75 research outputs found

    Probabilistic description logics for subjective uncertainty

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    We propose a family of probabilistic description logics (DLs) that are derived in a principled way from Halpern's probabilistic first-order logic. The resulting probabilistic DLs have a two-dimensional semantics similar to temporal DLs and are well-suited for representing subjective probabilities. We carry out a detailed study of reasoning in the new family of logics, concentrating on probabilistic extensions of the DLs ALC and EL, and showing that the complexity ranges from PTime via ExpTime and 2ExpTime to undecidable

    Heuristic Ranking in Tightly Coupled Probabilistic Description Logics

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    The Semantic Web effort has steadily been gaining traction in the recent years. In particular,Web search companies are recently realizing that their products need to evolve towards having richer semantic search capabilities. Description logics (DLs) have been adopted as the formal underpinnings for Semantic Web languages used in describing ontologies. Reasoning under uncertainty has recently taken a leading role in this arena, given the nature of data found on theWeb. In this paper, we present a probabilistic extension of the DL EL++ (which underlies the OWL2 EL profile) using Markov logic networks (MLNs) as probabilistic semantics. This extension is tightly coupled, meaning that probabilistic annotations in formulas can refer to objects in the ontology. We show that, even though the tightly coupled nature of our language means that many basic operations are data-intractable, we can leverage a sublanguage of MLNs that allows to rank the atomic consequences of an ontology relative to their probability values (called ranking queries) even when these values are not fully computed. We present an anytime algorithm to answer ranking queries, and provide an upper bound on the error that it incurs, as well as a criterion to decide when results are guaranteed to be correct.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence (UAI2012

    Ontology-Based Query Answering for Probabilistic Temporal Data: Extended Version

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    We investigate ontology-based query answering for data that are both temporal and probabilistic, which might occur in contexts such as stream reasoning or situation recognition with uncertain data. We present a framework that allows to represent temporal probabilistic data, and introduce a query language with which complex temporal and probabilistic patterns can be described. Specifically, this language combines conjunctive queries with operators from linear time logic as well as probability operators. We analyse the complexities of evaluating queries in this language in various settings. While in some cases, combining the temporal and the probabilistic dimension in such a way comes at the cost of increased complexity, we also determine cases for which this increase can be avoided.This is an extended version of the article to appear in the proceedings of AAAI 2019

    Reasoning in Many Dimensions : Uncertainty and Products of Modal Logics

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    Probabilistic Description Logics (ProbDLs) are an extension of Description Logics that are designed to capture uncertainty. We study problems related to these logics. First, we investigate the monodic fragment of Probabilistic first-order logic, show that it has many nice properties, and are able to explain the complexity results obtained for ProbDLs. Second, in order to identify well-behaved, in best-case tractable ProbDLs, we study the complexity landscape for different fragments of ProbEL; amongst others, we are able to identify a tractable fragment. We then study the reasoning problem of ontological query answering, but apply it to probabilistic data. Therefore, we define the framework of ontology-based access to probabilistic data and study the computational complexity therein. In the final part of the thesis, we study the complexity of the satisfiability problem in the two-dimensional modal logic KxK. We are able to close a gap that has been open for more than ten years

    Ontology-Mediated Query Answering for Probabilistic Temporal Data with EL Ontologies: Extended Version

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    Especially in the field of stream reasoning, there is an increased interest in reasoning about temporal data in order to detect situations of interest or complex events. Ontologies have been proved a useful way to infer missing information from incomplete data, or simply to allow for a higher order vocabulary to be used in the event descriptions. Motivated by this, ontology-based temporal query answering has been proposed as a means for the recognition of situations and complex events. But often, the data to be processed do not only contain temporal information, but also probabilistic information, for example because of uncertain sensor measurements. While there has been a plethora of research on ontologybased temporal query answering, only little is known so far about querying temporal probabilistic data using ontologies. This work addresses this problem by introducing a temporal query language that extends a well-investigated temporal query language with probability operators, and investigating the complexity of answering queries using this query language together with ontologies formulated in the description logic EL

    Completion-based computation of most specific concepts with limited role-depth for EL and Prob-EL⁰¹

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    In Description Logics the reasoning service most specific concept (msc) constructs a concept description that generalizes an ABox individual into a concept description. For the Description Logic EL the msc may not exist, if computed with respect to general EL-TBoxes or cyclic ABoxes. However, it is still possible to find a concept description that is the msc up to a fixed role-depth, i.e. with respect to a maximal nesting of quantifiers. In this report we present a practical approach for computing the roledepth bounded msc, based on the polynomial-time completion algorithm for EL. We extend these methods to Prob-EL⁰¹c , which is a probabilistic variant of EL. Together with the companion report [9] this report devises computation methods for the bottom-up construction of knowledge bases for EL and Prob-EL⁰¹c

