Inconsistency-tolerant Semantics Research Articles

An argumentative approach for handling inconsistency in prioritized Datalog ± ontologies

Prioritized Datalog ± is a well-studied formalism for modelling ontological knowledge and data, and has a success story in many applications in the (Semantic) Web and in other domains. Since the information content on the Web is both inherently context-dependent and frequently updated, the occurrence of a logical inconsistency is often inevitable. This phenomenon has led the research community to develop various types of inconsistency-tolerant semantics over the last few decades. Although the study of query answering under inconsistency-tolerant semantics is well-understood, the problem of explaining query answering under such semantics took considerably less attention, especially in the scenario where the facts are prioritized. In this paper, we aim to fill this gap. More specifically, we use Dung’s abstract argumentation framework to address the problem of explaining inconsistency-tolerant query answering in Datalog ± KB where facts are prioritized, or preordered. We clarify the relationship between preferred repair semantics and various notions of extensions for argumentation frameworks. The strength of such argumentation-based approach is the explainability; users can more easily understand why different points of views are conflicting and why the query answer is entailed (or not) under different semantics. To this end we introduce the formal notion of a dialogical explanation, and show how it can be used to both explain showing why query results hold and not hold according to the known semantics in inconsistent Datalog ± knowledge bases.

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.

Conflict-Based Inconsistency-Tolerant Query Answering

In this paper, we place ourselves in the context of inconsistency-tolerant query answering over lightweight ontologies, which aims to query a set of conflicting facts using an ontology that represents generic knowledge about a particular domain. Existing inconsistency-tolerant semantics typically consist in selecting some of (maximal) consistent subsets of facts, called repairs. We explore a novel strategy to select the most relevant repairs based on the stratification of the assertional base into priority levels that we automatically induce from the ontology. We propose a method that exploits conflict statistical regularities between facts to induce an embedding, in which each fact is represented by a vector. Based on Euclidean distances between facts, we classify the assertions from the most reliable to the least important ones. We then use these distances to define relevant repairs. Interestingly enough, we show that the obtained repair is done in polynomial time.

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.

On the Complexity of Consistent Query Answering in the Presence of Simple Ontologies

Consistent query answering is a standard approach for producing meaningful query answers when data is inconsistent. Recent work on consistent query answering in the presence of ontologies has shown this problem to be intractable in data complexity even for ontologies expressed in lightweight description logics. In order to better understand the source of this intractability, we investigate the complexity of consistent query answering for simple ontologies consisting only of class subsumption and class disjointness axioms. We show that for conjunctive queries with at most one quantified variable, the problem is first-order expressible; for queries with at most two quantified variables, the problem has polynomial data complexity but may not be first-order expressible; and for three quantified variables, the problem may become co-NP-hard in data complexity. For queries having at most two quantified variables, we further identify a necessary and sufficient condition for first-order expressibility. In order to be able to handle arbitrary conjunctive queries, we propose a novel inconsistency-tolerant semantics and show that under this semantics, first-order expressibility is always guaranteed. We conclude by extending our positive results to DL-Lite ontologies without inverse.

A Short Survey on Inconsistency Handling in Ontology-Mediated Query Answering

This paper provides a concise overview of the literature on inconsistency handling for ontology-mediated query answering, a topic which has grown into an active area of research over the last decade. The focus of this survey is on the case where errors are localized in the data (i.e., the ontology is deemed reliable) and where inconsistency-tolerant semantics are employed with the aim of obtaining meaningful information from inconsistent knowledge bases.

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.

Ontology-mediated query answering over temporal and inconsistent data

Stream-based reasoning systems process data stemming from different sources that are received over time. In this kind of applications, reasoning needs to cope with the temporal dimension and should be resilient against inconsistencies in the data. Motivated by such settings, this paper addresses the problem of handling inconsistent data in a temporal version of ontology-mediated query answering. We consider a recently proposed temporal query language that combines conjunctive queries with operators of propositional linear temporal logic (LTL), and consider these under three inconsistency-tolerant semantics that have been introduced for querying inconsistent description logic knowledge bases. We investigate their complexity for temporal EL ⊥ and DL-LiteR knowledge bases. In particular, we consider two different cases, depending on the presence of negations in the query. Furthermore, we complete the complexity picture for the consistent case. We also provide two approaches toward practical algorithms for inconsistency-tolerant temporal query answering.

