I had a fun ride attending a very interesting lecture this semester called Programming Paradigms. I learned about the four main paradigms that exist: imperative, object-oriented, functional and logic programming. Now, I'm sure every developer has heard about imperative, OO and functional, but to be honest I had no idea what logic programming was about. I was intrigued, what could this paradigm I had never heard about be, what does it excel in and could it be useful for day-to-day programming problems? The book The Pragmatic Programmer has a tip called "Invest Regularly in Your Knowledge Portfolio": Different languages solve the same problems in different ways.

We propose a family of probabilistic description logics (DLs) that are derived in a principled way from Halpern's probabilistic first-order logic. The resulting probabilistic DLs have a two-dimensional semantics similar to temporal DLs and are well-suited for representing subjective probabilities. We carry out a detailed study of reasoning in the new family of logics, concentrating on probabilistic extensions of the DLs ALC and EL, and showing that the complexity ranges from PTime via ExpTime and 2ExpTime to undecidable.

Whenever one separates sociology and technology, one misses the point.

Automatic translation from natural language descriptions into programs is a long-standing challenging problem. In this work, we consider a simple yet important sub-problem: translation from textual descriptions to If-Then programs. We devise a novel neural network architecture for this task which we train end-to-end. Specifically, we introduce Latent Attention, which computes multiplicative weights for the words in the description in a two-stage process with the goal of better leveraging the natural language structures that indicate the relevant parts for predicting program elements. Our architecture reduces the error rate by 28.57% compared to prior art. We also propose a one-shot learning scenario of If-Then program synthesis and simulate it with our existing dataset. We demonstrate a variation on the training procedure for this scenario that outperforms the original procedure, significantly closing the gap to the model trained with all data.

We present discriminative Gaifman models, a novel family of relational machine learning models. Gaifman models learn feature representations bottom up from representations of locally connected and bounded-size regions of knowledge bases (KBs). Considering local and bounded-size neighborhoods of knowledge bases renders logical inference and learning tractable, mitigates the problem of overfitting, and facilitates weight sharing. Gaifman models sample neighborhoods of knowledge bases so as to make the learned relational models more robust to missing objects and relations which is a common situation in open-world KBs. We present the core ideas of Gaifman models and apply them to large-scale relational learning problems. We also discuss the ways in which Gaifman models relate to some existing relational machine learning approaches.

Statistical relational models provide compact encodings of probabilistic dependencies in relational domains, but result in highly intractable graphical models. The goal of lifted inference is to carry out probabilistic inference without needing to reason about each individual separately, by instead treating exchangeable, undistinguished objects as a whole. In this paper, we study the domain recursion inference rule, which, despite its central role in early theoretical results on domain-lifted inference, has later been believed redundant. We show that this rule is more powerful than expected, and in fact significantly extends the range of models for which lifted inference runs in time polynomial in the number of individuals in the domain. This includes an open problem called S4, the symmetric transitivity model, and a first-order logic encoding of the birthday paradox. We further identify new classes S2FO2 and S2RU of domain-liftable theories, which respectively subsume FO2 and recursively unary theories, the largest classes of domain-liftable theories known so far, and show that using domain recursion can achieve exponential speedup even in theories that cannot fully be lifted with the existing set of inference rules.

We study the effectiveness of neural sequence models for premise selection in automated theorem proving, one of the main bottlenecks in the formalization of mathematics. We propose a two stage approach for this task that yields good results for the premise selection task on the Mizar corpus while avoiding the handengineered featuresof existing state-of-the-art models. To our knowledge, this is the first time deep learning has been applied to theorem proving on a large scale.

Disjunctive Answer Set Programming (ASP) is a powerful declarative programming paradigm whose main decision problems are located on the second level of the polynomial hierarchy. Identifying tractable fragments and developing efficient algorithms for such fragments are thus important objectives in order to complement the sophisticated ASP systems available to date. Hard problems can become tractable if some problem parameter is bounded by a fixed constant; such problems are then called fixed-parameter tractable (FPT). While several FPT results for ASP exist, parameters that relate to directed or signed graphs representing the program at hand have been neglected so far. In this paper, we first give some negative observations showing that directed width measures on the dependency graph of a program do not lead to FPT results. We then consider the graph parameter of signed clique-width and present a novel dynamic programming algorithm that is FPT w.r.t. this parameter. Clique-width is more general than the well-known treewidth, and, to the best of our knowledge, ours is the first FPT algorithm for bounded clique-width for reasoning problems beyond SAT.

Social commitment protocols regulate interactions of agents in multiagent systems. Several methods have been developed to analyze properties of commitment protocols. However, analysis of an agent's behavior in a commitment protocol, which should take into account the agent's goals and beliefs, has received less attention. In this paper we present ProMoca framework to address this issue. Firstly, we develop an expressive formal language to model agents with respect to their commitments. Our language provides dedicated elements to define commitment protocols, and model agents in terms of their goals, behaviors, and beliefs. Furthermore, our language provides probabilistic and non-deterministic elements to model uncertainty in agents' beliefs. Secondly, we identify two essential properties of an agent with respect to a commitment protocol, namely compliance and goal satisfaction. We formalize these properties using a probabilistic variant of linear temporal logic. Thirdly, we adapt a probabilistic model checking algorithm to automatically analyze compliance and goal satisfaction properties. Finally, we present empirical results about efficiency and scalability of ProMoca.

The aim of this paper is to investigate the interplay between knowledge shared by a group of agents and its coalition ability. We investigate this relation in the standard context of imperfect information concurrent game. We assume that whenever a set of agents form a coalition to achieve a goal, they share their knowledge before acting. Based on this assumption, we propose a new semantics for alternating-time temporal logic with imperfect information and perfect recall. It turns out that this semantics is sufficient to preserve all the desirable properties of coalition ability in traditional coalitional logics. Meanwhile, we investigate how knowledge sharing within a group of agents contributes to its coalitional ability through the interplay of epistemic and coalition modalities. This work provides a partial answer to the question: which kind of group knowledge is required for a group to achieve their goals in the context of imperfect information.