In recent years, Machine Learning (ML) models have achieved remarkable success in various domains. However, these models also tend to demonstrate unsafe behaviors, precluding their deployment in safety-critical systems. To cope with this issue, ample research focuses on developing methods that guarantee the safe behaviour of a given ML model. A prominent example is shielding which incorporates an external component (a "shield") that blocks unwanted behavior. Despite significant progress, shielding suffers from a main setback: it is currently geared towards properties encoded solely in propositional logics (e.g., LTL) and is unsuitable for richer logics. This, in turn, limits the widespread applicability of shielding in many real-world systems. In this work, we address this gap, and extend shielding to LTL modulo theories, by building upon recent advances in reactive synthesis modulo theories. This allowed us to develop a novel approach for generating shields conforming to complex safety specifications in these more expressive, logics. We evaluated our shields and demonstrate their ability to handle rich data with temporal dynamics. To the best of our knowledge, this is the first approach for synthesizing shields for such expressivity.

Advanced Air Mobility (AAM) is a growing field that demands a deep understanding of legal, spatial and temporal concepts in navigation. Hence, any implementation of AAM is forced to deal with the inherent uncertainties of human-inhabited spaces. Enabling growth and innovation requires the creation of a system for safe and robust mission design, i.e., the way we formalize intentions and decide their execution as trajectories for the Unmanned Aerial Vehicle (UAV). Although legal frameworks have emerged to govern urban air spaces, their full integration into the decision process of autonomous agents and operators remains an open task. In this work we present ProMis, a system architecture for probabilistic mission design. It links the data available from various static and dynamic data sources with legal text and operator requirements by following principles of formal verification and probabilistic modeling. Hereby, ProMis enables the combination of low-level perception and high-level rules in AAM to infer validity over the UAV's state-space. To this end, we employ Hybrid Probabilistic Logic Programs (HPLP) as a unifying, intermediate representation between perception and action-taking. Furthermore, we present methods to connect ProMis with crowd-sourced map data by generating HPLP atoms that represent spatial relations in a probabilistic fashion. Our claims of the utility and generality of ProMis are supported by experiments on a diverse set of scenarios and a discussion of the computational demands associated with probabilistic missions.

Large Language Models (LLMs) possess extensive foundational knowledge and moderate reasoning abilities, making them suitable for general task planning in open-world scenarios. However, it is challenging to ground a LLM-generated plan to be executable for the specified robot with certain restrictions. This paper introduces CLMASP, an approach that couples LLMs with Answer Set Programming (ASP) to overcome the limitations, where ASP is a non-monotonic logic programming formalism renowned for its capacity to represent and reason about a robot's action knowledge. CLMASP initiates with a LLM generating a basic skeleton plan, which is subsequently tailored to the specific scenario using a vector database. This plan is then refined by an ASP program with a robot's action knowledge, which integrates implementation details into the skeleton, grounding the LLM's abstract outputs in practical robot contexts. Our experiments conducted on the VirtualHome platform demonstrate CLMASP's efficacy. Compared to the baseline executable rate of under 2% with LLM approaches, CLMASP significantly improves this to over 90%.

In recent years, the impact of machine learning (ML) and artificial intelligence (AI) in society has been absolutely remarkable. This impact is expected to continue in the foreseeable future. However,the adoption of AI/ML is also a cause of grave concern. The operation of the most advances AI/ML models is often beyond the grasp of human decision makers. As a result, decisions that impact humans may not be understood and may lack rigorous validation. Explainable AI (XAI) is concerned with providing human decision-makers with understandable explanations for the predictions made by ML models. As a result, XAI is a cornerstone of trustworthy AI. Despite its strategic importance, most work on XAI lacks rigor, and so its use in high-risk or safety-critical domains serves to foster distrust instead of contributing to build much-needed trust. Logic-based XAI has recently emerged as a rigorous alternative to those other non-rigorous methods of XAI. This paper provides a technical survey of logic-based XAI, its origins, the current topics of research, and emerging future topics of research. The paper also highlights the many myths that pervade non-rigorous approaches for XAI.

Autoformalization, the conversion of natural language mathematics into formal languages, offers significant potential for advancing mathematical reasoning. However, existing efforts are limited to formal languages with substantial online corpora and struggle to keep pace with rapidly evolving languages like Lean 4. To bridge this gap, we propose a new benchmark \textbf{Form}alization for \textbf{L}ean~\textbf{4} (\textbf{\name}) designed to evaluate the autoformalization capabilities of large language models (LLMs). This benchmark encompasses a comprehensive assessment of questions, answers, formal statements, and proofs. Additionally, we introduce a \textbf{P}rocess-\textbf{S}upervised \textbf{V}erifier (\textbf{PSV}) model that leverages the precise feedback from Lean 4 compilers to enhance autoformalization. Our experiments demonstrate that the PSV method improves autoformalization, enabling higher accuracy using less filtered training data. Furthermore, when fine-tuned with data containing detailed process information, PSV can leverage the data more effectively, leading to more significant improvements in autoformalization for Lean 4. Our dataset and code are available at \url{https://github.com/rookie-joe/PDA}.

