Belief Revision in Expressive Knowledge Representation Formalisms

We live in an era of data and information, where an immeasurable amount of discoveries, findings, events, news, and transactions are generated every second. Governments, companies, or individuals have to employ and process all that data for knowledge-based decision-making (i.e. a decision-making process that uses predetermined criteria to measure and ensure the optimal outcome for a specific topic), which then prompt them to view the knowledge as valuable resource. In this knowledge-based view, the capability to create and utilize knowledge is the key source of an organization or individual’s competitive advantage. This dynamic nature of knowledge leads us to the study of belief revision (or belief change), an area which emerged from work in philosophy and then impacted further developments in computer science and artificial intelligence. In belief revision area, the AGM postulates by Alchourrón, Gärdenfors, and Makinson continue to represent a cornerstone in research related to belief change. Katsuno and Mendelzon (K&M) adopted the AGM postulates for changing belief bases and characterized AGM belief base revision in propositional logic over finite signatures. In this thesis, two research directions are considered. In the first, by considering the semantic point of view, we generalize K&M’s approach to the setting of (multiple) base revision in arbitrary Tarskian logics, covering all logics with a classical model-theoretic semantics and hence a wide variety of logics used in knowledge representation and beyond. Our generic formulation applies to various notions of “base”, such as belief sets, arbitrary or finite sets of sentences, or single sentences. The core result is a representation theorem showing a two-way correspondence between AGM base revision operators and certain “assignments”: functions mapping belief bases to total — yet not transitive — “preference” relations between interpretations. Alongside, we present a companion result for the case when the AGM postulate of syntax-independence is abandoned. We also provide a characterization of all logics for which our result can be strengthened to assignments producing transitive preference relations (as in K&M’s original work), giving rise to two more representation theorems for such logics, according to syntax dependence vs. independence. The second research direction in this thesis explores two approaches for revising description logic knowledge bases under fixed-domain semantics, namely model-based approach and individual-based approach. In this logical setting, models of the knowledge bases can be enumerated and can be computed to produce the revision result, semantically. We show a characterization of the AGM revision operator for this logic and present a concrete model-based revision approach via distance between interpretations. In addition, by weakening the KB based on certain domain elements, a novel individual-based revision operator is provided as an alternative approach

Expressive probabilistic description logics

AbstractThe work in this paper is directed towards sophisticated formalisms for reasoning under probabilistic uncertainty in ontologies in the Semantic Web. Ontologies play a central role in the development of the Semantic Web, since they provide a precise definition of shared terms in web resources. They are expressed in the standardized web ontology language OWL, which consists of the three increasingly expressive sublanguages OWL Lite, OWL DL, and OWL Full. The sublanguages OWL Lite and OWL DL have a formal semantics and a reasoning support through a mapping to the expressive description logics SHIF(D) and SHOIN(D), respectively. In this paper, we present the expressive probabilistic description logics P-SHIF(D) and P-SHOIN(D), which are probabilistic extensions of these description logics. They allow for expressing rich terminological probabilistic knowledge about concepts and roles as well as assertional probabilistic knowledge about instances of concepts and roles. They are semantically based on the notion of probabilistic lexicographic entailment from probabilistic default reasoning, which naturally interprets this terminological and assertional probabilistic knowledge as knowledge about random and concrete instances, respectively. As an important additional feature, they also allow for expressing terminological default knowledge, which is semantically interpreted as in Lehmann's lexicographic entailment in default reasoning from conditional knowledge bases. Another important feature of this extension of SHIF(D) and SHOIN(D) by probabilistic uncertainty is that it can be applied to other classical description logics as well. We then present sound and complete algorithms for the main reasoning problems in the new probabilistic description logics, which are based on reductions to reasoning in their classical counterparts, and to solving linear optimization problems. In particular, this shows the important result that reasoning in the new probabilistic description logics is decidable/computable. Furthermore, we also analyze the computational complexity of the main reasoning problems in the new probabilistic description logics in the general as well as restricted cases

