Inconsistent Knowledge Bases Research Articles

Selecting accepted assertions in partially ordered inconsistent DL-Lite knowledge bases

The problem of inconsistency handling in knowledge bases has received considerable research attention in several settings and has met many applications. Inconsistency usually stems from the fact that the information available for reasoning, query answering and decision-making tasks is obtained from different, scattered and potentially unreliable information sources. Performing these tasks is often computationally expensive, especially for knowledge bases in which the data is endowed with preferences and/or uncertainty. In the context of formal ontologies, enriching the assertions (i.e. the data pieces) with conceptual knowledge makes the query answering task harder computationally. Tractable results have been successfully established for the lightweight languages of the DL-Lite family. In this paper, we present two tractable methods for handling inconsistency in partially ordered lightweight ontologies. In essence, both methods are inspired from the well-known Intersection of ABox Repair (IAR) semantics, which proceeds by replacing the initial inconsistent knowledge base with the intersection of all of its maximally consistent sub-bases. The first method assumes a partial preorder over the knowledge base and identifies the accepted assertions, called ‘elected’, in polynomial time in data complexity. The second method captures uncertainty quantitatively in the framework of possibility theory and identifies the so-called ‘π-accepted’ assertions, also in polynomial time in data complexity. However, both characterisations require the conflict set to be readily available. This constitutes a serious limitation in frameworks and applications where the conflict set cannot be exhibited efficiently. In this paper, we propose a new and equivalent characterisation for each method. We show that the elected assertions and also the π-accepted assertions can be identified in polynomial time in the size of the dataset for lightweight ontologies.

Evaluating the role of the diagnostic radiographer in identifying child safeguarding concerns: A knowledge, attitude and practice survey approach

IntroductionChild safeguarding and the appropriate identification of suspected victims represents a global phenomenon. Diagnostic imaging is acknowledged as a contributory diagnostic service but the role of the radiographer in the identification and escalation process is less well understood. MethodA Knowledge, Attitude and Practice (KAP) survey was constructed to evaluate knowledge base in the context of the patient–radiographer interaction, the shaping of attitude towards child safeguarding and attitudes held towards their role plus the actual practical experiences of managing child safeguarding concerns. ResultsRespondents demonstrated a inconsistent knowledge base with respect to physical, social and radiographic signs and symptoms of child safeguarding concern. A positive attitude towards the role of the radiographer in child safeguarding was demonstrated but one that was shaped more by experience than pre-registration education.Assessment of concerns was chiefly influenced by clinical history and appreciation of aetiology. Practically, radiographers have infrequent involvement with the identification and escalation of concerns. Whilst some statistically significant relationships between responses and demographics did exist, these were either sporadic or argued to be a result of natural variation. ConclusionAssessment of physical and social signs of child safeguarding concern are argued to be becoming more challenging. Radiological signs continue to be visible to radiographers but with increasing use of other imaging modalities these signs are becoming more varied in nature and are providing new challenges. Radiographers are capable of escalation when required to do so. Implications for practiceTo maximise the contribution of the profession, education needs to account for imaging modality worked with, in combination with an understanding of related aetiology. Previously existing concerns with respect to escalating processes are no longer in evidence and radiographers are both willing and able to contribute to that process.

Paraconsistent inference relations induced from inconsistency measures

This article presents a family of paraconsistent inference relations which aim at reasoning with inconsistent knowledge bases. These inference relations are defined from inconsistency measures. We check under which conditions these inference relations satisfy a series of properties for nonmonotonic reasoning. We also show that they are paraconsistent when the corresponding inconsistency measures satisfy some rationality postulates, and even strictly paraconsistent in most cases. In addition, some dependencies and incompatibilities among some rationality postulates are shown.

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.

