Inductive Logic Programming in Databases: from Datalog to DL+log

In this paper we address an issue that has been brought to the attention of the database community with the advent of the Semantic Web, i.e. the issue of how ontologies (and semantics conveyed by them) can help solving typical database problems, through a better understanding of KR aspects related to databases. In particular, we investigate this issue from the ILP perspective by considering two database problems, (i) the definition of views and (ii) the definition of constraints, for a database whose schema is represented also by means of an ontology. Both can be reformulated as ILP problems and can benefit from the expressive and deductive power of the KR framework DL+log. We illustrate the application scenarios by means of examples. Keywords: Inductive Logic Programming, Relational Databases, Ontologies, Description Logics, Hybrid Knowledge Representation and Reasoning Systems. Note: To appear in Theory and Practice of Logic Programming (TPLP).Comment: 30 pages, 3 figures, 2 tables

Reverse engineering queries in ontology-enriched systems: the case of expressive horn description logic ontologies

We introduce the query-by-example (QBE) paradigm for query answering in the presence of ontologies. Intuitively, QBE permits non-expert users to explore the data by providing examples of the information they (do not) want, which the system then generalizes into a query. Formally, we study the following question: given a knowledge base and sets of positive and negative examples, is there a query that returns all positive but none of the negative examples? We focus on description logic knowledge bases with ontologies formulated in Horn-ALCI and (unions of) conjunctive queries. Our main contributions are characterizations, algorithms and tight complexity bounds for QBE

Structural Sampling for Statistical Software Testing

Structural Statistical Software Testing exploits the control flow graph of the program being tested to construct test cases. While test cases can easily be extracted from {em feasible paths} in the control flow graph, that is, paths which are actually exerted for some values of the program input, the feasible path region is a tiny fraction of the graph paths (less than $10^{-5}]$ for medium size programs). The S4T algorithm presented in this paper aims to address this limitation; as an Active Relational Learning Algorithm, it uses the few feasible paths initially available to sample new feasible paths. The difficulty comes from the non-Markovian nature of the feasible path concept, due to the long-range dependencies between the nodes in the control flow graph. Experimental validation on real-world and artificial problems demonstrates significant improvements compared to the state of the art

