Abstract dialectical frameworks (ADFs) are a formalism for representing knowledge about abstract arguments and various logical relationships between them. This work studies ADFs in detail. Firstly, we use the framework of approximation fixpoint theory to define various semantics that are known from related knowledge representation formalisms also for ADFs. We then analyse the computational complexity of a variety of reasoning problems related to ADFs. Afterwards, we also analyse the formal expressiveness in terms of realisable sets of interpretations and show how ADFs fare in comparison to other formalisms. Finally, we show how ADFs can be put to use in instantiated argumentation, where researchers try to assign meaning to sets of defeasible and strict rules. The main outcomes of our work show that in particular the sublanguage of bipolar ADFs are a useful knowledge representation formalism with meaningful representational capabilities and acceptable computational properties.

We provide a systematic in-depth study of the semantics of abstract dialectical frameworks (ADFs), a recent generalisation of Dung\''s abstract argumentation frameworks. This is done by associating with an ADF its characteristic one-step consequence operator and defining various semantics for ADFs as different fixpoints of this operator. We first show that several existing semantical notions are faithfully captured by our definition, then proceed to define new ADF semantics and show that they are proper generalisations of existing argumentation semantics from the literature. Most remarkably, this operator-based approach allows us to compare ADFs to related nonmonotonic formalisms like Dung argumentation frameworks and propositional logic programs. We use polynomial, faithful and modular translations to relate the formalisms, and our results show that both abstract argumentation frameworks and abstract dialectical frameworks are at most as expressive as propositional normal logic programs.

<p>Real-world datasets are rarely clean. This causes the discrepancy between the claimed performance of machine learning algorithms on paper, and their actual performance on real-world problems. When dealing with missing or hidden information in a dataset, researchers have been using heuristic imputation methods since the first day of machine learning. However, it is known that many imputation methods do not have theoretical guarantees in various machine learning tasks, including clustering, community detection, sparsity recovery, to name a few. On the other hand, theoretical machine learning papers often follow simplistic assumptions, which are rarely fulfilled in real-world datasets. My research focuses on developing statistically and computationally efficient learning algorithms with provable guarantees under novel incomplete and latent assumptions. We consider problems with arguably more realistic incomplete and latent assumptions.We provide analysis to community detection in various network models, inference with latent variables in an arbitrary planted model, federated myopic community detection, and high-order tensor models. We analyze the interaction between the missing or latent structures and the inference / recoverability conditions, and proposed algorithms to solve the problems efficiently. <br> <br> Our main contributions in this thesis are as follows.<br> </p> <ol> <li>We analyze the information-theoretic limits for the recovery of node labels in several network models. We analyze the information-theoretic limits for community detection. We carefully construct restricted ensembles for a subclass of network models, and provide a series of novel results. </li> <li>We analyze the necessary and sufficient conditions for exact inference of a latent model. We show that exact inference can be achieved using a semidefinite programming approach without knowing either the latent variables or their domain. Our analysis predicts the experimental correctness of SDP with high accuracy, showing the suitability of our focus on the Karush-Kuhn-Tucker conditions and the spectrum of a properly defined matrix.</li> <li>We study the problem of recovering the community structure of a network under federated myopic learning. Under this paradigm, we have several clients, each of them having a myopic view, i.e., observing a small subgraph of the network. Each client sends a censored evidence graph to a central server. We provide an efficient algorithm, which computes a consensus signed weighted graph from clients evidence, and recovers the underlying network structure in the central server. We analyze the topological structure conditions of the network, as well as the signal and noise levels of the clients that allow for recovery of the network structure. Our analysis shows that exact recovery is possible and can be achieved in polynomial time.</li> <li>We study the problem of exact partitioning of high-order models. We consider two different high-order assumptions, and show that exact partitioning of high-order planted models is achievable through solving a convex optimization problem with a novel Carathéodory symmetric tensor cone in one case, and with a tensor nuclear norm constraint in the other.</li> <li>We study the problem of inference in high-order structured prediction tasks. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality.</li> <li>We study the problem of partial recovery through semidefinite programming. We are interested in the scenarios in which the SDP returns a solution that is partially correct without any rounding. We analyze the optimality condition of partial recovery and provide statistical and topological guarantees. </li> </ol>