Handling temporality in human activity reasoning

Human-aware Artificial Intelligent systems are goal directed autonomous systems that are capable of interacting, collaborating, and teaming with humans. Activity reasoning is a formal reasoning approach that aims to provide common sense reasoning capabilities to these interactive and intelligent systems. This reasoning can be done by considering evidences –which may be conflicting–related to activities a human performs. In this context, it is important to consider the temporality of such evidence in order to distinguish activities and to analyse the relations between activities. Our approach is based on formal argumentation reasoning, specifically, Timed Argumentation Frameworks (TAF), which is an appropriate technique for dealing with inconsistencies in knowledge bases. Our approach involves two steps: local selection and global selection. In the local selection, a model of the world and of the human’s mind is constructed in form of hypothetical fragments of activities (pieces of evidences) by considering a set of observations. These hypothetical fragments have two kinds of relations: a conflict relation and a temporal relation. Based on these relations, the argumentation attack notion is defined. We define two forms of attacks namely the strong and the weak attack. The former has the same characteristics of attacks in TAF whereas for the latter the TAF approach has to be extended. For determining consistent sets of hypothetical fragments, that are part of an activity or are part of a set of non-conflicting activities, extension-based argumentation semantics are applied. In the global selection, the degrees of fulfillment of activities is determined. We study some properties of our approach and apply it to a scenario where a human performs activities with different temporal relations.

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.

On quasi-inconsistency and its complexity

We address the issue of analyzing potential inconsistencies in knowledge bases. This refers to knowledge bases that contain rules which will always be activated together, and the knowledge base will become inconsistent, should these rules be activated. We investigate this problem in the context of the industrial use-case of business rule management, where it is often required that sets of (only) rules are analyzed for potential inconsistencies, e.g., during business rule modelling. To this aim, we introduce the notion of quasi-inconsistency, which is a formalization of the above-mentioned problem of potential inconsistencies. We put a specific focus on the analysis of computational complexity of some involved problems and show that many of them are intractable.

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.

An Argumentation-Based Approach for Computing Inconsistency Degree in Possibilistic Lightweight Ontologies

Reasoning with inconsistent ontologies plays an important role in Semantic Web applications. An important feature of argument theory is that it is able to naturally handle inconsistencies in ontologies and allows a user to represent information in the form of an argument. In argumentation, given an inconsistent knowledge base, arguments compete to decide which are the accepted consequences. In this paper, we are interested in using the argumentation for the inconsistency degree of uncertain knowledge bases expressed in possibilistic DL-Lite (the key notion in reasoning from a possibilistic DL-Lite knowledge base) without going through the negative closure. In the present work, the terminological base is assumed to be fully certain and the uncertainty is only considered on the assertion based. We proved that it is coherent and feasible to use Dung’s abstract argumentation theory to compute the inconsistency degree and how argumentation semantics relate to the state of the art of handling inconsistency.

Pareto optimality and strategy-proofness in group argument evaluation

An inconsistent knowledge base can be abstracted as a set of arguments and a defeat relation among them. There can be more than one consistent way to evaluate such an argumentation graph. Collective argument evaluation is the problem of aggregating the opinions of multiple agents on how a given set of arguments should be evaluated. It is crucial not only to ensure that the outcome is logically consistent, but also satisfies measures of social optimality and immunity to strategic manipulation. This is because agents have their individual preferences about what the outcome ought to be. In the current paper, we analyze three previously introduced argument-based aggregation operators with respect to Pareto optimality and strategy proofness under different general classes of agent preferences. We highlight fundamental trade-offs between strategic manipulability and social optimality on one hand, and classical logical criteria on the other. Our results motivate further investigation into the relationship between social choice and argumentation theory. The results are also relevant for choosing an appropriate aggregation operator given the criteria that are considered more important, as well as the nature of agents' preferences.

Explanatory dialogues with argumentative faculties over inconsistent knowledge bases

We introduce a formal model of explanatory dialogue called EDS. We extend this model by including argumentation capacities to facilitate knowledge acquisition in inconsistent knowledge bases. To prove the relevance of such model we provide the dalek (DiALectical Explanation in Knowledge-bases) framework that implements this model. We show the usefulness of the framework on a real-world application in the domain of Durum Wheat sustainability improvement within the ANR (French National Agency) funded Dur-Dur project. The preliminary pilot evaluation of the framework with agronomy experts gives a promising indication on the impact of explanation dialogues on the improvement of the knowledge’s content.

