Non-monotonic logic programming is the basis for a declarative problem solving paradigm known as answer set programming (ASP). Departing from the seminal definition by Gelfond and Lifschitz in 1988 for simple normal logic programs, various answer set semantics have been proposed for extensions. We consider two important questions: (1) Should the minimal model property, constraint monotonicity and foundedness as defined in the literature be mandatory conditions for an answer set semantics in general? (2) If not, what other properties could be considered as general principles for answer set semantics? We address the two questions. First, it seems that the three aforementioned conditions may sometimes be too strong, and we illustrate with examples that enforcing them may exclude expected answer sets. Second, we evolve the Gelfond answer set (GAS) principles for answer set construction by refining the Gelfond's rationality principle to well-supportedness, minimality w.r.t. negation by default and minimality w.r.t. epistemic negation. The principle of well-supportedness guarantees that every answer set is constructible from if-then rules obeying a level mapping and is thus free of circular justification, while the two minimality principles ensure that the formalism minimizes knowledge both at the level of answer sets and of world views. Third, to embody the refined GAS principles, we extend the notion of well-supportedness substantially to answer sets and world views, respectively. Fourth, we define new answer set semantics in terms of the refined GAS principles. Fifth, we use the refined GAS principles as an alternative baseline to intuitively assess the existing answer set semantics. Finally, we analyze the computational complexity.

The verification of transactions in blockchain networks presents a bifurcation in protocol implementation: one pathway aligns with complete state replication through full nodes, while the alternative, as outlined in Nakamoto's seminal whitepaper [1], advocates simplified payment verification (SPV) wherein clients validate transactions via header-only proofs. This paper formalises and mathematically models the latter, extending it beyond its conceptual origin into a fully specified, implementable, and security-provable protocol. In doing so, we consolidate foundational concepts from the original whitepaper, correct widespread misinterpretations, and construct a complete formal model using automata theory, game-theoretic reasoning, and complexity-theoretic metrics. This treatise employs a layered structure: beginning with an exegesis of the SPV concept as it appears in the original protocol specification, we examine the trajectory of mis-implementations, diverging threat models, and false economic assumptions. Subsequent sections provide a rigorous formalisation of SPV in a low-bandwidth adversarial context. This includes the introduction of protocol optimisations that conform to the Bitcoin protocol as defined in 2008, with proofs grounded in computational and information-theoretic primitives. Later sections analyse game-theoretic cost models for misbehaviour, followed by a discussion of implementation artefacts and evaluation in simulated hostile environments. The final structure includes appendices detailing code listings, mathematical proofs, and graphical models that substantiate the proposed design.

Just like power, water, and transportation systems, wireless networks are a crucial societal infrastructure. As natural and human-induced disruptions continue to grow, wireless networks must be resilient. This requires them to withstand and recover from unexpected adverse conditions, shocks, unmodeled disturbances and cascading failures. Unlike robustness and reliability, resilience is based on the understanding that disruptions will inevitably happen. Resilience, as elasticity, focuses on the ability to bounce back to favorable states, while resilience as plasticity involves agents and networks that can flexibly expand their states and hypotheses through real-time adaptation and reconfiguration. This situational awareness and active preparedness, adapting world models and counterfactually reasoning about potential system failures and the best responses, is a core aspect of resilience. This article will first disambiguate resilience from reliability and robustness, before delving into key mathematical foundations of resilience grounded in abstraction, compositionality and emergence. Subsequently, we focus our attention on a plethora of techniques and methodologies pertaining to the unique characteristics of resilience, as well as their applications through a comprehensive set of use cases. Ultimately, the goal of this paper is to establish a unified foundation for understanding, modeling, and engineering resilience in wireless communication systems, while laying a roadmap for the next-generation of resilient-native and intelligent wireless systems.

Large Language Models (LLMs) have rapidly transformed the landscape of artificial intelligence, enabling natural language interfaces and dynamic orchestration of software components. However, their reliance on probabilistic inference limits their effectiveness in domains requiring strict logical reasoning, discrete decision-making, and robust interpretability. This paper investigates these limitations and proposes a neurosymbolic approach that augments LLMs with logic-based reasoning modules, particularly leveraging Prolog predicates and composable toolsets. By integrating first-order logic and explicit rule systems, our framework enables LLMs to decompose complex queries into verifiable sub-tasks, orchestrate reliable solutions, and mitigate common failure modes such as hallucination and incorrect step decomposition. We demonstrate the practical benefits of this hybrid architecture through experiments on the DABStep benchmark, showing improved precision, coverage, and system documentation in multi-step reasoning tasks. Our results indicate that combining LLMs with modular logic reasoning restores engineering rigor, enhances system reliability, and offers a scalable path toward trustworthy, interpretable AI agents across complex domains.