<p>Causality is central to scientific inquiry across many disciplines including epidemiology, medicine, and economics, to name a few. Researchers are usually interested not only in knowing how two events are correlated, but also in whether one causes the other and, if so, how. In general, the scientific practice seeks not just a surface description of the observed data, but rather deeper explanations, such as predicting the effects of interventions. The answer to such questions does not lie in the data alone and requires a qualitative understanding of the underlying data-generating process; a knowledge that is articulated in a causal diagram.</p> <p>And yet, delineating the true, underlying causal diagram requires knowledge and assumptions that are usually not available in many non-trivial and large-scale situations. Hence, this dissertation develops necessary theory and algorithms towards realizing a data-driven framework for causal inference. More specifically, this work provides fundamental treatments of the following research questions:</p> <p><br></p> <p><strong>Effect Identification under Markov Equivalence.</strong> One common task in many data sciences applications is to answer questions about the effect of new interventions, like: 'what would happen to <em>Y</em> while observing <em>Z=z</em> if we force <em>X</em> to take the value <em>x</em>?'. Formally, this is known as <em>causal effect identification</em>, where the goal is to determine whether a post-interventional distribution is computable from the combination of an observational distribution and assumptions about the underlying domain represented by a causal diagram. In this dissertation, we assume as the input of the task a less informative structure known as a partial ancestral graph (PAG), which represents a Markov equivalence class of causal diagrams, learnable from observational data. We develop tools and algorithms for this relaxed setting and characterize identifiable effects under necessary and sufficient conditions.</p> <p><br></p> <p><strong>Causal Discovery from Interventions.</strong> A causal diagram imposes constraints on the corresponding generated data; conditional independences are one such example. Given a mixture of observational and experimental data, the goal is to leverage the constraints imprinted in the data to infer the set of causal diagrams that are compatible with such constraints. In this work, we consider soft interventions, such that the mechanism of an intervened variable is modified without fully eliminating the effect of its direct causes, and investigate two settings where the targets of the interventions could be known or unknown to the data scientist. Accordingly, we introduce the first general graphical characterizations to test whether two causal diagrams are indistinguishable given the constraints in the available data. We also develop algorithms that, given a mixture of observational and interventional data, learn a representation of the equivalence class.</p>

<p>Graphs are the natural framework of many of today’s highest impact computing applications: from online social networking, to Web search, to product recommendations, to chemistry, to bioinformatics, to knowledge bases, to mobile ad-hoc networking. To develop successful applications in these domains, we often need representation learning methods ---models mapping nodes, edges, subgraphs or entire graphs to some meaningful vector space. Such models are studied in the machine learning subfield of graph representation learning (GRL). Previous GRL research has focused on learning node or entire graph representations through associational tasks. In this work I study higher-order (k>1-node) representations of graphs in the context of both associational and counterfactual tasks.<br> </p>

In my Ph.D. dissertation, I have studied problems arising in various aspects of preferences: preference modeling, preference learning, and preference reasoning, when preferences concern outcomes ranging over combinatorial domains. Preferences is a major research component in artificial intelligence (AI) and decision theory, and is closely related to the social choice theory considered by economists and political scientists. In my dissertation, I have exploited emerging connections between preferences in AI and social choice theory. Most of my research is on qualitative preference representations that extend and combine existing formalisms such as conditional preference nets, lexicographic preference trees, answer-set optimization programs, possibilistic logic, and conditional preference networks; on learning problems that aim at discovering qualitative preference models and predictive preference information from practical data; and on preference reasoning problems centered around qualitative preference optimization and aggregation methods. Applications of my research include recommender systems, decision support tools, multi-agent systems, and Internet trading and marketing platforms.