Localising iceberg inconsistencies

In artificial intelligence, it is important to handle and analyse inconsistency in knowledge bases. Inconsistent pieces of information suggest questions like “where is the inconsistency?” and “how severe is it?”. Inconsistency measures have been proposed to tackle the latter issue, but the former seems underdeveloped and is the focus of this paper. Minimal inconsistent sets have been the main tool to localise inconsistency, but we argue that they are like the exposed part of an iceberg, failing to capture contradictions hidden under the water. Using classical propositional logic, we develop methods to characterise when a formula is contributing to the inconsistency in a knowledge base and when a set of formulas can be regarded as a primitive conflict. To achieve this, we employ an abstract consequence operation to “look beneath the water level”, generalising the minimal inconsistent set concept and the related free formula notion. We apply the framework presented to the problem of measuring inconsistency in knowledge bases, putting forward relaxed forms for two debatable postulates for inconsistency measures. Finally, we discuss the computational complexity issues related to the introduced concepts.

Big Graph Analyses: From Queries to Dependencies and Association Rules

This position paper provides an overview of our recent advances in the study of big graphs, from theory to systems to applications. We introduce a theory of bounded evaluability, to query big graphs by accessing a bounded amount of the data. Based on this, we propose a framework to query big graphs with constrained resources. Beyond queries, we propose functional dependencies for graphs, to detect inconsistencies in knowledge bases and catch spams in social networks. As an example application of big graph analyses, we extend association rules from itemsets to graphs for social media marketing. We also identify open problems in connection with querying, cleaning and mining big graphs.

A distance-based framework for inconsistency-tolerant reasoning and inconsistency measurement in DL-Lite

In this paper, we present a distance-based framework for DL-Lite based on the notion of features. Within this framework, we propose a distance-based paraconsistent semantics for DL-Lite where meaningful conclusions can be rationally drawn even from an inconsistent knowledge base and we develop a distance-based inconsistency measurement for DL-Lite to provide more informative metrics which can tell the differences between axioms causing inconsistency and among inconsistent knowledge. Furthermore, we investigate several important logical properties (e.g., consistency preservation, closure consistency, splitting property etc.) of the entailment relation based on the new semantics and show its advantages in non-monotonic reasoning for DL-Lite. Finally, we show that our two distance-based inconsistency measures are basic inconsistency measures where some good properties hold such as Free Axiom Independence and Dominance of inconsistency etc.

Stream-based inconsistency measurement

Inconsistency measures have been proposed to assess the severity of inconsistencies in knowledge bases of classical logic in a quantitative way. In general, computing the value of inconsistency is a computationally hard task as it is based on the satisfiability problem which is itself NP-complete. In this work, we address the problem of measuring inconsistency in knowledge bases that are accessed in a stream of propositional formulæ. That is, the formulæ of a knowledge base cannot be accessed directly but only once through processing of the stream. This work is a first step towards practicable inconsistency measurement for applications such as Linked Open Data, where huge amounts of information is distributed across the web and a direct assessment of the quality or inconsistency of this information is infeasible due to its size. Here we discuss the problem of stream-based inconsistency measurement on classical logic, in order to make use of existing measures for classical logic. However, it turns out that inconsistency measures defined on the notion of minimal inconsistent subsets are usually not apt to be used in the streaming scenario. In order to address this issue, we adapt measures defined on paraconsistent logics and also present a novel inconsistency measure based on the notion of a hitting set. We conduct an extensive empirical analysis on the behavior of these different inconsistency measures in the streaming scenario, in terms of runtime, accuracy, and scalability. We conclude that for two of these measures, the stream-based variant of the new inconsistency measure and the stream-based variant of the contension inconsistency measure, large-scale inconsistency measurement in streaming scenarios is feasible.

A Dialogue System for Coherent Reasoning with Inconsistent Knowledge Bases

Traditionally, the AI community assumes that a knowledge base must be consistent. Despite that, there are many applications where, due to the existence of rules with exceptions, inconsistent knowledge must be considered. One way of restoring consistency is to withdraw conflicting rules; however, this will destroy part of the knowledge. Indeed, a better alternative would be to give precedence to exceptions. This paper proposes a dialogue system for coherent reasoning with inconsistent knowledge, which resolves conflicts by using precedence relations of three kinds: explicit precedence relation, which is synthesized from precedence rules; implicit precedence relation, which is synthesized from defeasible rules; mixed precedence relation, which is synthesized by combining explicit and implicit precedence relations.

