While AI techniques have found many successful applications in autonomous systems, many of them permit behaviours that are difficult to interpret and may lead to uncertain results. We follow the "verification as planning" paradigm and propose to use model checking techniques to solve planning and goal reasoning problems for autonomous systems. We give a new formulation of Goal Task Network (GTN) that is tailored for our model checking based framework. We then provide a systematic method that models GTNs in the model checker Process Analysis Toolkit (PAT). We present our planning and goal reasoning system as a framework called Goal Reasoning And Verification for Independent Trusted Autonomous Systems (GRAVITAS) and discuss how it helps provide trustworthy plans in an uncertain environment. Finally, we demonstrate the proposed ideas in an experiment that simulates a survey mission performed by the REMUS-100 autonomous underwater vehicle.

The problem of deciding the validity (QSAT) of quantified Boolean formulas (QBF) is a vivid research area in both theory and practice. In the field of parameterized algorithmics, the well-studied graph measure treewidth turned out to be a successful parameter. A well-known result by Chen in parameterized complexity is that QSAT when parameterized by the treewidth of the primal graph of the input formula together with the quantifier depth of the formula is fixed-parameter tractable. More precisely, the runtime of such an algorithm is polynomial in the formula size and exponential in the treewidth, where the exponential function in the treewidth is a tower, whose height is the quantifier depth. A natural question is whether one can significantly improve these results and decrease the tower while assuming the Exponential Time Hypothesis (ETH). In the last years, there has been a growing interest in the quest of establishing lower bounds under ETH, showing mostly problem-specific lower bounds up to the third level of the polynomial hierarchy. Still, an important question is to settle this as general as possible and to cover the whole polynomial hierarchy. In this work, we show lower bounds based on the ETH for arbitrary QBFs parameterized by treewidth (and quantifier depth). More formally, we establish lower bounds for QSAT and treewidth, namely, that under ETH there cannot be an algorithm that solves QSAT of quantifier depth i in runtime significantly better than i-fold exponential in the treewidth and polynomial in the input size. In doing so, we provide a versatile reduction technique to compress treewidth that encodes the essence of dynamic programming on arbitrary tree decompositions. Further, we describe a general methodology for a more fine-grained analysis of problems parameterized by treewidth that are at higher levels of the polynomial hierarchy.

Answer set programming (ASP) is a declarative problem solvi ng paradigm for nonmonotonic reasoning. ASP allows intuitiive represe ntation of combinatorial search and optimization problems and is widely use d for knowledge representation and reasoning in various applications like plan generation, natural language processing etc [14, 15]. But ASP can not dea l with fuzzy information, where attributes and truth degrees lie in a con tinuous range of values. Fuzzy Answer Set Programming (F ASP) is proposed as a n extension of ASP that allows graded truth values from the interval [0,1 ]. Theoretical advancement of F ASP is remarkable [18, 32, 9, 22, 23]. Howeve r, this approach performs reasoning with absolutely certain but vagu e information and doesn't involve reasoning with uncertain information.

The growing adoption of ITsystems for the modelling and execution of (business) processes or services has thrust the scientific investigation towards techniques and tools which support complex forms of process analysis. These techniques, nowadays grouped under the umbrella of the Process Mining research area, typically rely on observation of past (tracked and logged) process executions. A first important limitation in this field is the fact that the majority of the techniques paired with concrete tool support only consider activities, but lack the ability to take into account the data objects manipulated by these activities. Second, Process Mining techniques mainly rely on complete observations of terminated process executions. In many real cases, however, only incomplete log information is available. This paper tackles these two shortcomings by proposing an approach to exploit reach-ability to reason on imperative data-aware process models and possibly incomplete process executions. The contribution of this paper is twofold: first, it formulates the trace completion as a reachability problem over data-aware models and second, it provides a rigorous mapping between our data-aware models and three important paradigms for reasoning about dynamic systems, namely Action Languages, Classical Planning, and Model-Checking. This allows us to exploit and extensively evaluate the available tools for the above paradigms to solve the trace repair problem. The rigorous encoding of our data-aware models, based on a common interpretation of the semantics of Action Languages, Classical Planning, and Model-Checking in terms of transition systems, paired with a first comprehensive assessment of the performances of their tools in computing reachability for data-aware workflow net languages, provide a solid contribution to advancing the state-of-the-art on the concrete exploitation of formal verification techniques on business processes.

It is feasible and practically-valuable to bridge the characteristics between graph neural networks (GNNs) and logical reasoning. Despite considerable efforts and successes witnessed in learning Boolean satisfiability (SAT), it remains an open question of learning GNN-based solvers for more complex predicate logic formulae. In this work, we conjectures with theoretically support discussion, that generally defined GNNs present some limitations in reasoning about a set of assignments and proving the unsatisfiability (UNSAT) in Boolean formulae. It implies that GNNs may probably fail in learning the logical reasoning tasks if they contain UNSAT as the sub-problem, thus, included by most of predicate logic reasoning problems.

