On expressibility of non-monotone operators in SPARQL

SPARQL, a query language for RDF graphs, is one of the key technologies for the Semantic Web. The expressivity and complexity of various fragments of SPARQL have been studied extensively. It is usually assumed that the optional matching operator OPTIONAL has only two graph patterns as arguments. The specification of SPARQL, however, defines it as a ternary operator, with an additional filter condition. We address the problem of expressibility of the full ternary OPTIONAL via the simplified binary version and show that it is possible, but only with an exponential blowup in the size of the query (under common complexity-theoretic assumptions). We also study expressibility of other non-monotone SPARQL operators via optional matching and each other

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

Reverse Engineering of Temporal Queries Mediated by LTL Ontologies

In reverse engineering of database queries, we aim to construct a query from a given set of answers and non-answers; it can then be used to explore the data further or as an explanation of the answers and non-answers. We investigate this query-by-example problem for queries formulated in positive fragments of linear temporal logic LTL over timestamped data, focusing on the design of suitable query languages and the combined and data complexity of deciding whether there exists a query in the given language that separates the given answers from non-answers. We consider both plain LTL queries and those mediated by LTL-ontologies.Comment: To be published in IJCAI 2023 proceeding

Event Processing and Stream Reasoning with ETALIS

This thesis presents the ETALIS Language for Events (ELE), a declarative rule-based language for Event Processing (EP) and Stream Reasoning (SR). ELE features a well-defined semantics, and provides strong event processing and reasoning capabilities. In this work we present ELE and show how its EP and SR capabilities have the potential to provide powerful real time intelligence. We provide a prototype implementation of the language, and present evaluation results for a few implemented scenarios

Reverse engineering of temporal queries mediated by LTL ontologies

In reverse engineering of database queries, we aim to construct a query from a given set of answers and non-answers; it can then be used to explore the data further or as an explanation of the answers and non-answers. We investigate this query-by-example problem for queries formulated in positive fragments of linear temporal logic LTL over time-stamped data, focusing on the design of suitable query languages and the combined and data complexity of deciding whether there exists a query in the given language that separates the given answers from non-answers. We consider both plain LTL queries and those mediated by LTL-ontologies

Abstraction in ontology-based data management

In many aspects of our society there is growing awareness and consent on the need for data-driven approaches that are resilient, transparent, and fully accountable. But in order to fulfil the promises and benefits of a data-driven society, it is necessary that the data services exposed by the organisations' information systems are well-documented, and their semantics is clearly specified. Effectively documenting data services is indeed a crucial issue for organisations, not only for governing their own data, but also for interoperation purposes. In this thesis, we propose a new approach to automatically associate formal semantic descriptions to data services, thus bringing them into compliance with the FAIR guiding principles, i.e., make data services automatically Findable, Accessible, Interoperable, and Reusable (FAIR). We base our proposal on the Ontology-based Data Management (OBDM) paradigm, where a domain ontology is used to provide a semantic layer mapped to the data sources of an organisation, thus abstracting from the technical details of the data layer implementation. The basic idea is to characterise or explain the semantics of a given data service expressed as query over the source schema in terms of a query over the ontology. Thus, the query over the ontology represents an abstraction of the given data service in terms of the domain ontology through the mapping, and, together with the elements in the vocabulary of the ontology, such abstraction forms a basis for annotating the given data service with suitable metadata expressing its semantics. We illustrate a formal framework for the task of automatically produce a semantic characterisation of a given data service expressed as a query over the source schema. The framework is based on three semantically well-founded notions, namely perfect, sound, and complete source-to-ontology rewriting, and on two associated basic computational problems, namely verification and computation. The former verifies whether a given query over the ontology is a perfect (respectively, sound, complete) source-to-ontology rewriting of a given data service expressed as a query over the source schema, whereas the latter computes one such rewriting, provided it exists. We provide an in-depth complexity analysis of these two computational problems in a very general scenario which uses languages amongst the most popular considered in the literature of managing data through an ontology. Furthermore, since we study also cases where the target query language for expressing source-to-ontology rewritings allows inequality atoms, we also investigate the problem of answering queries with inequalities over lightweight ontologies, a problem that has been rarely addressed. In another direction, we study and advocate the use of a non-monotonic target query language for expressing source-to-ontology rewritings. Last but not least, we outline a detailed related work, which illustrates how the results achieved in this thesis notably contributes to new results in the Semantic Web context, in the relational database theory, and in view-based query processing

Graph Structures for Knowledge Representation and Reasoning

This open access book constitutes the thoroughly refereed post-conference proceedings of the 6th International Workshop on Graph Structures for Knowledge Representation and Reasoning, GKR 2020, held virtually in September 2020, associated with ECAI 2020, the 24th European Conference on Artificial Intelligence. The 7 revised full papers presented together with 2 invited contributions were reviewed and selected from 9 submissions. The contributions address various issues for knowledge representation and reasoning and the common graph-theoretic background, which allows to bridge the gap between the different communities

Pseudo-contractions as Gentle Repairs

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