We propose ECPv2, a scalable and theoretically grounded algorithm for global optimization of Lipschitz-continuous functions with unknown Lipschitz constants. Building on the Every Call is Precious (ECP) framework, which ensures that each accepted function evaluation is potentially informative, ECPv2 addresses key limitations of ECP, including high computational cost and overly conservative early behavior. ECPv2 introduces three innovations: (i) an adaptive lower bound to avoid vacuous acceptance regions, (ii) a Worst-m memory mechanism that restricts comparisons to a fixed-size subset of past evaluations, and (iii) a fixed random projection to accelerate distance computations in high dimensions. We theoretically show that ECPv2 retains ECP's no-regret guarantees with optimal finite-time bounds and expands the acceptance region with high probability. We further empirically validate these findings through extensive experiments and ablation studies. Using principled hyperparameter settings, we evaluate ECPv2 across a wide range of high-dimensional, non-convex optimization problems. Across benchmarks, ECPv2 consistently matches or outperforms state-of-the-art optimizers, while significantly reducing wall-clock time.

Artificial Intelligence (AI) systems are increasingly deployed in legal contexts, where their opacity raises significant challenges for fairness, accountability, and trust. The so-called ``black box problem'' undermines the legitimacy of automated decision-making, as affected individuals often lack access to meaningful explanations. In response, the field of Explainable AI (XAI) has proposed a variety of methods to enhance transparency, ranging from example-based and rule-based techniques to hybrid and argumentation-based approaches. This paper promotes computational models of arguments and their role in providing legally relevant explanations, with particular attention to their alignment with emerging regulatory frameworks such as the EU General Data Protection Regulation (GDPR) and the Artificial Intelligence Act (AIA). We analyze the strengths and limitations of different explanation strategies, evaluate their applicability to legal reasoning, and highlight how argumentation frameworks -- by capturing the defeasible, contestable, and value-sensitive nature of law -- offer a particularly robust foundation for explainable legal AI. Finally, we identify open challenges and research directions, including bias mitigation, empirical validation in judicial settings, and compliance with evolving ethical and legal standards, arguing that computational argumentation is best positioned to meet both technical and normative requirements of transparency in the law domain.

Auto-Regressive (AR) models have recently gained prominence in image generation, often matching or even surpassing the performance of diffusion models. However, one major limitation of AR models is their sequential nature, which processes tokens one at a time, slowing down generation compared to models like GANs or diffusion-based methods that operate more efficiently. While speculative decoding has proven effective for accelerating LLMs by generating multiple tokens in a single forward, its application in visual AR models remains largely unexplored. In this work, we identify a challenge in this setting, which we term \textit{token selection ambiguity}, wherein visual AR models frequently assign uniformly low probabilities to tokens, hampering the performance of speculative decoding. To overcome this challenge, we propose a relaxed acceptance condition referred to as LANTERN that leverages the interchangeability of tokens in latent space. This relaxation restores the effectiveness of speculative decoding in visual AR models by enabling more flexible use of candidate tokens that would otherwise be prematurely rejected. Furthermore, by incorporating a total variation distance bound, we ensure that these speed gains are achieved without significantly compromising image quality or semantic coherence. Experimental results demonstrate the efficacy of our method in providing a substantial speed-up over speculative decoding. In specific, compared to a na\"ive application of the state-of-the-art speculative decoding, LANTERN increases speed-ups by $\mathbf{1.75}\times$ and $\mathbf{1.76}\times$, as compared to greedy decoding and random sampling, respectively, when applied to LlamaGen, a contemporary visual AR model.

Dialectical frameworks are a unifying model of formal argumentation, where argumentative relations between arguments are represented by assigning acceptance conditions to atomic arguments. Their generality allow them to cover a number of different approaches with varying forms of representing the argumentation structure. Boolean regulatory networks are used to model the dynamics of complex biological processes, taking into account the interactions of biological compounds, such as proteins or genes. These models have proven highly useful for comprehending such biological processes, allowing to reproduce known behaviour and testing new hypotheses and predictions in silico, for example in the context of new medical treatments. While both these approaches stem from entirely different communities, it turns out that there are striking similarities in their appearence. In this paper, we study the relation between these two formalisms revealing their communalities as well as their differences, and introducing a correspondence that allows to establish novel results for the individual formalisms.

An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant Isabelle/HOL. This approach allows for the computer-assisted analysis of abstract dialectical frameworks using automated and interactive reasoning tools within a uniform logic environment. Exemplary applications include the formal analysis and verification of meta-theoretical properties, and the generation of interpretations and extensions under specific semantic constraints.