We study the problem of learning properties of nodes in tree structures. Those properties are specified by logical formulas, such as formulas from first-order or monadic second-order logic. We think of the tree as a database encoding a large dataset and therefore aim for learning algorithms which depend at most sublinearly on the size of the tree. We present a learning algorithm for quantifier-free formulas where the running time only depends polynomially on the number of training examples, but not on the size of the background structure. By a previous result on strings we know that for general first-order or monadic second-order (MSO) formulas a sublinear running time cannot be achieved. However, we show that by building an index on the tree in a linear time preprocessing phase, we can achieve a learning algorithm for MSO formulas with a logarithmic learning phase.

State of the art algorithms for many pattern recognition problems rely on deep network models. Training these models requires a large labeled dataset and considerable computational resources. Also, it is difficult to understand the working of these learned models, limiting their use in some critical applications. Towards addressing these limitations, our architecture draws inspiration from research in cognitive systems, and integrates the principles of commonsense logical reasoning, inductive learning, and deep learning. In the context of answering explanatory questions about scenes and the underlying classification problems, the architecture uses deep networks for extracting features from images and for generating answers to queries. Between these deep networks, it embeds components for non-monotonic logical reasoning with incomplete commonsense domain knowledge, and for decision tree induction. It also incrementally learns and reasons with previously unknown constraints governing the domain's states. We evaluated the architecture in the context of datasets of simulated and real-world images, and a simulated robot computing, executing, and providing explanatory descriptions of plans. Experimental results indicate that in comparison with an ``end to end'' architecture of deep networks, our architecture provides better accuracy on classification problems when the training dataset is small, comparable accuracy with larger datasets, and more accurate answers to explanatory questions. Furthermore, incremental acquisition of previously unknown constraints improves the ability to answer explanatory questions, and extending non-monotonic logical reasoning to support planning and diagnostics improves the reliability and efficiency of computing and executing plans on a simulated robot.

Given a set of Datalog rules, facts, and a query, answers to the query can be inferred bottom-up starting from the facts or top-down starting from the query. For efficiency, top-down evaluation is extended with memoization of inferred facts, and bottom-up evaluation is performed after transformations to make rules driven by the demand from the query. Prior work has shown their precise complexity analysis and relationships. However, when Datalog is extended with even stratified negation, which has a simple and universally accepted semantics, transformations to make rules demand-driven may result in non-stratified negation, which has had many complex semantics and evaluation methods. This paper presents (1) a simple extension to demand transformation, a transformation to make rules demand-driven for Datalog without negation, to support stratified negation, and (2) a simple extension to an optimal bottom-up evaluation method for Datalog with stratified negation, to handle non-stratified negation in the resulting rules. We show that the method provides precise complexity guarantees. It is also optimal in that only facts needed for top-down evaluation of the query are inferred and each firing of a rule to infer such a fact takes worst-case constant time. We extend the precise relationship between top-down evaluation and demand-driven bottom-up evaluation to Datalog with stratified negation. Finally, we show experimental results for performance, as well as applications to previously challenging examples.

The aim of my Ph.D. thesis concerns Reasoning in Highly Reactive Environments. As reasoning in highly reactive environments, we identify the setting in which a knowledge-based agent, with given goals, is deployed in an environment subject to repeated, sudden and possibly unknown changes. This is for instance the typical setting in which, e.g., artificial agents for video-games (the so called "bots"), cleaning robots, bomb clearing robots, and so on are deployed. In all these settings one can follow the classical approach in which the operations of the agent are distinguished in "sensing" the environment with proper interface devices, "thinking", and then behaving accordingly using proper actuators. In order to operate in an highly reactive environment, an artificial agent needs to be: 1. Responsive -> The agent must be able to react repeatedly and in a reasonable amount of time; 2. Elastic -> The agent must stay reactive also under varying workload; 3. Resilient -> The agent must stay responsive also in case of internal failure or failure of one of the programmed actions in the environment. Nowadays, thanks to new technologies in the field of Artificial Intelligence, it is already technically possible to create AI agents that are able to operate in reactive environments. Nevertheless, several issues stay unsolved, and are subject of ongoing research.

Boolean networks are conventionally used to represent and simulate gene regulatory networks. In the analysis of the dynamic of a Boolean network, the attractors are the objects of a special attention. In this work, we propose a novel approach based on Answer Set Programming (ASP) to express Boolean networks and simulate the dynamics of such networks. Our work focuses on the identification of the attractors, it relies on the exhaustive enumeration of all the attractors of synchronous and asynchronous Boolean networks. We applied and evaluated the proposed approach on real biological networks, and the obtained results indicate that this novel approach is promising.