We investigate conjunctive normal form (CNF) encodings of a function represented with a smooth decomposable negation normal form (DNNF). Several encodings of DNNFs and decision diagrams were considered by (Abio et al. 2016). The authors differentiate between encodings which implement consistency or domain consistency from encodings which implement unit refutation completeness or propagation completeness (in both cases implements means by unit propagation). The difference is that in the former case we do not care about properties of the encoding with respect to the auxiliary variables while in the latter case we treat all variables (the input ones and the auxiliary ones) in the same way. The latter case is useful if a DNNF is a part of a problem containing also other constraints and a SAT solver is used to test satisfiability. The currently known encodings of smooth DNNF theories implement domain consistency. Building on this and the result of (Abio et al. 2016) on an encoding of decision diagrams which implements propagation completeness, we present a new encoding of a smooth DNNF which implements propagation completeness. This closes the gap left open in the literature on encodings of DNNFs.

We describe the concept of logical scaffolds, which can be used to improve the quality of software that relies on AI components. We explain how some of the existing ideas on runtime monitors for perception systems can be seen as a specific instance of logical scaffolds. Furthermore, we describe how logical scaffolds may be useful for improving AI programs beyond perception systems, to include general prediction systems and agent behavior models. Keywords: AI · Autonomous systems · Formal methods. 1 Introduction Recent progress in AI has led to possible deployment in a wide variety of important domains. This includes safety-critical cyberphysical systems such as automobiles [1] and airplanes [7], but also decision making systems in diverse domains including legal [15] and military applications [3].

Humans are capable of abstracting away irrelevant details when studying problems. This is especially noticeable for problems over grid-cells, as humans are able to disregard certain parts of the grid and focus on the key elements important for the problem. Recently, the notion of abstraction has been introduced for Answer Set Programming (ASP), a knowledge representation and reasoning paradigm widely used in problem solving, with the potential to understand the key elements of a program that play a role in finding a solution. The present paper takes this further and empowers abstraction to deal with structural aspects, and in particular with hierarchical abstraction over the domain. We focus on obtaining the reasons for unsolvability of problems on grids, and show the possibility to automatically achieve human-like abstractions that distinguish only the relevant part of the grid. A user study on abstract explanations confirms the similarity of the focus points in machine vs. human explanations and reaffirms the challenge of employing abstraction to obtain machine explanations.

This paper formally compares some central notions from two well-known formalisms for rule-based argumentation, DeLP and ASPIC+. The comparisons especially focus on intuitive adequacy and inter-translatability, consistency, and closure properties. As for differences in the definitions of arguments and attack, it turns out that DeLP's definitions are intuitively appealing but that they may not fully comply with Caminada and Amgoud's rationality postulates of strict closure and indirect consistency. For some special cases, the DeLP definitions are shown to fare better than ASPIC+. Next, it is argued that there are reasons to consider a variant of DeLP with grounded semantics, since in some examples its current notion of warrant arguably has counterintuitive consequences and may lead to sets of warranted arguments that are not admissible. Finally, under some minimality and consistency assumptions on ASPIC+ arguments, a one-to-many correspondence between ASPIC+ arguments and DeLP arguments is identified in such a way that if the DeLP warranting procedure is changed to grounded semantics, then DeLP notion of warrant and ASPIC+'s notion of justification are equivalent. This result is proven for three alternative definitions of attack.

The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network. This paper addresses the synthesis of these Boolean functions from constraints on their domain and emerging dynamical properties of the resulting network. The dynamical properties relate to the existence and absence of trajectories between partially observed configurations, and to the stable behaviours (fixpoints and cyclic attractors). The synthesis is expressed as a Boolean satisfiability problem relying on Answer-Set Programming with a parametrized complexity, and leads to a complete non-redundant characterization of the set of solutions. Considered constraints are particularly suited to address the synthesis of models of cellular differentiation processes, as illustrated on a case study. The scalability of the approach is demonstrated on random networks with scale-free structures up to 100 to 1,000 nodes depending on the type of constraints.

