arXiv subjects

Bernardo Cuenca Grau

Publications and source records attributed to Bernardo Cuenca Grau.

34 records · Page 2Linked to original sources

arXiv2018

The Window Validity Problem in Rule-Based Stream Reasoning

Rule-based temporal query languages provide the expressive power and flexibility required to capture in a natural way complex analysis tasks over streaming data. Stream processing applications, however, typically require near real-time response using limited resources. In particular, it becomes essential that the underpinning query language has favourable computational properties and that stream processing algorithms are able to keep only a small number of previously received facts in memory at any point in time without sacrificing correctness. In this paper, we propose a recursive fragment of temporal Datalog with tractable data complexity and study the properties of a generic stream reasoning algorithm for this fragment. We focus on the window validity problem as a way to minimise the number of time points for which the stream reasoning algorithm needs to keep data in memory at any point in time.

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arXiv2018

Consequence-based Reasoning for Description Logics with Disjunction, Inverse Roles, Number Restrictions, and Nominals

We present a consequence-based calculus for concept subsumption and classification in the description logic ALCHOIQ, which extends ALC with role hierarchies, inverse roles, number restrictions, and nominals. By using standard transformations, our calculus extends to SROIQ, which covers all of OWL 2 DL except for datatypes. A key feature of our calculus is its pay-as-you-go behaviour: unlike existing algorithms, our calculus is worst-case optimal for all the well-known proper fragments of ALCHOIQ, albeit not for the full logic.

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arXiv2018

Stratified Negation in Limit Datalog Programs

There has recently been an increasing interest in declarative data analysis, where analytic tasks are specified using a logical language, and their implementation and optimisation are delegated to a general-purpose query engine. Existing declarative languages for data analysis can be formalised as variants of logic programming equipped with arithmetic function symbols and/or aggregation, and are typically undecidable. In prior work, the language of $\mathit{limit\ programs}$ was proposed, which is sufficiently powerful to capture many analysis tasks and has decidable entailment problem. Rules in this language, however, do not allow for negation. In this paper, we study an extension of limit programs with stratified negation-as-failure. We show that the additional expressive power makes reasoning computationally more demanding, and provide tight data complexity bounds. We also identify a fragment with tractable data complexity and sufficient expressivity to capture many relevant tasks.

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arXiv2017

Foundations of Declarative Data Analysis Using Limit Datalog Programs

Motivated by applications in declarative data analysis, we study $\mathit{Datalog}_{\mathbb{Z}}$---an extension of positive Datalog with arithmetic functions over integers. This language is known to be undecidable, so we propose two fragments. In $\mathit{limit}~\mathit{Datalog}_{\mathbb{Z}}$ predicates are axiomatised to keep minimal/maximal numeric values, allowing us to show that fact entailment is coNExpTime-complete in combined, and coNP-complete in data complexity. Moreover, an additional $\mathit{stability}$ requirement causes the complexity to drop to ExpTime and PTime, respectively. Finally, we show that stable $\mathit{Datalog}_{\mathbb{Z}}$ can express many useful data analysis tasks, and so our results provide a sound foundation for the development of advanced information systems.

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arXiv2017

The Bag Semantics of Ontology-Based Data Access

Ontology-based data access (OBDA) is a popular approach for integrating and querying multiple data sources by means of a shared ontology. The ontology is linked to the sources using mappings, which assign views over the data to ontology predicates. Motivated by the need for OBDA systems supporting database-style aggregate queries, we propose a bag semantics for OBDA, where duplicate tuples in the views defined by the mappings are retained, as is the case in standard databases. We show that bag semantics makes conjunctive query answering in OBDA coNP-hard in data complexity. To regain tractability, we consider a rather general class of queries and show its rewritability to a generalisation of the relational calculus to bags.

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arXiv2016

Extending Consequence-Based Reasoning to SRIQ

Consequence-based calculi are a family of reasoning algorithms for description logics (DLs), and they combine hypertableau and resolution in a way that often achieves excellent performance in practice. Up to now, however, they were proposed for either Horn DLs (which do not support disjunction), or for DLs without counting quantifiers. In this paper we present a novel consequence-based calculus for SRIQ---a rich DL that supports both features. This extension is non-trivial since the intermediate consequences that need to be derived during reasoning cannot be captured using DLs themselves. The results of our preliminary performance evaluation suggest the feasibility of our approach in practice.

