We introduce learning programs by learning from failures. In this approach, an inductive logic programming (ILP) system (the learner) decomposes the learning problem into three separate stages: generate, test, and constrain. In the generate stage, the learner generates a hypothesis (a logic program) that satisfies a set of hypothesis constraints (constraints on the syntactic form of hypotheses). In the test stage, the learner tests the hypothesis against training examples. A hypothesis fails when it does not entail all the positive examples or entails a negative example. If a hypothesis fails, then, in the constrain stage, the learner learns constraints from the failed hypothesis to prune the hypothesis space, i.e. to constrain subsequent hypothesis generation. For instance, if a hypothesis is too general (entails a negative example), the constraints prune generalisations of the hypothesis. If a hypothesis is too specific (does not entail all the positive examples), the constraints prune specialisations of the hypothesis. This loop repeats until (1) the learner finds a hypothesis that entails all the positive and none of the negative examples, or (2) there are no more hypotheses to test. We implement our idea in Popper, an ILP system which combines answer set programming and Prolog. Popper supports infinite domains, reasoning about lists and numbers, learning optimal (textually minimal) programs, and learning recursive programs. Our experimental results on three diverse domains (number theory problems, robot strategies, and list transformations) show that (1) constraints drastically improve learning performance, and (2) Popper can substantially outperform state-of-the-art ILP systems, both in terms of predictive accuracies and learning times.

Our goal is to model expert decision processes in Bridge. To do so, we propose a methodology involving human experts, black box decision programs, and relational supervised machine learning systems. The aim is to obtain a global model for this decision process, that is both expressive and has high predictive performance. Following the success of supervised methods of the deep network family, and a growing pressure from society imposing that automated decision processes be made more transparent, a growing number of AI researchers are (re)exploring techniques to interpret, justify, or explain "black box" classifiers (referred to as the Black Box Outcome Explanation Problem [Guidotti et al., 2019]). It is a question of building, a posteriori, explicit models in symbolic languages, most often in the form of rules or deci-Daniel Braun, Colin Deheeger, Jean Pierre Desmoulins, Jean Baptiste Fantun, Swann Legras, Alexis Rimbaud, Céline Rouveirol, Henry Soldano and Véronique Ventos NukkAI, Paris, France Henry Soldano and Céline Rouveirol Université Sorbonne Paris-Nord, L.I.P.N UMR-CNRS 7030 Villetaneuse, France

ESF thus beckons the valuation of ecosystem services (VES) as a means to signalling nature's contribution to the (re)production of value (Barbier et al., 2009; Villa et al., 2009; Fisher et al., 2010; Gómez-Baggethun et al., 2016); for value is the central category of modern capitalist societies, and the valorisation of value -- i.e., economic growth sublimated into economic development -- their driving force (see, e.g., Mankiw (2016) and Holden et al. (2017)). VES is, in this sense, inscribed in an interpretive approach to modern capitalist praxis, not only invoking assumptions that are instrumentally validated in a retroactive manner, but also taking for granted precisely those historical and material conditions which VES is meant to interpret and, in doing so, reproduce. Overlooking the historical basis of ESF and VES has important practical consequences. When VES practitioners elicit value, a moment or specific field of the social praxis embodied in the valorisation of value is inaugurated, allowing value to mediate other social constructs built around the idea of nature. Since the patterns of actions that make up the capitalist social praxis are presupposed within this new ambit, value takes on a transhistorical quality that justifies its allencompassing and unreflective usage (see, e.g., Badura et al. (2016) and Gómez-Baggethun and Martín-López (2015)).

The goal of Inductive Logic Programming (ILP) is to learn a program that explains a set of examples in the context of some pre-existing background knowledge. Until recently, most research on ILP targeted learning Prolog programs. Our own ILASP system instead learns Answer Set Programs, including normal rules, choice rules and hard and weak constraints. Learning such expressive programs widens the applicability of ILP considerably; for example, enabling preference learning, learning common-sense knowledge, including defaults and exceptions, and learning non-deterministic theories. In this paper, we first give a general overview of ILASP's learning framework and its capabilities. This is followed by a comprehensive summary of the evolution of the ILASP system, presenting the strengths and weaknesses of each version, with a particular emphasis on scalability.

Knowledge graph embeddings are now a widely adopted approach to knowledge representation in which entities and relationships are embedded in vector spaces. In this chapter, we introduce the reader to the concept of knowledge graph embeddings by explaining what they are, how they can be generated and how they can be evaluated. We summarize the state-of-the-art in this field by describing the approaches that have been introduced to represent knowledge in the vector space. In relation to knowledge representation, we consider the problem of explainability, and discuss models and methods for explaining predictions obtained via knowledge graph embeddings.

Data science is a cornerstone of current business practices. A major obstacle to its adoption is that most data analysis techniques are beyond the reach of typical end-users. Spreadsheets are a prime example of this phenomenon: despite being central in all sorts of data processing pipelines, the functionality necessary for processing and analyzing spreadsheets is hidden behind the high wall of spreadsheet formulas, which most end-users can neither write nor understand [Chambers and Scaffidi, 2010]. As a result, spreadsheets are often manipulated and analyzed manually. This increases the chance of making mistakes and prevents scaling beyond small data sets. Lowering the barrier to entry for specifying and solving data science tasks would help ameliorating these issues. Making data science tools more accessible would lower the cost of designing data processing pipelines and taking datadriven decisions. At the same time, accessible data science tools can prevent non-experts from relying on fragile heuristics and improvised solutions. The question we ask is then: is it possible to enable nontechnical end-users to specify and solve data science tasks that match their needs?

In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) D, whose intuitive meaning is that "normally/typically Cs are also Ds". This extension is based on a minimal model semantics corresponding to a notion of rational closure, built upon preferential models. We recall the basic concepts underlying preferential Description Logics. We also present two extensions of the preferential semantics: on the one hand, we consider probabilistic extensions, based on a distributed semantics that is suitable for tackling the problem of commonsense concept combination, on the other hand, we consider other strengthening of the rational closure semantics and construction to avoid the so called "blocking of property inheritance problem".

I know thou wilt say "ay," And I will take thy word. Yet if thou swear'st Thou mayst prove false. At lovers' perjuries, They say, Jove laughs.

Existential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in the context of ontology-mediated query answering. Forward chaining, also known as the chase, is a fundamental tool for computing universal models of knowledge bases, which consist of existential rules and facts. Several chase variants have been defined, which differ on the way they handle redundancies. A set of existential rules is bounded if it ensures the existence of a bound on the depth of the chase, independently from any set of facts. Deciding if a set of rules is bounded is an undecidable problem for all chase variants. Nevertheless, when computing universal models, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound remains unknown or even very large. Hence, we investigate the decidability of the k-boundedness problem, which asks whether the depth of the chase for a given set of rules is bounded by an integer k. We identify a general property which, when satisfied by a chase variant, leads to the decidability of k-boundedness. We then show that the main chase variants satisfy this property, namely the oblivious, semi-oblivious (aka Skolem), and restricted chase, as well as their breadth-first versions. This paper is under consideration for publication in Theory and Practice of Logic Programming.

We consider three modern roles for logic in artificial intelligence, which are based on the theory of tractable Boolean circuits: (1) logic as a basis for computation, (2) logic for learning from a combination of data and knowledge, and (3) logic for reasoning about the behavior of machine learning systems.