existential Rules and Description Logics: Decidability and Complexity

This work investigates the decidability and complexity of database query answering under guarded existential rules with nonmonotonic negation according to the classical stable model semantics. In this setting, existential quantification is interpreted via Skolem functions, and the unique name assumption is adopted. As a first result, we show the decidability of answering first-order queries based on such rules by a translation into the satisfiability problem for guarded second-order formulas having the tree-model property. To obtain precise complexity results for unions of conjunctive queries, we transform the original problem in polynomial time into an intermediate problem that is easier to analyze: query answering for guarded disjunctive existential rules with stratified negation. We obtain precise bounds for the general setting and for various restricted settings. We also consider extensions of the original formalism with negative constraints, keys, and the possibility of negated atoms in queries. Finally, we show how the above results can be used to provide decidability and complexity results for a natural adaptation of the stable model semantics to description logics such as ELHI and the DL-Lite family.

Preferred Explanations for Ontology-Mediated Queries under Existential Rules

Recently, explanations for query answers under existential rules have been investigated, where an explanation is an inclusion-minimal subset of a given database that, together with the ontology, entails the query. In this paper, we take a step further and study explanations under different minimality criteria. In particular, we first study cardinality-minimal explanations and hence focus on deriving explanations of minimum size. We then study a more general preference order induced by a weight distribution. We assume that every database fact is annotated with a (penalization) weight, and we are interested in explanations with minimum overall weight. For both preference orders, we study a variety of explanation problems, such as recognizing a preferred explanation, all preferred explanations, a relevant or necessary fact, and the existence of a preferred explanation not containing forbidden sets of facts. We provide a detailed complexity analysis for all the aforementioned problems, thereby providing a more complete picture for explaining query answers under existential rules.

Efficient Datalog Rewriting for Query Answering in TGD Ontologies

Tuple-generating dependencies (TGDs or existential rules) are an expressive constraint language for ontology-mediated query answering and thus query answering is of high complexity. Existing systems based on first-order rewriting methods can lead to queries too large for DBMS to handle. It is shown that datalog rewriting can result in more compact queries, yet previously proposed datalog rewriting methods are mostly inefficient for implementation. In this paper, we fill the gap by proposing an efficient datalog rewriting approach for answering conjunctive queries over TGDs, and identify and combine existing fragments of TGDs for which our rewriting method terminates. We implemented a prototype system Drewer, and experiments show that it is able to handle a wide range of benchmarks in the literature. Moreover, Drewer shows superior performance over state-of-the-art systems on both the compactness of rewriting and the efficiency of query answering.

Merging existential rules programs in multi-agent contexts through credibility accrual

Merging operators represent a significant tool to extract a consistent and informative view from a set of agents. The consideration of practical scenarios where some agents can be more credible than others has contributed to substantially increase the interest in developing systems working with trust models. In this context, we propose an approach to the problem of merging knowledge in a multiagent scenario where every agent assigns to other agents a value reflecting its perception on how credible each agent is. The focus of this paper is the introduction of an operator for merging Datalog± ontologies considering agents’ credibility. We present a procedure to enhance a conflict resolution strategy by exploiting the credibility attached to a set of formulas; the approach is based on accrual functions that calculate the value of formulas according to the credibility of the agents that inform them. We show how our new operator can obtain the best-valued knowledge base among consistent bases available, according to the credibilities attached to the sources.

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.

Restricted Chase Termination for Existential Rules: A Hierarchical Approach and Experimentation

AbstractThe chase procedure for existential rules is an indispensable tool for several database applications, where its termination guarantees the decidability of these tasks. Most previous studies have focused on the skolem chase variant and its termination analysis. It is known that the restricted chase variant is a more powerful tool in termination analysis provided a database is given. But all-instance termination presents a challenge since the critical database and similar techniques do not work. In this paper, we develop a novel technique to characterize the activeness of all possible cycles of a certain length for the restricted chase, which leads to the formulation of a framework of parameterized classes of the finite restricted chase, called $k$-$\mathsf{safe}(\Phi)$ rule sets. This approach applies to any class of finite skolem chase identified with a condition of acyclicity. More generally, we show that the approach can be applied to the hierarchy of bounded rule sets previously only defined for the skolem chase. Experiments on a collection of ontologies from the web show the applicability of the proposed methods on real-world ontologies.

Characterizing Boundedness in Chase Variants

AbstractExistential 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 existence of a bound on the depth of the chase, independently from any set of facts. Deciding if a set of rules is bounded is an undecidable problem for all chase variants. Nevertheless, when computing universal models, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound remains unknown or even very large. Hence, we investigate the decidability of the k-boundedness problem, which asks whether the depth of the chase for a given set of rules is bounded by an integer k. We identify a general property which, when satisfied by a chase variant, leads to the decidability of k-boundedness. We then show that the main chase variants satisfy this property, namely the oblivious, semi-oblivious (aka Skolem), and restricted chase, as well as their breadth-first versions.

Explanations for Inconsistency-Tolerant Query Answering under Existential Rules

Querying inconsistent knowledge bases is a problem that has attracted a great deal of interest over the last decades. While several semantics of query answering have been proposed, and their complexity is rather well-understood, little attention has been paid to the problem of explaining query answers. Explainability has recently become a prominent problem in different areas of AI. In particular, explaining query answers allows users to understand not only what is entailed by an inconsistent knowledge base, but also why. In this paper, we address the problem of explaining query answers for existential rules under three popular inconsistency-tolerant semantics, namely, the ABox repair, the intersection of repairs, and the intersection of closed repairs semantics. We provide a thorough complexity analysis for a wide range of existential rule languages and for different complexity measures.