Dynamic Consistency Checking in Goal-Directed Answer Set Programming

AbstractIn answer set programming, inconsistencies arise when the constraints placed on a program become unsatisfiable. In this paper, we introduce a technique fordynamic consistency checkingfor our goal-directed method for computing answer sets, under which only those constraints deemed relevant to the partial answer set are tested, allowing inconsistent knowledgebases to be successfully queried. However, the algorithm guarantees that, if a program has at least one consistent answer set, any partial answer set returned will be a subset of some consistent answer set.

Rich preference-based argumentation frameworks

An argumentation framework is seen as a directed graph whose nodes are arguments and arcs are attacks between the arguments. Acceptable sets of arguments, called extensions, are computed using a semantics. Existing semantics are solely based on the attacks and do not take into account other important criteria like the intrinsic strengths of arguments.The contribution of this paper is three fold. First, we study how preferences issued from differences in strengths of arguments can help in argumentation frameworks. We show that they play two distinct and complementary roles: (i) to repair the attack relation between arguments, (ii) to refine the evaluation of arguments. Despite the importance of both roles, only the first one is tackled in existing literature. In a second part of this paper, we start by showing that existing models that repair the attack relation with preferences do not perform well in certain situations and may return counter-intuitive results. We then propose a new abstract and general framework which treats properly both roles of preferences. The third part of this work is devoted to defining a bridge between the argumentation-based and the coherence-based approaches for handling inconsistency in knowledge bases, in particular when priorities between formulae are available. We focus on two well-known models, namely the preferred sub-theories introduced by Brewka and the demo-preferred sets defined by Cayrol, Royer and Saurel. For each of these models, we provide an instantiation of our abstract framework which is in full correspondence with it.

Identifying the Class of Maxi-Consistent Operators in Argumentation

Dung’s abstract argumentation theory can be seen as a general framework for non-monotonic reasoning. An important question is then: what is the class of logics that can be subsumed as instantiations of this theory? The goal of this paper is to identify and study the large class of logic-based instantiations of Dung’s theory which correspond to the maxi-consistent operator, i.e. to the function which returns maximal consistent subsets of an inconsistent knowledge base. In other words, we study the class of instantiations where very extension of the argumentation system corresponds to exactly one maximal consistent subset of the knowledge base. We show that an attack relation belonging to this class must be conflict-dependent, must not be valid, must not be conflict-complete, must not be symmetric etc. Then, we show that some attack relations serve as lower or upper bounds of the class (e.g. if an attack relation contains canonical undercut then it is not a member of this class). By using our results, we show for all existing attack relations whether or not they belong to this class. We also define new attack relations which are members of this class. Finally, we interpret our results and discuss more general questions, like: what is the added value of argumentation in such a setting? We believe that this work is a first step towards achieving our long-term goal, which is to better understand the role of argumentation and, particularly, the expressivity of logic-based instantiations of Dung-style argumentation frameworks.

Inconsistency measures for probabilistic logics

Inconsistencies in knowledge bases are of major concern in knowledge representation and reasoning. In formalisms that employ model-based reasoning mechanisms inconsistencies render a knowledge base useless due to the non-existence of a model. In order to restore consistency an analysis and understanding of inconsistencies are mandatory. Recently, the field of inconsistency measurement has gained some attention for knowledge representation formalisms based on classical logic. An inconsistency measure is a tool that helps the knowledge engineer in obtaining insights into inconsistencies by assessing their severity. In this paper, we investigate inconsistency measurement in probabilistic conditional logic, a logic that incorporates uncertainty and focuses on the role of conditionals, i.e. if–then rules. We do so by extending inconsistency measures for classical logic to the probabilistic setting. Further, we propose novel inconsistency measures that are specifically tailored for the probabilistic case. These novel measures use distance measures to assess the distance of a knowledge base to a consistent one and therefore takes the crucial role of probabilities into account. We analyze the properties of the discussed measures and compare them using a series of rationality postulates.