Dans cette thèse, nous nous intéressons au problème d'interrogation de bases de connaissances composées de données et d'une ontologie, qui représente des connaissances générales sur le domaine d'application. Parmi les différents formalismes permettant de représenter les connaissances ontologiques, nous considérons ici un fragment de la logique du premier ordre appelé règles existentielles (aussi connues sous le nom de ``tuple generating dependencies'' et Datalog+/-). Le problème fondamental de conséquence logique au cœur de cette thèse demande si une requête conjonctive est conséquence d'une base de connaissances. Les règles existentielles étant très expressives, ce problème est indécidable. Toutefois, différentes restrictions sur les ensembles de règles ont été proposées afin d'obtenir sa décidabilité.La contribution de cette thèse est double. Premièrement, nous proposons un outil qui nous permet d'unifier puis d'étendre la plupart des classes de règles connues reposant sur des notions d'acyclicité assurant la finitude du chaînage avant. Deuxièmement, nous étudions la compatibilité des classes décidables de règles existentielles connues avec un type de connaissance souvent nécessaire dans les ontologies: la transitivité de relations binaires. Nous aidons à clarifier le paysage des résultats positifs et négatifs liés à cette question et fournissons une approche permettant de combiner la transitivité avec les règles existentielles linéaires. / In this thesis we investigate the issue of querying knowledge bases composed of data and general background knowledge, called an ontology. Ontological knowledge can be represented under different formalisms and we consider here a fragment of first-order logic called existential rules (also known as tuple-generating dependencies and Datalog+/-).The fundamental entailment problem at the core of this thesis asks if a conjunctive query is entailed by an existential rule knowledge base. General existential rules are highly expressive, however at the cost of undecidability. Various restrictions on sets of rules have been proposed to regain the decidability of the entailment problem.Our specific contribution is two-fold. First, we propose a new tool that allows to unify and extend most of the known existential rule classes that rely on acyclicity conditions to tame infinite forward chaining, without increasing the complexity of the acyclicity recognition. Second, we study the compatibility of known decidable rule classes with a frequently required modeling construct, namely transitivity of binary relations. We help clarifying the picture of negative and positive results on this question, and provide a technique to safely combine transitivity with one of the simplest, yet useful, decidable rule classes, namely linear rules.

L'objectif du problème appelé "Ontology-based data access" (OBDA) est d'améliorer la réponse à des requêtes en prenant en compte des connaissances d'ordre général durant l'évaluation des requêtes. Ces connaissances générales sont représentées à l'aide d'une ontologie, qui est exprimée dans cette thèse grâce à des formules logiques du premier ordre, appelées règles existentielles, et aussi connues sous le nom de "tuple-generating dependencies" et Datalog+/-. L'expressivité des formules utilisées est telle que l'évaluation de requêtes devient un problème indécidable, et cela a conduit la communauté à définir de nombreux cas décidables, c'est-à-dire des restrictions sur les ensembles de règles existentielles considérés. La contribution de cette thèse est double : tout d'abord, nous proposons une vue unifiée sur une grande fraction des cas décidables connus, et fournissons par là même une analyse de complexité et un algorithme optimal dans le pire des cas. Nous considérons également l'approche couramment utilisée de réécriture de requêtes, et proposons un algorithme générique qui permet de surmonter certaines causes évidentes d'explosion combinatoire qui rendent les approches classiques pratiquement inapplicables. / Ontology-based data access (OBDA) aims at enriching query answering by taking general background knowledge into account when evaluating queries. This background knowledge is represented by means of an ontology, that is expressed in this thesis by a very expressive class of first-order formulas, called existential rules (sometimes also tuple-generating dependencies and Datalog+/-). The high expressivity of the used formalism results in the undecidability of query answering, and numerous decidable classes (that is, restrictions on the sets of existential rules) have been proposed in the literature. The contribution of this thesis is two-fold: first, we propose a unified view of a large part of these classes, together with a complexity analysis and a worst-case optimal algorithm for the introduced generic class. Second, we consider the popular approach of query rewriting, and propose a generic algorithm that overcomes trivial causes of combinatorial explosion that make classical approaches inapplicable.