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arXiv2015

Controlled Query Evaluation for Datalog and OWL 2 Profile Ontologies

We study confidentiality enforcement in ontologies under the Controlled Query Evaluation framework, where a policy specifies the sensitive information and a censor ensures that query answers that may compromise the policy are not returned. We focus on censors that ensure confidentiality while maximising information access, and consider both Datalog and the OWL 2 profiles as ontology languages.

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arXiv2015

Computing Horn Rewritings of Description Logics Ontologies

We study the problem of rewriting an ontology O1 expressed in a DL L1 into an ontology O2 in a Horn DL L2 such that O1 and O2 are equisatisfiable when extended with an arbitrary dataset. Ontologies that admit such rewritings are amenable to reasoning techniques ensuring tractability in data complexity. After showing undecidability whenever L1 extends ALCF, we focus on devising efficiently checkable conditions that ensure existence of a Horn rewriting. By lifting existing techniques for rewriting Disjunctive Datalog programs into plain Datalog to the case of arbitrary first-order programs with function symbols, we identify a class of ontologies that admit Horn rewritings of polynomial size. Our experiments indicate that many real-world ontologies satisfy our sufficient conditions and thus admit polynomial Horn rewritings.

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arXiv2014

Ontology Module Extraction via Datalog Reasoning

Module extraction - the task of computing a (preferably small) fragment M of an ontology T that preserves entailments over a signature S - has found many applications in recent years. Extracting modules of minimal size is, however, computationally hard, and often algorithmically infeasible. Thus, practical techniques are based on approximations, where M provably captures the relevant entailments, but is not guaranteed to be minimal. Existing approximations, however, ensure that M preserves all second-order entailments of T w.r.t. S, which is stronger than is required in many applications, and may lead to large modules in practice. In this paper we propose a novel approach in which module extraction is reduced to a reasoning problem in datalog. Our approach not only generalises existing approximations in an elegant way, but it can also be tailored to preserve only specific kinds of entailments, which allows us to extract significantly smaller modules. An evaluation on widely-used ontologies has shown very encouraging results.

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arXiv2014

Datalog Rewritability of Disjunctive Datalog Programs and its Applications to Ontology Reasoning

We study the problem of rewriting a disjunctive datalog program into plain datalog. We show that a disjunctive program is rewritable if and only if it is equivalent to a linear disjunctive program, thus providing a novel characterisation of datalog rewritability. Motivated by this result, we propose weakly linear disjunctive datalog---a novel rule-based KR language that extends both datalog and linear disjunctive datalog and for which reasoning is tractable in data complexity. We then explore applications of weakly linear programs to ontology reasoning and propose a tractable extension of OWL 2 RL with disjunctive axioms. Our empirical results suggest that many non-Horn ontologies can be reduced to weakly linear programs and that query answering over such ontologies using a datalog engine is feasible in practice.

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arXiv2014

Acyclicity Notions for Existential Rules and Their Application to Query Answering in Ontologies

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 chase termination. In this paper, we present two new acyclicity notions called model-faithful acyclicity (MFA) and model-summarising acyclicity (MSA). Furthermore, we investigate the landscape of the known acyclicity notions and establish a complete taxonomy of all notions known to us. Finally, we show that MFA and MSA generalise most of these notions. Existential rules are closely related to the Horn fragments of the OWL 2 ontology language; furthermore, several prominent OWL 2 reasoners implement CQ answering by using the chase to materialise all relevant facts. In order to avoid termination problems, many of these systems handle only the OWL 2 RL profile of OWL 2; furthermore, some systems go beyond OWL 2 RL, but without any termination guarantees. In this paper we also investigate whether various acyclicity notions can provide a principled and practical solution to these problems. On the theoretical side, we show that query answering for acyclic ontologies is of lower complexity than for general ontologies. On the practical side, we show that many of the commonly used OWL 2 ontologies are MSA, and that the number of facts obtained by materialisation is not too large. Our results thus suggest that principled development of materialisation-based OWL 2 reasoners is practically feasible.