Linear temporal logic (LTL) is widely used to formally specify complex tasks for autonomy. Unlike usual tasks defined by reward functions only, LTL tasks are noncumulative and require memory-dependent strategies. In this work, we introduce a method to learn optimal controller strategies that maximize the satisfaction probability of LTL specifications of the desired tasks in stochastic games, which are natural extensions of Markov Decision Processes (MDPs) to systems with adversarial inputs. Our approach constructs a product game using the deterministic automaton derived from the given LTL task and a reward machine based on the acceptance condition of the automaton; thus, allowing for the use of a model-free RL algorithm to learn an optimal controller strategy. Since the rewards and the transition probabilities of the reward machine do not depend on the number of sets defining the acceptance condition, our approach is scalable to a wide range of LTL tasks, as we demonstrate on several case studies.

This paper studies the control synthesis of motion planning subject to uncertainties. The uncertainties are considered in robot motion and environment properties, giving rise to the probabilistic labeled Markov decision process (MDP). A model-free reinforcement learning (RL) is developed to generate a finite-memory control policy to satisfy high-level tasks expressed in linear temporal logic (LTL) formulas. One of the novelties is to translate LTL into a limit deterministic generalized B\"uchi automaton (LDGBA) and develop a corresponding embedded LDGBA (E-LDGBA) by incorporating a tracking-frontier function to overcome the issue of sparse accepting rewards, resulting in improved learning performance without increasing computational complexity. Due to potentially conflicting tasks, a relaxed product MDP is developed to allow the agent to revise its motion plan without strictly following the desired LTL constraints if the desired tasks can only be partially fulfilled. An expected return composed of violation rewards and accepting rewards is developed. The designed violation function quantifies the differences between the revised and the desired motion planning, while the accepting rewards are designed to enforce the satisfaction of the acceptance condition of the relaxed product MDP. Rigorous analysis shows that any RL algorithm that optimizes the expected return is guaranteed to find policies that, in decreasing order, can 1) satisfy acceptance condition of relaxed product MDP and 2) reduce the violation cost over long-term behaviors. Also, we validate the control synthesis approach via simulation and experimental results.

Abstract dialectical frameworks (ADFs) are a recently introduced powerful generalization of Dung’s popular abstract argumentation frameworks (AFs). Inspired by similar work for AFs, we introduce a decomposition scheme for ADFs, which proceeds along the ADF’s strongly connected components. We find that, for several semantics, the decomposition-based version coincides with the original semantics, whereas for others, it gives rise to a new semantics. These new semantics allow us to deal with pertinent problems such as odd-length negative cycles in a more general setting, that for instance also encompasses logic programs. We perform an exhaustive analysis of the computational complexity of these new, so-called naive-based semantics. The results are quite interesting, for some of them involve little-known classes of the so-called Boolean hierarchy (another hierarchy in between classes of the polynomial hierarchy). Furthermore, in credulous and sceptical entailment, the complexity can be different depending on whether we check for truth or falsity of a specific statement.

Generalizing the attack structure in argumentation frameworks (AFs) has been studied in different ways. Most prominently, the binary attack relation of Dung frameworks has been extended to the notion of collective attacks. The resulting formalism is often termed SETAFs. Another approach is provided via abstract dialectical frameworks (ADFs), where acceptance conditions specify the relation between arguments; restricting these conditions naturally allows for so-called support-free ADFs. The aim of the paper is to shed light on the relation between these two different approaches. To this end, we investigate and compare the expressiveness of SETAFs and support-free ADFs under the lens of 3-valued semantics. Our results show that it is only the presence of unsatisfiable acceptance conditions in support-free ADFs that discriminate the two approaches.

This letter proposes a novel reinforcement learning method for the synthesis of a control policy satisfying a control specification described by a linear temporal logic formula. We assume that the controlled system is modeled by a Markov decision process (MDP). We transform the specification to a limit-deterministic B\"uchi automaton (LDBA) with several accepting sets that accepts all infinite sequences satisfying the formula. The LDBA is augmented so that it explicitly records the previous visits to accepting sets. We take a product of the augmented LDBA and the MDP, based on which we define a reward function. The agent gets rewards whenever state transitions are in an accepting set that has not been visited for a certain number of steps. Consequently, sparsity of rewards is relaxed and optimal circulations among the accepting sets are learned. We show that the proposed method can learn an optimal policy when the discount factor is sufficiently close to one.