This document is designed to be a first-year graduate-level introduction to probabilistic programming. It not only provides a thorough background for anyone wishing to use a probabilistic programming system, but also introduces the techniques needed to design and build these systems. It is aimed at people who have an undergraduate-level understanding of either or, ideally, both probabilistic machine learning and programming languages. We start with a discussion of model-based reasoning and explain why conditioning as a foundational computation is central to the fields of probabilistic machine learning and artificial intelligence. We then introduce a simple first-order probabilistic programming language (PPL) whose programs define static-computation-graph, finite-variable-cardinality models. In the context of this restricted PPL we introduce fundamental inference algorithms and describe how they can be implemented in the context of models denoted by probabilistic programs. In the second part of this document, we introduce a higher-order probabilistic programming language, with a functionality analogous to that of established programming languages. This affords the opportunity to define models with dynamic computation graphs, at the cost of requiring inference methods that generate samples by repeatedly executing the program. Foundational inference algorithms for this kind of probabilistic programming language are explained in the context of an interface between program executions and an inference controller. This document closes with a chapter on advanced topics which we believe to be, at the time of writing, interesting directions for probabilistic programming research; directions that point towards a tight integration with deep neural network research and the development of systems for next-generation artificial intelligence applications.

We propose a generic numerical measure of the inconsistency of a database with respect to a set of integrity constraints. It is based on an abstract repair semantics. In particular, an inconsistency measure associated to cardinality-repairs is investigated in detail. More specifically, it is shown that it can be computed via answer-set programs, but sometimes its computation can be intractable in data complexity. However, polynomial-time fixed-parameter exact computation, and also deterministic and randomized approximations are exhibited. The behavior of this measure under small updates is analyzed. Furthermore, alternative inconsistency measures are proposed and discussed.

Given one or two examples, humans are good at understanding how to solve a problem independently of its domain, because they are able to detect what the problem is and to choose the appropriate background knowledge according to the context. For instance, presented with the string "8/17/2017" to be transformed to "17th of August of 2017", humans will process this in two steps: (1) they recognise that it is a date and (2) they map the date to the 17th of August of 2017. Inductive Programming (IP) aims at learning declarative (functional or logic) programs from examples. Two key advantages of IP are the use of background knowledge and the ability to synthesise programs from a few input/output examples (as humans do). In this paper we propose to use IP as a means for automating repetitive data manipulation tasks, frequently presented during the process of {\em data wrangling} in many data manipulation problems. Here we show that with the use of general-purpose declarative (programming) languages jointly with generic IP systems and the definition of domain-specific knowledge, many specific data wrangling problems from different application domains can be automatically solved from very few examples. We also propose an integrated benchmark for data wrangling, which we share publicly for the community.

New generations of distributed systems are opening novel perspectives for logic programming (LP): on the one hand, service-oriented architectures represent nowadays the standard approach for distributed systems engineering; on the other hand, pervasive systems mandate for situated intelligence. In this paper we introduce the notion of Logic Programming as a Service (LPaaS) as a means to address the needs of pervasive intelligent systems through logic engines exploited as a distributed service. First we define the abstract architectural model by re-interpreting classical LP notions in the new context; then we elaborate on the nature of LP interpreted as a service by describing the basic LPaaS interface. Finally, we show how LPaaS works in practice by discussing its implementation in terms of distributed tuProlog engines, accounting for basic issues such as interoperability and configurability.

This article proposes the axiomatizations of contingency logics of various natural classes of neighborhood frames. In particular, by defining a suitable canonical neighborhood function, we give sound and complete axiomatizations of monotone contingency logic and regular contingency logic, thereby answering two open questions raised by Bakhtiari, van Ditmarsch, and Hansen. The canonical function is inspired by a function proposed by Kuhn in~1995. We show that Kuhn's function is actually equal to a related function originally given by Humberstone.

Recent progress in logic programming (e.g., the development of the Answer Set Programming paradigm) has made it possible to teach it to general undergraduate and even middle/high school students. Given the limited exposure of these students to computer science, the complexity of downloading, installing and using tools for writing logic programs could be a major barrier for logic programming to reach a much wider audience. We developed onlineSPARC, an online answer set programming environment with a self contained file system and a simple interface. It allows users to type/edit logic programs and perform several tasks over programs, including asking a query to a program, getting the answer sets of a program, and producing a drawing/animation based on the answer sets of a program.

Artificial Intelligence (AI) approaches to problem-solving and decision-making are becoming more and more complex, leading to a decrease in the understandability of solutions. The European Union's new General Data Protection Regulation tries to tackle this problem by stipulating a "right to explanation" for decisions made by AI systems. One of the AI paradigms that may be affected by this new regulation is Answer Set Programming (ASP). Thanks to the emergence of efficient solvers, ASP has recently been used for problem-solving in a variety of domains, including medicine, cryptography, and biology. To ensure the successful application of ASP as a problem-solving paradigm in the future, explanations of ASP solutions are crucial. In this survey, we give an overview of approaches that provide an answer to the question of why an answer set is a solution to a given problem, notably off-line justifications, causal graphs, argumentative explanations and why-not provenance, and highlight their similarities and differences. Moreover, we review methods explaining why a set of literals is not an answer set or why no solution exists at all.

We enable aProbLog---a probabilistic logical programming approach---to reason in presence of uncertain probabilities represented as Beta-distributed random variables. We achieve the same performance of state-of-the-art algorithms for highly specified and engineered domains, while simultaneously we maintain the flexibility offered by aProbLog in handling complex relational domains. Our motivation is that faithfully capturing the distribution of probabilities is necessary to compute an expected utility for effective decision making under uncertainty: unfortunately, these probability distributions can be highly uncertain due to sparse data. To understand and accurately manipulate such probability distributions we need a well-defined theoretical framework that is provided by the Beta distribution, which specifies a distribution of probabilities representing all the possible values of a probability when the exact value is unknown.

Recent research in extensions of Answer Set Programming has included a renewed interest in the language of Epistemic Specifications, which adds modal operators K ("known") and M ("may be true") to provide for more powerful introspective reasoning and enhanced capability, particularly when reasoning with incomplete information. An epistemic logic program is a set of rules in this language. Infused with the research has been the desire for an efficient solver to enable the practical use of such programs for problem solving. In this paper, we report on the current state of development of epistemic logic program solvers.

Institute of Logic and Computation, TU Wien, Vienna, Austria (email: {zeynep,eiter}@kr.tuwien.ac.at) submitted 1 January 2003; revised 1 January 2003; accepted 1 January 2003 ASP programs are a convenient tool for problem solving, whereas with large problem instances the size of the state space can be prohibitive. We consider abstraction as a means of over-approximation and introduce a method to automatically abstract (possibly non-ground) ASP programs that preserves their structure, while reducing the size of the problem.