Nielsen transformation is a standard approach for solving word equations: by repeatedly splitting equations and applying simplification steps, equations are rewritten until a solution is reached. When solving a conjunction of word equations in this way, the performance of the solver will depend considerably on the order in which equations are processed. In this work, the use of Graph Neural Networks (GNNs) for ranking word equations before and during the solving process is explored. For this, a novel graph-based representation for word equations is presented, preserving global information across conjuncts, enabling the GNN to have a holistic view during ranking. To handle the variable number of conjuncts, three approaches to adapt a multi-classification task to the problem of ranking equations are proposed. The training of the GNN is done with the help of minimum unsatisfiable subsets (MUSes) of word equations. The experimental results show that, compared to state-of-the-art string solvers, the new framework solves more problems in benchmarks where each variable appears at most once in each equation.

We introduce BayesL, a novel logical framework for specifying, querying, and verifying the behaviour of Bayesian networks (BNs). BayesL (pronounced "Basil") is a structured language that allows for the creation of queries over BNs. It facilitates versatile reasoning concerning causal and evidence-based relationships, and permits comprehensive what-if scenario evaluations without the need for manual modifications to the model.

Interactive theorem provers (ITPs) are powerful tools for the formal verification of mathematical proofs down to the axiom level. However, their lack of a natural language interface remains a significant limitation. Recent advancements in large language models (LLMs) have enhanced the understanding of natural language inputs, paving the way for autoformalization - the process of translating natural language proofs into formal proofs that can be verified. Despite these advancements, existing autoformalization approaches are limited to verifying complete proofs and lack the capability for finer, sentence-level verification. To address this gap, we propose StepProof, a novel autoformalization method designed for granular, step-by-step verification. StepProof breaks down complete proofs into multiple verifiable subproofs, enabling sentence-level verification. Experimental results demonstrate that StepProof significantly improves proof success rates and efficiency compared to traditional methods. Additionally, we found that minor manual adjustments to the natural language proofs, tailoring them for step-level verification, further enhanced StepProof's performance in autoformalization.

With the deep penetration of Artificial Intelligence (AI) in the transportation sector, intelligent cockpits, autonomous driving, and intelligent road networks are developing at an unprecedented pace. However, the data ecosystems of these three key areas are increasingly fragmented and incompatible. Especially, existing testing methods rely on data stacking, fail to cover all edge cases, and lack flexibility. To address this issue, this paper introduces the concept of "Query as Test" (QaT). This concept shifts the focus from rigid, prescripted test cases to flexible, on-demand logical queries against a unified data representation. Specifically, we identify the need for a fundamental improvement in data storage and representation, leading to our proposal of "Extensible Scenarios Notations" (ESN). ESN is a novel declarative data framework based on Answer Set Programming (ASP), which uniformly represents heterogeneous multimodal data from the cockpit, vehicle, and road as a collection of logical facts and rules. This approach not only achieves deep semantic fusion of data, but also brings three core advantages: (1) supports complex and flexible semantic querying through logical reasoning; (2) provides natural interpretability for decision-making processes; (3) allows for on-demand data abstraction through logical rules, enabling fine-grained privacy protection. We further elaborate on the QaT paradigm, transforming the functional validation and safety compliance checks of autonomous driving systems into logical queries against the ESN database, significantly enhancing the expressiveness and formal rigor of the testing. Finally, we introduce the concept of "Validation-Driven Development" (VDD), which suggests to guide developments by logical validation rather than quantitative testing in the era of Large Language Models, in order to accelerating the iteration and development process.

This draft is a working document, having a summary of nighty-four (94) papers with additional sections on Traceability of Software Requirements (Section 4), Formal Methods and Its Tools (Section 5), Unifying Theories of Programming (UTP) and Theory of Institutions (Section 6). Please refer to abstract of [7,8]. Key difference of this draft from our recently anticipated ones with similar titles, i.e. AACS 2025 [7] and SAIV 2025 [8] is: [7] is a two page submission to ADAPT Annual Conference, Ireland. Submitted on 18th of March, 2025, it went through the light-weight blind review and accepted for poster presentation. Conference was held on 15th of May, 2025; [8] is a nine page paper with additional nine pages of references and summary tables, submitted to Symposium on AI Verification (SAIV 2025) on 24th of April, 2025. It went through rigorous review process. The uploaded version on arXiv.org [8] is the improved one of the submission, after addressing the specific suggestions to improve the paper.

Action languages are formal models of parts of natural language that are designed to describe effects of actions. Many of these languages can be viewed as high level notations of answer set programs structured to represent transition systems. However, the form of answer set programs considered in the earlier work is quite limited in comparison with the modern Answer Set Programming (ASP) language, which allows several useful constructs for knowledge representation, such as choice rules, aggregates, and abstract constraint atoms. We propose a new action language called BC+, which closes the gap between action languages and the modern ASP language. The main idea is to define the semantics of BC+ in terms of general stable model semantics for propositional formulas, under which many modern ASP language constructs can be identified with shorthands for propositional formulas. Language BC+ turns out to be sufficiently expressive to encompass the best features of other action languages, such as languages B, C, C+, and BC. Computational methods available in ASP solvers are readily applicable to compute BC+, which led to an implementation of the language by extending system cplus2asp.