Knowledge base ontological debugging guided by linguistic evidence

Le résumé en français n'a pas été communiqué par l'auteur.When they grow in size, knowledge bases (KBs) tend to include sets of axioms which are intuitively absurd but nonetheless logically consistent. This is particularly true of data expressed in OWL, as part of the Semantic Web framework, which favors the aggregation of set of statements from multiple sources of knowledge, with overlapping signatures.Identifying nonsense is essential if one wants to avoid undesired inferences, but the sparse usage of negation within these datasets generally prevents the detection of such cases on a strict logical basis. And even if the KB is inconsistent, identifying the axioms responsible for the nonsense remains a non trivial task. This thesis investigates the usage of automatically gathered linguistic evidence in order to detect and repair violations of common sense within such datasets. The main intuition consists in exploiting distributional similarity between named individuals of an input KB, in order to identify consequences which are unlikely to hold if the rest of the KB does. Then the repair phase consists in selecting axioms to be preferably discarded (or at least amended) in order to get rid of the nonsense. A second strategy is also presented, which consists in strengthening the input KB with a foundational ontology, in order to obtain an inconsistency, before performing a form of knowledge base debugging/revision which incorporates this linguistic input. This last step may also be applied directly to an inconsistent input KB. These propositions are evaluated with different sets of statements issued from the Linked Open Data cloud, as well as datasets of a higher quality, but which were automatically degraded for the evaluation. The results seem to indicate that distributional evidence may actually constitute a relevant common ground for deciding between conflicting axioms

Knowledge base ontological debugging guided by linguistic evidence

Le résumé en français n'a pas été communiqué par l'auteur.When they grow in size, knowledge bases (KBs) tend to include sets of axioms which are intuitively absurd but nonetheless logically consistent. This is particularly true of data expressed in OWL, as part of the Semantic Web framework, which favors the aggregation of set of statements from multiple sources of knowledge, with overlapping signatures.Identifying nonsense is essential if one wants to avoid undesired inferences, but the sparse usage of negation within these datasets generally prevents the detection of such cases on a strict logical basis. And even if the KB is inconsistent, identifying the axioms responsible for the nonsense remains a non trivial task. This thesis investigates the usage of automatically gathered linguistic evidence in order to detect and repair violations of common sense within such datasets. The main intuition consists in exploiting distributional similarity between named individuals of an input KB, in order to identify consequences which are unlikely to hold if the rest of the KB does. Then the repair phase consists in selecting axioms to be preferably discarded (or at least amended) in order to get rid of the nonsense. A second strategy is also presented, which consists in strengthening the input KB with a foundational ontology, in order to obtain an inconsistency, before performing a form of knowledge base debugging/revision which incorporates this linguistic input. This last step may also be applied directly to an inconsistent input KB. These propositions are evaluated with different sets of statements issued from the Linked Open Data cloud, as well as datasets of a higher quality, but which were automatically degraded for the evaluation. The results seem to indicate that distributional evidence may actually constitute a relevant common ground for deciding between conflicting axioms

Dealing with Inconsistencies and Updates in Description Logic Knowledge Bases

The main purpose of an "Ontology-based Information System" (OIS) is to provide an explicit description of the domain of interest, called ontology, and let all the functions of the system be based on such representation, thus freeing the users from the knowledge about the physical repositories where the real data reside. The functionalities that an OIS should provide to the user include both query answering, whose goal is to extract information from the system, and update, whose goal is to modify the information content of the system in order to reflect changes in the domain of interest. The "ontology" is a formal, high quality intentional representation of the domain, designed in such a way to avoid inconsistencies in the modeling of concepts and relationships. On the contrary, the extensional level of the system, constituted by a set of autonomous, heterogeneous data sources, is built independently from the conceptualization represented by the ontology, and therefore may contain information that is incoherent with the ontology itself. This dissertation presents a detailed study on the problem of dealing with inconsistencies in OISs, both in query answering, and in performing updates. We concentrate on the case where the knowledge base in the OISs is expressed in Description Logics, especially the logics of the DL-lite family. As for query answering, we propose both semantical frameworks that are inconsistency-tolerant, and techniques for answering unions of conjunctive queries posed to OISs under such inconsistency-tolerant semantics. As for updates, we present an approach to compute the result of updating a possibly inconsistent OIS with both insertion and deletion of extensional knowledge

Current and Future Challenges in Knowledge Representation and Reasoning

Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as machine learning and reasoning under uncertainty. In July 2022 a Dagstuhl Perspectives workshop was held on Knowledge Representation and Reasoning. The goal of the workshop was to describe the state of the art in the field, including its relation with other areas, its shortcomings and strengths, together with recommendations for future progress. We developed this manifesto based on the presentations, panels, working groups, and discussions that took place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge Representation: its origins, goals, milestones, and current foci; its relation to other disciplines, especially to Artificial Intelligence; and on its challenges, along with key priorities for the next decade

Foundational Ontologies meet Ontology Matching: A Survey

Ontology matching is a research area aimed at finding ways to make different ontologies interoperable. Solutions to the problem have been proposed from different disciplines, including databases, natural language processing, and machine learning. The role of foundational ontologies for ontology matching is an important one. It is multifaceted and with room for development. This paper presents an overview of the different tasks involved in ontology matching that consider foundational ontologies. We discuss the strengths and weaknesses of existing proposals and highlight the challenges to be addressed in the future