Advances on belief base dynamics

The main goal underlying the research area of belief change consists in finding appropriate ways of modelling the belief state of a rational agent and, additionally, the changes which occur in such a state when the agent receives new information. The most important model of belief change is the so-called AGM model, proposed in [AGM85]. In this model, the belief state of an agent is represented by a belief set—a deductively closed set of sentences. A change consists in adding or removing a specific sentence from a belief set to obtain a new belief set. Two of the main shortcomings pointed out to the AGM model of belief change are the use of belief sets to represent belief states and the (unrealistic) acceptance of any new piece of information. In this thesis we address both those issues. We present axiomatic characterizations for ensconcement-based contractions and for brutal contractions, two kinds of belief bases contraction operators introduced in [Wil94b] that are based on the concept of ensconcement, which is a generalization to the case of belief bases of the concept of epistemic entrenchment introduced in [Ga¨r88, GM88]. We compare the axiomatic characterizations of these operators with those of other well-known base contraction operators and study the interrelations among the former and the contraction operators based on epistemic entrenchments. We study non-prioritized base change operators, namely shielded base contractions and credibility-limited base revisions. We propose several different classes of shielded base contractions and obtain axiomatic characterizations for each one of them. Additionally we thoroughly investigate the interrelations (in the sense of inclusion) among all those classes. Afterwards we perform a similar study for credibility-limited base revisions. Finally, we study the interrelation between the different proposed classes of operators of credibility-limited base revision and of shielded contraction by means of the consistency-preserving Levi identity and the Harper identity.O objetivo principal da a´rea de revis˜ao de cren¸cas ´e encontrar modelos que permitam modelar o estado de cren¸cas de um agente racional, bem como as mudan¸cas que ocorrem nesse estado de cren¸cas quando o agente recebe novas informa¸co˜es. O modelo mais influente desta ´area ´e o chamado modelo AGM proposto em [AGM85]. Neste modelo, o estado de cren¸cas de um agente ´e representado por um conjunto de cren¸cas—conjunto de f´ormulas dedutivamente fechado. Uma mudan¸ca consiste em adicionar ou remover uma fo´rmula espec´ıfica de um conjunto de cren¸cas para obter um novo conjunto de crenc¸as. Dois dos principais problemas apontados ao modelo AGM sa˜o o uso de conjuntos de cren¸cas para representar estados de cren¸ca e a aceita¸ca˜o (irrealista) de qualquer nova informa¸ca˜o. Nesta tese abordamos ambas as quest˜oes. Apresentamos caracteriza¸co˜es axiom´aticas para contra¸c˜oes baseadas em ensconcements e para contra¸c˜oes brutais, dois tipos de operadores de contrac¸˜ao em bases de cren¸cas introduzidos em [Wil94b] e que se baseiam no conceito de ensconcement— generaliza¸ca˜o em bases de cren¸cas, do conceito de epistemic entrenchment introduzido em [Ga¨r88, GM88]. Comparamos as caracteriza¸c˜oes axiom´aticas destes operadores com as de outros operadores de contrac¸˜ao em bases bem conhecidos e estudamos as inter-rela¸co˜es entre os primeiros e os operadores de contra¸ca˜o baseados em epistemic entrenchments. Estudamos operadores de mudanc¸as de crenc¸as na˜o-priorizados em bases, nomeadamente contra¸c˜oes protegidas e revis˜oes com limite de credibilidade. Propomos v´arias classes de operadores de contra¸c˜oes protegidas e obtemos teoremas de representa¸ca˜o para cada uma dessas classes. Investigamos, igualmente, as inter-rela¸co˜es (no sentido de inclusa˜o) entre todas essas classes. Posteriormente, realizamos um estudo semelhante para reviso˜es com limite de credibilidade. Finalmente, estudamos a inter-relac¸˜ao entre as diferentes classes propostas de operadores (definidos em bases de cren¸cas) de revis˜ao com limite de credibilidade e de contra¸co˜es protegidas atrav´es da identidade de Levi conservadora-da-consistˆencia e da identidade de Harper

Against the Virtual: Kleinherenbrink’s Externality Thesis and Deleuze’s Machine Ontology

Drawing from Arjen Kleinherenbrink's recent book, Against Continuity: Gilles Deleuze's Speculative Realism (2019), this paper undertakes a detailed review of Kleinherenbrink's fourfold "externality thesis" vis-à-vis Deleuze's machine ontology. Reading Deleuze as a philosopher of the actual, this paper renders Deleuzean syntheses as passive contemplations, pulling other (passive) entities into an (active) experience and designating relations as expressed through contraction. In addition to reviewing Kleinherenbrink's book (which argues that the machine ontology is a guiding current that emerges in Deleuze's work after Difference and Repetition) alongside much of Deleuze's oeuvre, we relate and juxtapose Deleuze's machine ontology to positions concerning externality held by a host of speculative realists. Arguing that the machine ontology has its own account of interaction, change, and novelty, we ultimately set to prove that positing an ontological "cut" on behalf of the virtual realm is unwarranted because, unlike the realm of actualities, it is extraneous to the structure of becoming-that is, because it cannot be homogenous, any theory of change vis-à-vis the virtual makes it impossible to explain how and why qualitatively different actualities are produced

The power of linear programming for general-valued CSPs

Let $D$, called the domain, be a fixed finite set and let $\Gamma$, called the valued constraint language, be a fixed set of functions of the form $f:D^m\to\mathbb{Q}\cup\{\infty\}$, where different functions might have different arity $m$. We study the valued constraint satisfaction problem parametrised by $\Gamma$, denoted by VCSP$(\Gamma)$. These are minimisation problems given by $n$ variables and the objective function given by a sum of functions from $\Gamma$, each depending on a subset of the $n$ variables. Finite-valued constraint languages contain functions that take on only rational values and not infinite values. Our main result is a precise algebraic characterisation of valued constraint languages whose instances can be solved exactly by the basic linear programming relaxation (BLP). For a valued constraint language $\Gamma$, BLP is a decision procedure for $\Gamma$ if and only if $\Gamma$ admits a symmetric fractional polymorphism of every arity. For a finite-valued constraint language $\Gamma$, BLP is a decision procedure if and only if $\Gamma$ admits a symmetric fractional polymorphism of some arity, or equivalently, if $\Gamma$ admits a symmetric fractional polymorphism of arity 2. Using these results, we obtain tractability of several novel classes of problems, including problems over valued constraint languages that are: (1) submodular on arbitrary lattices; (2) $k$-submodular on arbitrary finite domains; (3) weakly (and hence strongly) tree-submodular on arbitrary trees.Comment: A full version of a FOCS'12 paper by the last two authors (arXiv:1204.1079) and an ICALP'13 paper by the first author (arXiv:1207.7213) to appear in SIAM Journal on Computing (SICOMP