The prevailing approaches in Network Intrusion Detection Systems (NIDS) are often hampered by issues such as high resource consumption, significant computational demands, and poor interpretability. Furthermore, these systems generally struggle to identify novel, rapidly changing cyber threats. This paper delves into the potential of incorporating Neurosymbolic Artificial Intelligence (NSAI) into NIDS, combining deep learning's data-driven strengths with symbolic AI's logical reasoning to tackle the dynamic challenges in cybersecurity, which also includes detailed NSAI techniques introduction for cyber professionals to explore the potential strengths of NSAI in NIDS. The inclusion of NSAI in NIDS marks potential advancements in both the detection and interpretation of intricate network threats, benefiting from the robust pattern recognition of neural networks and the interpretive prowess of symbolic reasoning. By analyzing network traffic data types and machine learning architectures, we illustrate NSAI's distinctive capability to offer more profound insights into network behavior, thereby improving both detection performance and the adaptability of the system. This merging of technologies not only enhances the functionality of traditional NIDS but also sets the stage for future developments in building more resilient, interpretable, and dynamic defense mechanisms against advanced cyber threats. The continued progress in this area is poised to transform NIDS into a system that is both responsive to known threats and anticipatory of emerging, unseen ones.

The usage of Rational Speech Acts (RSA) framework has been successful in building \emph{pragmatic} program synthesizers that return programs which, in addition to being logically consistent with user-generated examples, account for the fact that a user chooses their examples informatively. We present a general method of amortizing the slow, exact RSA synthesizer. Our method first query the exact RSA synthesizer to compile a communication dataset. The dataset contains a number of example-dependent rankings of subsets of programs. It then distills a \textit{single} global ranking of all programs as an approximation to every ranking in the dataset. This global ranking is then used at inference time to rank multiple logically consistent candidate programs generated from a fast, non-pragmatic synthesizer. Experiments on two program synthesis domains using our ranking method resulted in orders of magnitudes of speed ups compared to the exact RSA synthesizer, while being more accurate than a non-pragmatic synthesizer when communicating with humans. Finally, we prove that in the special case of synthesis from a single example, this approximation is exact.

We propose DFAMiner, a passive learning tool for learning minimal separating deterministic finite automata (DFA) from a set of labelled samples. Separating automata are an interesting class of automata that occurs generally in regular model checking and has raised interest in foundational questions of parity game solving. We first propose a simple and linear-time algorithm that incrementally constructs a three-valued DFA (3DFA) from a set of labelled samples given in the usual lexicographical order. This 3DFA has accepting and rejecting states as well as don't-care states, so that it can exactly recognise the labelled examples. We then apply our tool to mining a minimal separating DFA for the labelled samples by minimising the constructed automata via a reduction to solving SAT problems. Empirical evaluation shows that our tool outperforms current state-of-the-art tools significantly on standard benchmarks for learning minimal separating DFAs from samples. Progress in the efficient construction of separating DFAs can also lead to finding the lower bound of parity game solving, where we show that DFAMiner can create optimal separating automata for simple languages with up to 7 colours. Future improvements might offer inroads to better data structures.

Explanation generation frameworks aim to make AI systems' decisions transparent and understandable to human users. However, generating explanations in uncertain environments characterized by incomplete information and probabilistic models remains a significant challenge. In this paper, we propose a novel framework for generating probabilistic monolithic explanations and model reconciling explanations. Monolithic explanations provide self-contained reasons for an explanandum without considering the agent receiving the explanation, while model reconciling explanations account for the knowledge of the agent receiving the explanation. For monolithic explanations, our approach integrates uncertainty by utilizing probabilistic logic to increase the probability of the explanandum. For model reconciling explanations, we propose a framework that extends the logic-based variant of the model reconciliation problem to account for probabilistic human models, where the goal is to find explanations that increase the probability of the explanandum while minimizing conflicts between the explanation and the probabilistic human model. We introduce explanatory gain and explanatory power as quantitative metrics to assess the quality of these explanations. Further, we present algorithms that exploit the duality between minimal correction sets and minimal unsatisfiable sets to efficiently compute both types of explanations in probabilistic contexts. Extensive experimental evaluations on various benchmarks demonstrate the effectiveness and scalability of our approach in generating explanations under uncertainty.

This paper presents a novel simplification calculus for propositional logic derived from Peirce's existential graphs' rules of inference and implication graphs. Our rules can be applied to propositional logic formulae in nested form, are equivalence-preserving, guarantee a monotonically decreasing number of variables, clauses and literals, and maximise the preservation of structural problem information. Our techniques can also be seen as higher-level SAT preprocessing, and we show how one of our rules (TWSR) generalises and streamlines most of the known equivalence-preserving SAT preprocessing methods. In addition, we propose a simplification procedure based on the systematic application of two of our rules (EPR and TWSR) which is solver-agnostic and can be used to simplify large Boolean satisfiability problems and propositional formulae in arbitrary form, and we provide a formal analysis of its algorithmic complexity in terms of space and time. Finally, we show how our rules can be further extended with a novel n-ary implication graph to capture all known equivalence-preserving preprocessing procedures.