The theory of argumentation frameworks ($AF$s) has been a useful tool for artificial intelligence. The research of the connection between $AF$s and logic is an important branch. This paper generalizes the encoding method by encoding $AF$s as logical formulas in different propositional logic systems. It studies the relationship between models of an AF by argumentation semantics, including Dung's classical semantics and Gabbay's equational semantics, and models of the encoded formulas by semantics of propositional logic systems. Firstly, we supplement the proof of the regular encoding function in the case of encoding $AF$s to the 2-valued propositional logic system. Then we encode $AF$s to 3-valued propositional logic systems and fuzzy propositional logic systems and explore the model relationship. This paper enhances the connection between $AF$s and propositional logic systems. It also provides a new way to construct new equational semantics by choosing different fuzzy logic operations.

Compliance with the GDPR privacy regulation places a significant burden on organisations regarding the handling of personal data. The perceived efforts and risks of complying with the GDPR further increase when data processing activities span across organisational boundaries, as is the case in both small-scale data sharing settings and in large-scale international data spaces. This paper addresses these concerns by proposing a case-generic method for automated normative reasoning that establishes legal arguments for the lawfulness of data processing activities. The arguments are established on the basis of case-specific legal qualifications made by privacy experts, bringing the human in the loop. The obtained expert system promotes transparency and accountability, remains adaptable to extended or altered interpretations of the GDPR, and integrates into novel or existing distributed data processing systems. This result is achieved by defining a formal ontology and semantics for automated normative reasoning based on an analysis of the purpose-limitation principle of the GDPR. The ontology and semantics are implemented in eFLINT, a domain-specific language for specifying and reasoning with norms. The XACML architecture standard, applicable to both access and usage control, is extended, demonstrating how GDPR-based normative reasoning can integrate into (existing, distributed) systems for data processing. The resulting system is designed and critically assessed in reference to requirements extracted from the GPDR.

There is now a large body of techniques, many based on formal methods, for describing and realizing complex robotics tasks, including those involving a variety of rich goals and time-extended behavior. This paper explores the limits of what sorts of tasks are specifiable, examining how the precise grounding of specifications, that is, whether the specification is given in terms of the robot's states, its actions and observations, its knowledge, or some other information,is crucial to whether a given task can be specified. While prior work included some description of particular choices for this grounding, our contribution treats this aspect as a first-class citizen: we introduce notation to deal with a large class of problems, and examine how the grounding affects what tasks can be posed. The results demonstrate that certain classes of tasks are specifiable under different combinations of groundings.

In this paper, we examine the use of Conformal Language Modelling (CLM) alongside Answer Set Programming (ASP) to enhance the performance of standard open-weight LLMs on complex multi-step reasoning tasks. Using the StepGame dataset, which requires spatial reasoning, we apply CLM to generate sets of ASP programs from an LLM, providing statistical guarantees on the correctness of the outputs. Experimental results show that CLM significantly outperforms baseline models that use standard sampling methods, achieving substantial accuracy improvements across different levels of reasoning complexity. Additionally, the LLM-as-Judge metric enhances CLM's performance, especially in assessing structurally and logically correct ASP outputs. However, calibrating CLM with diverse calibration sets did not improve generalizability for tasks requiring much longer reasoning steps, indicating limitations in handling more complex tasks.

Logic programming (LP) is typically understood through operational semantics (e.g., SLD-resolution) or model-theoretic interpretations (e.g., the least Herbrand model). This paper introduces a novel perspective on LP by defining a ``support'' relation that explicates what a program ``knows''. This interpretation is shown to express classical and intuitionistic logic, as well as an intermediate logic, depending on certain choices regarding LP and the meanings of disjunction and negation. These results are formalized using the idea of base-extension semantics within proof-theoretic semantics. Our approach offers new insights into the logical foundations of LP and has potential applications in knowledge representation, automated reasoning, and formal verification.