Computing and Explaining Query Answers over Inconsistent DL-Lite Knowledge Bases


 
 
 Several inconsistency-tolerant semantics have been introduced for querying inconsistent description logic knowledge bases. The first contribution of this paper is a practical approach for computing the query answers under three well-known such semantics, namely the AR, IAR and brave semantics, in the lightweight description logic DL-LiteR. We show that query answering under the intractable AR semantics can be performed efficiently by using IAR and brave semantics as tractable approximations and encoding the AR entailment problem as a propositional satisfiability (SAT) problem. The second issue tackled in this work is explaining why a tuple is a (non-)answer to a query under these semantics. We define explanations for positive and negative answers under the brave, AR and IAR semantics. We then study the computational properties of explanations in DL-LiteR. For each type of explanation, we analyze the data complexity of recognizing (preferred) explanations and deciding if a given assertion is relevant or necessary. We establish tight connections between intractable explanation problems and variants of SAT, enabling us to generate explanations by exploiting solvers for Boolean satisfaction and optimization problems. Finally, we empirically study the efficiency of our query answering and explanation framework using a benchmark we built upon the well-established LUBM benchmark.
 
 

A Framework and Positive Results for IAR-answering

Inconsistency-tolerant semantics, like the IAR semantics, have been proposed as means to compute meaningful query answers over inconsistent Description Logic (DL) ontologies. So far query answering under the IAR semantics (IAR-answering) is known to be tractable only for arguably weak DLs like DL-Lite and the quite restricted EL⊥nr fragment of EL⊥. Towards providing a systematic study of IAR-answering, in the current paper we first present a general framework/algorithm for IAR-answering which applies to arbitrary DLs but need not terminate. Nevertheless, this framework allows us to develop a sufficient condition for tractability of IAR-answering and hence of termination of our algorithm. We then show that this condition is always satisfied by the arguably expressive DL DL-Litebool, providing the first positive result for IAR-answering over a non-Horn-DL. In addition, recent results show that this condition usually holds for real-world ontologies and techniques and algorithms for checking it in practice have also been studied recently; thus, overall our results are highly relevant in practice. Finally, we have provided a prototype implementation and a preliminary evaluation obtaining encouraging results.

How does incoherence affect inconsistency-tolerant semantics for Datalog±?

Fil: Deagustini, Cristhian Ariel David. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Bahia Blanca. Instituto de Ciencias e Ingenieria de la Computacion. Universidad Nacional del Sur. Departamento de Ciencias e Ingenieria de la Computacion. Instituto de Ciencias e Ingenieria de la Computacion; Argentina. Universidad Nacional de Entre Rios. Facultad de Ciencias de la Administracion; Argentina

Explaining Inconsistency-Tolerant Query Answering over Description Logic Knowledge Bases

Several inconsistency-tolerant semantics have been introduced for querying inconsistent description logic knowledge bases. This paper addresses the problem of explaining why a tuple is a (non-)answer to a query under such semantics. We define explanations for positive and negative answers under the brave, AR and IAR semantics. We then study the computational properties of explanations in the lightweight description logic DL-Lite_R. For each type of explanation, we analyze the data complexity of recognizing (preferred) explanations and deciding if a given assertion is relevant or necessary. We establish tight connections between intractable explanation problems and variants of propositional satisfiability (SAT), enabling us to generate explanations by exploiting solvers for Boolean satisfaction and optimization problems. Finally, we empirically study the efficiency of our explanation framework using the well-established LUBM benchmark.

