Neurosymbolic artificial intelligence (AI) is an emerging branch of AI that combines the strengths of symbolic AI and sub-symbolic AI. A major drawback of sub-symbolic AI is that it acts as a "black box", meaning that predictions are difficult to explain, making the testing & evaluation (T&E) and validation & verification (V&V) processes of a system that uses sub-symbolic AI a challenge. Since neurosymbolic AI combines the advantages of both symbolic and sub-symbolic AI, this survey explores how neurosymbolic applications can ease the V&V process. This survey considers two taxonomies of neurosymbolic AI, evaluates them, and analyzes which algorithms are commonly used as the symbolic and sub-symbolic components in current applications. Additionally, an overview of current techniques for the T&E and V&V processes of these components is provided. Furthermore, it is investigated how the symbolic part is used for T&E and V&V purposes in current neurosymbolic applications. Our research shows that neurosymbolic AI as great potential to ease the T&E and V&V processes of sub-symbolic AI by leveraging the possibilities of symbolic AI. Additionally, the applicability of current T&E and V&V methods to neurosymbolic AI is assessed, and how different neurosymbolic architectures can impact these methods is explored. It is found that current T&E and V&V techniques are partly sufficient to test, evaluate, verify, or validate the symbolic and sub-symbolic part of neurosymbolic applications independently, while some of them use approaches where current T&E and V&V methods are not applicable by default, and adjustments or even new approaches are needed. Our research shows that there is great potential in using symbolic AI to test, evaluate, verify, or validate the predictions of a sub-symbolic model, making neurosymbolic AI an interesting research direction for safe, secure, and trustworthy AI.

The Tactician's Web is a platform offering a large web of strongly interconnected, machine-checked, formal mathematical knowledge conveniently packaged for machine learning, analytics, and proof engineering. Built on top of the Coq proof assistant, the platform exports a dataset containing a wide variety of formal theories, presented as a web of definitions, theorems, proof terms, tactics, and proof states. Theories are encoded both as a semantic graph (rendered below) and as human-readable text, each with a unique set of advantages and disadvantages. Proving agents may interact with Coq through the same rich data representation and can be automatically benchmarked on a set of theorems. Tight integration with Coq provides the unique possibility to make agents available to proof engineers as practical tools.

Concepts abound in mathematics and its applications. They vary greatly between subject areas, and new ones are introduced in each mathematical paper or application. A formal theory builds a hierarchy of definitions, theorems and proofs that reference each other. When an AI agent is proving a new theorem, most of the mathematical concepts and lemmas relevant to that theorem may have never been seen during training. This is especially true in the Coq proof assistant, which has a diverse library of Coq projects, each with its own definitions, lemmas, and even custom tactic procedures used to prove those lemmas. It is essential for agents to incorporate such new information into their knowledge base on the fly. We work towards this goal by utilizing a new, large-scale, graph-based dataset for machine learning in Coq. We leverage a faithful graph-representation of Coq terms that induces a directed graph of dependencies between definitions to create a novel graph neural network, Graph2Tac (G2T), that takes into account not only the current goal, but also the entire hierarchy of definitions that led to the current goal. G2T is an online model that is deeply integrated into the users' workflow and can adapt in real time to new Coq projects and their definitions. It complements well with other online models that learn in real time from new proof scripts. Our novel definition embedding task, which is trained to compute representations of mathematical concepts not seen during training, boosts the performance of the neural network to rival state-of-the-art k-nearest neighbor predictors.

Past research into robotic planning with temporal logic specifications, notably Linear Temporal Logic (LTL), was largely based on singular formulas for individual or groups of robots. But with increasing task complexity, LTL formulas unavoidably grow lengthy, complicating interpretation and specification generation, and straining the computational capacities of the planners. A recent development has been the hierarchical representation of LTL [1] that contains multiple temporal logic specifications, providing a more interpretable framework. However, the proposed planning algorithm assumes the independence of robots within each specification, limiting their application to multi-robot coordination with complex temporal constraints. In this work, we formulated a decomposition-based hierarchical framework. At the high level, each specification is first decomposed into a set of atomic sub-tasks. We further infer the temporal relations among the sub-tasks of different specifications to construct a task network. Subsequently, a Mixed Integer Linear Program is utilized to assign sub-tasks to various robots. At the lower level, domain-specific controllers are employed to execute sub-tasks. Our approach was experimentally applied to domains of robotic navigation and manipulation. The outcomes of thorough simulations, which included comparative analyses, demonstrated the effectiveness of the proposed approach.