We explore neuro-symbolic approaches to generalize actionable knowledge, enabling embodied agents to tackle complex tasks more effectively in open-domain environments. A key challenge for embodied agents is the generalization of knowledge across diverse environments and situations, as limited experiences often confine them to their prior knowledge. To address this issue, we introduce a novel framework, NeSyC, a neuro-symbolic continual learner that emulates the hypothetico-deductive model by continually formulating and validating knowledge from limited experiences through the combined use of Large Language Models (LLMs) and symbolic tools. Specifically, we devise a contrastive generality improvement scheme within NeSyC, which iteratively generates hypotheses using LLMs and conducts contrastive validation via symbolic tools. This scheme reinforces the justification for admissible actions while minimizing the inference of inadmissible ones. Additionally, we incorporate a memory-based monitoring scheme that efficiently detects action errors and triggers the knowledge refinement process across domains. Experiments conducted on diverse embodied task benchmarks-including ALFWorld, VirtualHome, Minecraft, RLBench, and a real-world robotic scenario-demonstrate that NeSyC is highly effective in solving complex embodied tasks across a range of open-domain environments.

Microelectronic design verification remains a critical bottleneck in device development, traditionally mitigated by expanding verification teams and computational resources. Since the late 1990s, machine learning (ML) has been proposed to enhance verification efficiency, yet many techniques have not achieved mainstream adoption. This review, from the perspective of verification and ML practitioners, examines the application of ML in dynamic-based techniques for functional verification of microelectronic designs, and provides a starting point for those new to this interdisciplinary field. Historical trends, techniques, ML types, and evaluation baselines are analysed to understand why previous research has not been widely adopted in industry. The review highlights the application of ML, the techniques used and critically discusses their limitations and successes. Although there is a wealth of promising research, real-world adoption is hindered by challenges in comparing techniques, identifying suitable applications, and the expertise required for implementation. This review proposes that the field can progress through the creation and use of open datasets, common benchmarks, and verification targets. By establishing open evaluation criteria, industry can guide future research. Parallels with ML in software verification suggest potential for collaboration. Additionally, greater use of open-source designs and verification environments can allow more researchers from outside the hardware verification discipline to contribute to the challenge of verifying microelectronic designs.

Many procedures for SA T -related problems, in particular for those requiring the complete enumeration of satisfying truth assignments, rely their efficiency and effectiveness on the detection of (possibly small) partial assignments satisfying an input formula. Surprisingly, there seems to be no unique universally-agreed definition of formula satisfaction by a partial assignment in the literature. In this paper we analyze in deep the issue of satisfaction by partial assignments, raising a flag about some ambiguities and subtleties of this concept, and investigating their practical consequences. We identify two alternative notions that are implicitly used in the literature, namely verification and entailment, which coincide if applied to CNF formulas but differ and present complementary properties if applied to non-CNF or to existentially-quantified formulas. We show that, although the former is easier to check and as such is implicitly used by most current search procedures, the latter has better theoretical properties, and can improve the efficiency and effectiveness of enumeration procedures. 1 Introduction Motivations.

We develop a self-learning approach for conjecturing of induction predicates on a dataset of 16197 problems derived from the OEIS. These problems are hard for today's SMT and ATP systems because they require a combination of inductive and arithmetical reasoning. Starting from scratch, our approach consists of a feedback loop that iterates between (i) training a neural translator to learn the correspondence between the problems solved so far and the induction predicates useful for them, (ii) using the trained neural system to generate many new induction predicates for the problems, (iii) fast runs of the z3 prover attempting to prove the problems using the generated predicates, (iv) using heuristics such as predicate size and solution speed on the proved problems to choose the best predicates for the next iteration of training. The algorithm discovers on its own many interesting induction predicates, ultimately solving 5565 problems, compared to 2265 problems solved by CVC5, Vampire or Z3 in 60 seconds.

Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various automated reasoning tools in recent years. This paper presents a recipe for the simultaneous deployment of different forms of deep and shallow embeddings in classical higher-order logic, enabling not only flexible interactive and automated theorem proving and counterexample finding at meta and object level, but also automated faithfulness proofs between the logic embeddings. The approach, which is fruitful for logic education, research and application, is deliberately illustrated here using simple propositional modal logic. However, the work presented is conceptual in nature and not limited to such a simple logic context. Keywords: Logic embeddings Faithfulness Automated Reasoning 1 Motivation and Introduction Deep embeddings of logics, or more generally of domain-specific languages, in a suitable metalogic, such as the classical higher-order logic (HOL) [23,4], are typically based on explicitly introduced abstract data types that essentially axioma-tize the inductively defined character of the new language.