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arXiv2014

Reasoning over Ontologies with Hidden Content: The Import-by-Query Approach

There is currently a growing interest in techniques for hiding parts of the signature of an ontology Kh that is being reused by another ontology Kv. Towards this goal, in this paper we propose the import-by-query framework, which makes the content of Kh accessible through a limited query interface. If Kv reuses the symbols from Kh in a certain restricted way, one can reason over Kv U Kh by accessing only Kv and the query interface. We map out the landscape of the import-by-query problem. In particular, we outline the limitations of our framework and prove that certain restrictions on the expressivity of Kh and the way in which Kv reuses symbols from Kh are strictly necessary to enable reasoning in our setting. We also identify cases in which reasoning is possible and we present suitable import-by-query reasoning algorithms.

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arXiv2014

Completeness Guarantees for Incomplete Ontology Reasoners: Theory and Practice

To achieve scalability of query answering, the developers of Semantic Web applications are often forced to use incomplete OWL 2 reasoners, which fail to derive all answers for at least one query, ontology, and data set. The lack of completeness guarantees, however, may be unacceptable for applications in areas such as health care and defence, where missing answers can adversely affect the applications functionality. Furthermore, even if an application can tolerate some level of incompleteness, it is often advantageous to estimate how many and what kind of answers are being lost. In this paper, we present a novel logic-based framework that allows one to check whether a reasoner is complete for a given query Q and ontology T---that is, whether the reasoner is guaranteed to compute all answers to Q w.r.t. T and an arbitrary data set A. Since ontologies and typical queries are often fixed at application design time, our approach allows application developers to check whether a reasoner known to be incomplete in general is actually complete for the kinds of input relevant for the application. We also present a technique that, given a query Q, an ontology T, and reasoners R_1 and R_2 that satisfy certain assumptions, can be used to determine whether, for each data set A, reasoner R_1 computes more answers to Q w.r.t. T and A than reasoner R_2. This allows application developers to select the reasoner that provides the highest degree of completeness for Q and T that is compatible with the applications scalability requirements. Our results thus provide a theoretical and practical foundation for the design of future ontology-based information systems that maximise scalability while minimising or even eliminating incompleteness of query answers.

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arXiv2013

Computing Datalog Rewritings beyond Horn Ontologies

Rewriting-based approaches for answering queries over an OWL 2 DL ontology have so far been developed mainly for Horn fragments of OWL 2 DL. In this paper, we study the possibilities of answering queries over non-Horn ontologies using datalog rewritings. We prove that this is impossible in general even for very simple ontology languages, and even if PTIME = NP. Furthermore, we present a resolution-based procedure for $\SHI$ ontologies that, in case it terminates, produces a datalog rewriting of the ontology. Our procedure necessarily terminates on DL-Lite_{bool}^H ontologies---an extension of OWL 2 QL with transitive roles and Boolean connectives.

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arXiv2012

Evaluating Ontology Matching Systems on Large, Multilingual and Real-world Test Cases

In the field of ontology matching, the most systematic evaluation of matching systems is established by the Ontology Alignment Evaluation Initiative (OAEI), which is an annual campaign for evaluating ontology matching systems organized by different groups of researchers. In this paper, we report on the results of an intermediary OAEI campaign called OAEI 2011.5. The evaluations of this campaign are divided in five tracks. Three of these tracks are new or have been improved compared to previous OAEI campaigns. Overall, we evaluated 18 matching systems. We discuss lessons learned, in terms of scalability, multilingual issues and the ability do deal with real world cases from different domains.

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arXiv2010

First steps in the logic-based assessment of post-composed phenotypic descriptions

In this paper we present a preliminary logic-based evaluation of the integration of post-composed phenotypic descriptions with domain ontologies. The evaluation has been performed using a description logic reasoner together with scalable techniques: ontology modularization and approximations of the logical difference between ontologies.

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