A Graph-Based Approach for Query Answering Under Inconsistency-Tolerant Semantics

A Graph-Based Approach for Query Answering Under Inconsistency-Tolerant Semantics

Inconsistency-tolerant query answering in ontology-based data access

Ontology-based data access (OBDA) is receiving great attention as a new paradigm for managing information systems through semantic technologies. According to this paradigm, a Description Logic ontology provides an abstract and formal representation of the domain of interest to the information system, and is used as a sophisticated schema for accessing the data and formulating queries over them. In this paper, we address the problem of dealing with inconsistencies in OBDA. Our general goal is both to study DL semantical frameworks that are inconsistency-tolerant, and to devise techniques for answering unions of conjunctive queries under such inconsistency-tolerant semantics. Our work is inspired by the approaches to consistent query answering in databases, which are based on the idea of living with inconsistencies in the database, but trying to obtain only consistent information during query answering, by relying on the notion of database repair. We first adapt the notion of database repair to our context, and show that, according to such a notion, inconsistency-tolerant query answering is intractable, even for very simple DLs. Therefore, we propose a different repair-based semantics, with the goal of reaching a good compromise between the expressive power of the semantics and the computational complexity of inconsistency-tolerant query answering. Indeed, we show that query answering under the new semantics is first-order rewritable in OBDA, even if the ontology is expressed in one of the most expressive members of the DL-Lite family.

Towards Tractable and Practical ABox Abduction over Inconsistent Description Logic Ontologies

ABox abduction plays an important role in reasoning over description logic (DL) ontologies. However, it does not work with inconsistent DL ontologies. To tackle this problem while achieving tractability, we generalize ABox abduction from the classical semantics to an inconsistency-tolerant semantics, namely the Intersection ABox Repair (IAR) semantics, and propose the notion of IAR-explanations in inconsistent DL ontologies. We show that computing all minimal IAR-explanations is tractable in data complexity for first-order rewritable ontologies. However, the computational method may still not be practical due to a possibly large number of minimal IAR-explanations. Hence we propose to use preference information to reduce the number of explanations to be computed.

From Classical to Consistent Query Answering under Existential Rules

Querying inconsistent ontologies is an intriguing new problem that gave rise to a flourishing research activity in the description logic (DL) community. The computational complexity of consistent query answering under the main DLs is rather well understood; however, little is known about existential rules. The goal of the current work is to perform an in-depth analysis of the complexity of consistent query answering under the main decidable classes of existential rules enriched with negative constraints. Our investigation focuses on one of the most prominent inconsistency-tolerant semantics, namely, the AR semantics. We establish a generic complexity result, which demonstrates the tight connection between classical and consistent query answering. This result allows us to obtain in a uniform way a relatively complete picture of the complexity of our problem.

Inconsistency-Tolerant Query Answering in Ontology-Based Data Access

Ontology-based data access (OBDA) is receiving great attention as a new paradigm for managing information systems through semantic technologies. According to this paradigm, a Description Logic ontology provides an abstract and formal representation of the domain of interest to the information system, and is used as a sophisticated schema for accessing the data and formulating queries over them. In this paper, we address the problem of dealing with inconsistencies in OBDA. Our general goal is both to study DL semantical frameworks that are inconsistency-tolerant, and to devise techniques for answering unions of conjunctive queries under such inconsistency-tolerant semantics. Our work is inspired by the approaches to consistent query answering in databases, which are based on the idea of living with inconsistencies in the database, but trying to obtain only consistent information during query answering, by relying on the notion of database repair. We first adapt the notion of database repair to our context, and show that, according to such a notion, inconsistency-tolerant query answering is intractable, even for very simple DLs. Therefore, we propose a different repair-based semantics, with the goal of reaching a good compromise between the expressive power of the semantics and the computational complexity of inconsistency-tolerant query answering. Indeed, we show that query answering under the new semantics is first-order rewritable in OBDA, even if the ontology is expressed in one of the most expressive members of the DL-Lite family.

Querying Inconsistent Description Logic Knowledge Bases under Preferred Repair Semantics

Recently several inconsistency-tolerant semantics have been introduced for querying inconsistent description logic knowledge bases. Most of these semantics rely on the notion of a repair, defined as an inclusion-maximal subset of the facts (ABox) which is consistent with the ontology (TBox). In this paper, we study variants of two popular inconsistency-tolerant semantics obtained by replacing classical repairs by various types of preferred repair. We analyze the complexity of query answering under the resulting semantics, focusing on the lightweight logic DL-Lite_R. Unsurprisingly, query answering is intractable in all cases, but we nonetheless identify one notion of preferred repair, based upon priority levels, whose data complexity is "only" coNP-complete. This leads us to propose an approach combining incomplete tractable methods with calls to a SAT solver. An experimental evaluation of the approach shows good scalability on realistic cases.