    Reasoning in Description Logic Ontologies for Privacy Management

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    A rise in the number of ontologies that are integrated and distributed in numerous application systems may provide the users to access the ontologies with different privileges and purposes. In this situation, preserving confidential information from possible unauthorized disclosures becomes a critical requirement. For instance, in the clinical sciences, unauthorized disclosures of medical information do not only threaten the system but also, most importantly, the patient data. Motivated by this situation, this thesis initially investigates a privacy problem, called the identity problem, where the identity of (anonymous) objects stored in Description Logic ontologies can be revealed or not. Then, we consider this problem in the context of role-based access control to ontologies and extend it to the problem asking if the identity belongs to a set of known individuals of cardinality smaller than the number k. If it is the case that some confidential information of persons, such as their identity, their relationships or their other properties, can be deduced from an ontology, which implies that some privacy policy is not fulfilled, then one needs to repair this ontology such that the modified one complies with the policies and preserves the information from the original ontology as much as possible. The repair mechanism we provide is called gentle repair and performed via axiom weakening instead of axiom deletion which was commonly used in classical approaches of ontology repair. However, policy compliance itself is not enough if there is a possible attacker that can obtain relevant information from other sources, which together with the modified ontology still violates the privacy policies. Safety property is proposed to alleviate this issue and we investigate this in the context of privacy-preserving ontology publishing. Inference procedures to solve those privacy problems and additional investigations on the complexity of the procedures, as well as the worst-case complexity of the problems, become the main contributions of this thesis.:1. Introduction 1.1 Description Logics 1.2 Detecting Privacy Breaches in Information System 1.3 Repairing Information Systems 1.4 Privacy-Preserving Data Publishing 1.5 Outline and Contribution of the Thesis 2. Preliminaries 2.1 Description Logic ALC 2.1.1 Reasoning in ALC Ontologies 2.1.2 Relationship with First-Order Logic 2.1.3. Fragments of ALC 2.2 Description Logic EL 2.3 The Complexity of Reasoning Problems in DLs 3. The Identity Problem and Its Variants in Description Logic Ontologies 3.1 The Identity Problem 3.1.1 Description Logics with Equality Power 3.1.2 The Complexity of the Identity Problem 3.2 The View-Based Identity Problem 3.3 The k-Hiding Problem 3.3.1 Upper Bounds 3.3.2 Lower Bound 4. Repairing Description Logic Ontologies 4.1 Repairing Ontologies 4.2 Gentle Repairs 4.3 Weakening Relations 4.4 Weakening Relations for EL Axioms 4.4.1 Generalizing the Right-Hand Sides of GCIs 4.4.2 Syntactic Generalizations 4.5 Weakening Relations for ALC Axioms 4.5.1 Generalizations and Specializations in ALC w.r.t. Role Depth 4.5.2 Syntactical Generalizations and Specializations in ALC 5. Privacy-Preserving Ontology Publishing for EL Instance Stores 5.1 Formalizing Sensitive Information in EL Instance Stores 5.2 Computing Optimal Compliant Generalizations 5.3 Computing Optimal Safe^{\exists} Generalizations 5.4 Deciding Optimality^{\exists} in EL Instance Stores 5.5 Characterizing Safety^{\forall} 5.6 Optimal P-safe^{\forall} Generalizations 5.7 Characterizing Safety^{\forall\exists} and Optimality^{\forall\exists} 6. Privacy-Preserving Ontology Publishing for EL ABoxes 6.1 Logical Entailments in EL ABoxes with Anonymous Individuals 6.2 Anonymizing EL ABoxes 6.3 Formalizing Sensitive Information in EL ABoxes 6.4 Compliance and Safety for EL ABoxes 6.5 Optimal Anonymizers 7. Conclusion 7.1 Main Results 7.2 Future Work Bibliograph

    Temporalised Description Logics for Monitoring Partially Observable Events

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    Inevitably, it becomes more and more important to verify that the systems surrounding us have certain properties. This is indeed unavoidable for safety-critical systems such as power plants and intensive-care units. We refer to the term system in a broad sense: it may be man-made (e.g. a computer system) or natural (e.g. a patient in an intensive-care unit). Whereas in Model Checking it is assumed that one has complete knowledge about the functioning of the system, we consider an open-world scenario and assume that we can only observe the behaviour of the actual running system by sensors. Such an abstract sensor could sense e.g. the blood pressure of a patient or the air traffic observed by radar. Then the observed data are preprocessed appropriately and stored in a fact base. Based on the data available in the fact base, situation-awareness tools are supposed to help the user to detect certain situations that require intervention by an expert. Such situations could be that the heart-rate of a patient is rather high while the blood pressure is low, or that a collision of two aeroplanes is about to happen. Moreover, the information in the fact base can be used by monitors to verify that the system has certain properties. It is not realistic, however, to assume that the sensors always yield a complete description of the current state of the observed system. Thus, it makes sense to assume that information that is not present in the fact base is unknown rather than false. Moreover, very often one has some knowledge about the functioning of the system. This background knowledge can be used to draw conclusions about the possible future behaviour of the system. Employing description logics (DLs) is one way to deal with these requirements. In this thesis, we tackle the sketched problem in three different contexts: (i) runtime verification using a temporalised DL, (ii) temporalised query entailment, and (iii) verification in DL-based action formalisms

    Pseudo-contractions as Gentle Repairs

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    Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas
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