Probabilistic programming is a powerful abstraction for statistical machine learning. Applying static analysis methods to probabilistic programs could serve to optimize the learning process, automatically verify properties of models, and improve the programming interface for users. This field of static analysis for probabilistic programming (SAPP) is young and unorganized, consisting of a constellation of techniques with various goals and limitations. The primary aim of this work is to synthesize the major contributions of the SAPP field within an organizing structure and context. We provide technical background for static analysis and probabilistic programming, suggest a functional taxonomy for probabilistic programming languages, and analyze the applicability of major ideas in the SAPP field. We conclude that, while current static analysis techniques for probabilistic programs have practical limitations, there are a number of future directions with high potential to improve the state of statistical machine learning.

Transfer of Temporal Logic Formulas in Reinforcement Learning Zhe Xu and Ufuk Topcu Abstract Transferring high-level knowledge from a source task to a target task is an effective way to expedite reinforcement learning (RL). For example, propositional logic and first-order logic have been used as representations of such knowledge. We study the transfer of knowledge between tasks in which the timing of the events matters. We call such tasks temporal tasks . We concretize similarity between temporal tasks through a notion of logical transferability, and develop a transfer learning approach between different yet similar temporal tasks. We first propose an inference technique to extract metric interval temporal logic (MITL) formulas in sequential disjunctive normal form from labeled trajectories collected in RL of the two tasks. If logical transferability is identified through this inference, we construct a timed automaton for each sequential conjunctive subformula of the inferred MITL formulas from both tasks. We perform RL on the extended state which includes the locations and clock valuations of the timed automata for the source task. We then establish mappings between the corresponding components (clocks, locations, etc.) of the timed automata from the two tasks, and transfer the extended Q-functions based on the established mappings. Finally, we perform RL on the extended state for the target task, starting with the transferred extended Q-functions. Our results in two case studies show, depending on how similar the source task and the target task are, that the sampling efficiency for the target task can be improved by up to one order of magnitude by performing RL in the extended state space, and further improved by up to another order of magnitude using the transferred extended Q-functions. 1 Introduction Reinforcement learning (RL) has been successful in numerous applications.

We study classification problems over relational background structures for hypotheses that are defined using logics with counting. The aim of this paper is to find learning algorithms running in time sublinear in the size of the background structure. We show that hypotheses defined by FOCN(P)-formulas over structures of polylogarithmic degree can be learned in sublinear time. Furthermore, we prove that for structures of unbounded degree there is no sublinear learning algorithm for first-order formulas.

The explication and the generation of explanations are prominent topics in artificial intelligence and data science, in order to make methods and systems more transparent and understandable for humans. This paper investigates the problem of link analysis, specifically link prediction and anomalous link discovery in social networks using the declarative method of Answer set programming (ASP). Applying ASP for link prediction provides a powerful declarative approach, e. g., for incorporating domain knowledge for explicative prediction. In this context, we propose a novel method for generating explanations - as offline justifications - using declarative program transformations. The method itself is purely based on syntactic transformations of declarative programs, e. g., in an ASP formalism, using rule instrumentation. We demonstrate the efficacy of the proposed approach, exemplifying it in an application on link analysis in social networks, also including domain knowledge.

Answer Set Programming (ASP) has become, the paradigm of choice in the field of logic programming and non-monotonic reasoning. Thanks to the availability of efficient solvers, ASP has been successfully employed in a large number of application domains. The term GPU-computing indicates a recent programming paradigm aimed at enabling the use of modern parallel Graphical Processing Units (GPUs) for general purpose computing. In this paper we describe an approach to ASP-solving that exploits GPU parallelism. The design of a GPU-based solver poses various challenges due to the peculiarities of GPUs' software and hardware architectures and to the intrinsic nature of the satisfiability problem.