Artificial Intelligence is now recognized as a general-purpose technology with ample impact on human life. This work aims at understanding the evolution of AI and, in particular Machine learning, from the perspective of researchers' contributions to the field. In order to do so, we present several measures allowing the analyses of AI and machine learning researchers' impact, influence, and leadership over the last decades. This work also contributes, to a certain extent, to shed new light on the history and evolution of AI by exploring the dynamics involved in the field's evolution by looking at papers published at the flagship AI and machine learning conferences since the first International Joint Conference on Artificial Intelligence (IJCAI) held in 1969. AI development and evolution have led to increasing research output, reflected in the number of articles published over the last sixty years. We construct comprehensive citation collaboration and paper-author datasets and compute corresponding centrality measures to carry out our analyses. These analyses allow a better understanding of how AI has reached its current state of affairs in research. Throughout the process, we correlate these datasets with the work of the ACM Turing Award winners and the so-called two AI winters the field has gone through. We also look at self-citation trends and new authors' behaviors. Finally, we present a novel way to infer the country of affiliation of a paper from its organization. Therefore, this work provides a deep analysis of Artificial Intelligence history from information gathered and analysed from large technical venues datasets and suggests novel insights that can contribute to understanding and measuring AI's evolution.

Program synthesis is the task of automatically generating code based on a specification. In Syntax-Guided Synthesis (SyGuS) this specification is a combination of a syntactic template and a logical formula, and the result is guaranteed to satisfy both. We present a reinforcement-learning guided algorithm for SyGuS which uses Monte-Carlo Tree Search (MCTS) to search the space of candidate solutions. Our algorithm learns policy and value functions which, combined with the upper confidence bound for trees, allow it to balance exploration and exploitation. A common challenge in applying machine learning approaches to syntax-guided synthesis is the scarcity of training data. To address this, we present a method for automatically generating training data for SyGuS based on anti-unification of existing first-order satisfiability problems, which we use to train our MCTS policy. We implement and evaluate this setup and demonstrate that learned policy and value improve the synthesis performance over a baseline by over 26 percentage points in the training and testing sets. Our tool outperforms state-of-the-art tool cvc5 on the training set and performs comparably in terms of the total number of problems solved on the testing set (solving 23% of the benchmarks on which cvc5 fails). We make our data set publicly available, to enable further application of machine learning methods to the SyGuS problem.

Unit testing frameworks are nowadays considered a best practice, included in almost all modern software development processes, to achieve rapid development of correct specifications. Knowledge representation and reasoning paradigms such as Answer Set Programming (ASP), that have been used in industry-level applications, are not an exception. Indeed, the first unit testing specification language for ASP was proposed in 2011 as a feature of the ASPIDE development environment. Later, a more portable unit testing language was included in the LANA annotation language. In this paper we revisit both languages and tools for unit testing in ASP. We propose a new unit test specification language that allows one to inline tests within ASP programs, and we identify the computational complexity of the tasks associated with checking the various program-correctness assertions. Test-case specifications are transparent to the traditional evaluation, but can be interpreted by a specific testing tool. Thus, we present a novel environment supporting test driven development of ASP programs.

When reasoning about actions, e.g., by means of task planning or agent programming with Golog, the robot's actions are typically modeled on an abstract level, where complex actions such as picking up an object are treated as atomic primitives with deterministic effects and preconditions that only depend on the current state. However, when executing such an action on a robot it can no longer be seen as a primitive. Instead, action execution is a complex task involving multiple steps with additional temporal preconditions and timing constraints. Furthermore, the action may be noisy, e.g., producing erroneous sensing results and not always having the desired effects. While these aspects are typically ignored in reasoning tasks, they need to be dealt with during execution. In this thesis, we propose several approaches towards closing this gap.

Given a conditional sentence "P=>Q" (if P then Q) and respective facts, four different types of inferences are observed in human reasoning. Affirming the antecedent (AA) (or modus ponens) reasons Q from P; affirming the consequent (AC) reasons P from Q; denying the antecedent (DA) reasons -Q from -P; and denying the consequent (DC) (or modus tollens) reasons -P from -Q. Among them, AA and DC are logically valid, while AC and DA are logically invalid and often called logical fallacies. Nevertheless, humans often perform AC or DA as pragmatic inference in daily life. In this paper, we realize AC, DA and DC inferences in answer set programming. Eight different types of completion are introduced and their semantics are given by answer sets. We investigate formal properties and characterize human reasoning tasks in cognitive psychology. Those completions are also applied to commonsense reasoning in AI.

Effectively specifying and implementing robotic missions poses a set of challenges to software engineering for robotic systems. These challenges stem from the need to formalize and execute a robot's high-level tasks while considering various application scenarios and conditions, also known as contexts, in real-world operational environments. Writing correct mission specifications that explicitly account for multiple contexts can be tedious and error-prone. Furthermore, as the number of contexts, and consequently the complexity of the specification, increases, generating a correct-by-construction implementation (e.g., by using synthesis methods) can become intractable. A viable approach to address these issues is to decompose the mission specification into smaller, manageable sub-missions, with each sub-mission tailored to a specific context. Nevertheless, this compositional approach introduces its own set of challenges in ensuring the overall mission's correctness. In this paper, we propose a novel compositional framework for specifying and implementing contextual robotic missions using assume-guarantee contracts. The mission specification is structured in a hierarchical and modular fashion, allowing for each sub-mission to be synthesized as an independent robot controller. We address the problem of dynamically switching between sub-mission controllers while ensuring correctness under predefined conditions.