Rerepresenting and Restructuring Domain Theories: A Constructive Induction Approach

Theory revision integrates inductive learning and background knowledge by combining training examples with a coarse domain theory to produce a more accurate theory. There are two challenges that theory revision and other theory-guided systems face. First, a representation language appropriate for the initial theory may be inappropriate for an improved theory. While the original representation may concisely express the initial theory, a more accurate theory forced to use that same representation may be bulky, cumbersome, and difficult to reach. Second, a theory structure suitable for a coarse domain theory may be insufficient for a fine-tuned theory. Systems that produce only small, local changes to a theory have limited value for accomplishing complex structural alterations that may be required. Consequently, advanced theory-guided learning systems require flexible representation and flexible structure. An analysis of various theory revision systems and theory-guided learning systems reveals specific strengths and weaknesses in terms of these two desired properties. Designed to capture the underlying qualities of each system, a new system uses theory-guided constructive induction. Experiments in three domains show improvement over previous theory-guided systems. This leads to a study of the behavior, limitations, and potential of theory-guided constructive induction.Comment: See http://www.jair.org/ for an online appendix and other files accompanying this articl

Tree Projections and Constraint Optimization Problems: Fixed-Parameter Tractability and Parallel Algorithms

Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views, whose solutions are either already available or can be computed efficiently. The goal is to arrange portions of these views in a tree-like structure, called tree projection, which determines an efficiently solvable CSP instance equivalent to the original one. Deciding whether a tree projection exists is NP-hard. Solution methods have therefore been proposed in the literature that do not require a tree projection to be given, and that either correctly decide whether the given CSP instance is satisfiable, or return that a tree projection actually does not exist. These approaches had not been generalized so far on CSP extensions for optimization problems, where the goal is to compute a solution of maximum value/minimum cost. The paper fills the gap, by exhibiting a fixed-parameter polynomial-time algorithm that either disproves the existence of tree projections or computes an optimal solution, with the parameter being the size of the expression of the objective function to be optimized over all possible solutions (and not the size of the whole constraint formula, used in related works). Tractability results are also established for the problem of returning the best K solutions. Finally, parallel algorithms for such optimization problems are proposed and analyzed. Given that the classes of acyclic hypergraphs, hypergraphs of bounded treewidth, and hypergraphs of bounded generalized hypertree width are all covered as special cases of the tree projection framework, the results in this paper directly apply to these classes. These classes are extensively considered in the CSP setting, as well as in conjunctive database query evaluation and optimization

The Complexity of Manipulating kk-Approval Elections

An important problem in computational social choice theory is the complexity of undesirable behavior among agents, such as control, manipulation, and bribery in election systems. These kinds of voting strategies are often tempting at the individual level but disastrous for the agents as a whole. Creating election systems where the determination of such strategies is difficult is thus an important goal. An interesting set of elections is that of scoring protocols. Previous work in this area has demonstrated the complexity of misuse in cases involving a fixed number of candidates, and of specific election systems on unbounded number of candidates such as Borda. In contrast, we take the first step in generalizing the results of computational complexity of election misuse to cases of infinitely many scoring protocols on an unbounded number of candidates. Interesting families of systems include $k$-approval and $k$-veto elections, in which voters distinguish $k$ candidates from the candidate set. Our main result is to partition the problems of these families based on their complexity. We do so by showing they are polynomial-time computable, NP-hard, or polynomial-time equivalent to another problem of interest. We also demonstrate a surprising connection between manipulation in election systems and some graph theory problems