Answer Set Programming (ASP) is an emerging paradigm for declarative programming, in which a computational problem is specified by a logic program such that particular models, called answer sets, match solutions. ASP faces a growing range of applications, demanding for high-performance tools able to solve complex problems. ASP integrates ideas from a variety of neighboring fields. In particular, automated techniques to search for answer sets are inspired by Boolean Satisfiability (SAT) solving approaches. While the latter have firm proof-theoretic foundations, ASP lacks formal frameworks for characterizing and comparing solving methods. Furthermore, sophisticated search patterns of modern SAT solvers, successfully applied in areas like, e.g., model checking and verification, are not yet established in ASP solving. We address these deficiencies by, for one, providing proof-theoretic frameworks that allow for characterizing, comparing, and analyzing approaches to answer set computation. For another, we devise modern ASP solving algorithms that integrate and extend state-of-the-art techniques for Boolean constraint solving. We thus contribute to the understanding of existing ASP solving approaches and their interconnections as well as to their enhancement by incorporating sophisticated search patterns. The central idea of our approach is to identify atomic as well as composite constituents of a propositional logic program with Boolean variables. This enables us to describe fundamental inference steps, and to selectively combine them in proof-theoretic characterizations of various ASP solving methods. In particular, we show that different concepts of case analyses applied by existing ASP solvers implicate mutual exponential separations regarding their best-case complexities. We also develop a generic proof-theoretic framework amenable to language extensions, and we point out that exponential separations can likewise be obtained due to case analyses on them. We further exploit fundamental inference steps to derive Boolean constraints characterizing answer sets. They enable the conception of ASP solving algorithms including search patterns of modern SAT solvers, while also allowing for direct technology transfers between the areas of ASP and SAT solving. Beyond the search for one answer set of a logic program, we address the enumeration of answer sets and their projections to a subvocabulary, respectively. The algorithms we develop enable repetition-free enumeration in polynomial space without being intrusive, i.e., they do not necessitate any modifications of computations before an answer set is found. Our approach to ASP solving is implemented in clasp, a state-of-the-art Boolean constraint solver that has successfully participated in recent solver competitions. Although we do here not address the implementation techniques of clasp or all of its features, we present the principles of its success in the context of ASP solving. / Antwortmengenprogrammierung (engl. Answer Set Programming; ASP) ist ein Paradigma zum deklarativen Problemlösen, wobei Problemstellungen durch logische Programme beschrieben werden, sodass bestimmte Modelle, Antwortmengen genannt, zu Lösungen korrespondieren. Die zunehmenden praktischen Anwendungen von ASP verlangen nach performanten Werkzeugen zum Lösen komplexer Problemstellungen. ASP integriert diverse Konzepte aus verwandten Bereichen. Insbesondere sind automatisierte Techniken für die Suche nach Antwortmengen durch Verfahren zum Lösen des aussagenlogischen Erfüllbarkeitsproblems (engl. Boolean Satisfiability; SAT) inspiriert. Letztere beruhen auf soliden beweistheoretischen Grundlagen, wohingegen es für ASP kaum formale Systeme gibt, um Lösungsmethoden einheitlich zu beschreiben und miteinander zu vergleichen. Weiterhin basiert der Erfolg moderner Verfahren zum Lösen von SAT entscheidend auf fortgeschrittenen Suchtechniken, die in gängigen Methoden zur Antwortmengenberechnung nicht etabliert sind. Diese Arbeit entwickelt beweistheoretische Grundlagen und fortgeschrittene Suchtechniken im Kontext der Antwortmengenberechnung. Unsere formalen Beweissysteme ermöglichen die Charakterisierung, den Vergleich und die Analyse vorhandener Lösungsmethoden für ASP. Außerdem entwerfen wir moderne Verfahren zum Lösen von ASP, die fortgeschrittene Suchtechniken aus dem SAT-Bereich integrieren und erweitern. Damit trägt diese Arbeit sowohl zum tieferen Verständnis von Lösungsmethoden für ASP und ihrer Beziehungen untereinander als auch zu ihrer Verbesserung durch die Erschließung fortgeschrittener Suchtechniken bei. Die zentrale Idee unseres Ansatzes besteht darin, Atome und komposite Konstrukte innerhalb von logischen Programmen gleichermaßen mit aussagenlogischen Variablen zu assoziieren. Dies ermöglicht die Isolierung fundamentaler Inferenzschritte, die wir in formalen Charakterisierungen von Lösungsmethoden für ASP selektiv miteinander kombinieren können. Darauf aufbauend zeigen wir, dass unterschiedliche Einschränkungen von Fallunterscheidungen zwangsläufig zu exponentiellen Effizienzunterschieden zwischen den charakterisierten Methoden führen. Wir generalisieren unseren beweistheoretischen Ansatz auf logische Programme mit erweiterten Sprachkonstrukten und weisen analytisch nach, dass das Treffen bzw. Unterlassen von Fallunterscheidungen auf solchen Konstrukten ebenfalls exponentielle Effizienzunterschiede bedingen kann. Die zuvor beschriebenen fundamentalen Inferenzschritte nutzen wir zur Extraktion inhärenter Bedingungen, denen Antwortmengen genügen müssen. Damit schaffen wir eine Grundlage für den Entwurf moderner Lösungsmethoden für ASP, die fortgeschrittene, ursprünglich für SAT konzipierte, Suchtechniken mit einschließen und darüber hinaus einen transparenten Technologietransfer zwischen Verfahren zum Lösen von ASP und SAT erlauben. Neben der Suche nach einer Antwortmenge behandeln wir ihre Aufzählung, sowohl für gesamte Antwortmengen als auch für Projektionen auf ein Subvokabular. Hierfür entwickeln wir neuartige Methoden, die wiederholungsfreies Aufzählen in polynomiellem Platz ermöglichen, ohne die Suche zu beeinflussen und ggf. zu behindern, bevor Antwortmengen berechnet wurden.

abstract: Answer Set Programming (ASP) is one of the most prominent and successful knowledge representation paradigms. The success of ASP is due to its expressive non-monotonic modeling language and its efficient computational methods originating from building propositional satisfiability solvers. The wide adoption of ASP has motivated several extensions to its modeling language in order to enhance expressivity, such as incorporating aggregates and interfaces with ontologies. Also, in order to overcome the grounding bottleneck of computation in ASP, there are increasing interests in integrating ASP with other computing paradigms, such as Constraint Programming (CP) and Satisfiability Modulo Theories (SMT). Due to the non-monotonic nature of the ASP semantics, such enhancements turned out to be non-trivial and the existing extensions are not fully satisfactory. We observe that one main reason for the difficulties rooted in the propositional semantics of ASP, which is limited in handling first-order constructs (such as aggregates and ontologies) and functions (such as constraint variables in CP and SMT) in natural ways. This dissertation presents a unifying view on these extensions by viewing them as instances of formulas with generalized quantifiers and intensional functions. We extend the first-order stable model semantics by by Ferraris, Lee, and Lifschitz to allow generalized quantifiers, which cover aggregate, DL-atoms, constraints and SMT theory atoms as special cases. Using this unifying framework, we study and relate different extensions of ASP. We also present a tight integration of ASP with SMT, based on which we enhance action language C+ to handle reasoning about continuous changes. Our framework yields a systematic approach to study and extend non-monotonic languages. / Dissertation/Thesis / Ph.D. Computer Science 2013