The paper presents a doxastic deontic logic designed for autonomous decision‑making under conflicting norms and uncertain information. It extends Chellas' Minimal Deontic Logic with explicit conditional norms and integrates it with multi‑agent KD45 to allow norms to depend on agents’ beliefs about facts and other norms. The authors formulate a Doxastic Norm Compliance Optimization Problem, distinguishing subjective from objective optimization, and identify conditions where the two coincide and where optimal decisions can be computed via weighted partial MaxSAT in polynomial time.
By Thorsten Engesser, Agata Ciabattoni
The article surveys rule‑based languages—Datalog, answer set, and probabilistic logic programs—used as the symbolic component of neurosymbolic AI systems. It examines these languages across semantics, expressiveness, neural integration, and evaluation mechanisms, and analyzes over 50 recent systems in databases, machine learning, vision, and robotics. A decision matrix links application scenarios to required features, and the paper concludes with open research problems.
By Stefania Dumbrava, Efthymia Tsamoura
arXiv:2607. 07762v1 Announce Type: new Abstract: Modern machine learning (ML) increasingly relies on complex models whose behavior is difficult to characterize beyond empirical performance metrics.
By Thibaut Vidal, Julien Ferry
Modern machine learning (ML) increasingly relies on complex models whose behavior is difficult to characterize beyond empirical performance metrics. Across a wide range of tasks, including prediction, generation, and decision-making, models with similar empirical performance can exhibit markedly different properties in terms of their transparency, interpretability, robustness, fairness, privacy, and certifiability.
arXiv:2605. 04193v2 Announce Type: replace Abstract: Inductive Logic Programming (ILP) aims to learn interpretable first-order rules from data, but existing symbolic and neuro-symbolic approaches struggle to scale to noisy and probabilistic settings.
By Iman Sharifi, Peng Wei, Saber Fallah
arXiv:2608. 12325v1 Announce Type: new Abstract: Autonomous reasoning is among the most scientifically and economically motivating topics in AI today.
By Rachel Lawrence, Jacqueline Maasch
arXiv:2608. 11905v1 Announce Type: new Abstract: In many practical applications of generative AI systems, from tax rules to airline baggage allowance, responses to natural language queries must respect written policies or rules.
By Rahul Nair, Bastian Lipka, Elizabeth Daly
arXiv:2608. 16565v1 Announce Type: new Abstract: This cumulative habilitation thesis studies probabilistic circuits (PCs) as a powerful and tractable framework for reasoning and learning under uncertainty in artificial intelligence (AI).
By Robert Peharz
arXiv:2605. 30456v2 Announce Type: replace Abstract: Many learning tasks in science and engineering are characterized by sparse datasets, which limits the effectiveness of purely data-driven approaches.
By Shraman Pal, Can Li
The paper introduces mixed integer linear programming (MILP) formulations for training sparse disjunctive normal form (DNF) networks, which are small networks with a conjunctive hidden layer and a disjunctive output layer. By fixing the network structure and optimizing weights, the authors achieve globally optimized rule sets that balance misclassification costs against sparsity. Their enhanced formulation reduces integer decision variables and redundant constraints, and a combined initialization and dropout approach breaks weight symmetries to promote diverse, stable rule representations, leading to improved computational efficiency and competitive accuracy on synthetic and UCI datasets.
By Thomas Pammer, Johannes F\"urnkranz, Markus Sinnl
In many practical applications of generative AI systems, from tax rules to airline baggage allowance, responses to natural language queries must respect written policies or rules. We present a hybrid symbolic approach that expresses policies in formal logic and at inference time exploits the representation power of language models for fact extraction to ground predicates, and an answer set solver for reasoning such that responses are interpretable, auditable, and as we show, accurate and robust under input perturbations.
arXiv:2605. 01797v2 Announce Type: replace Abstract: Integration of Answer Set Programming (ASP) with neural networks has emerged as a promising tool in Neuro-symbolic AI.
By Thomas Eiter, Katsumi Inoue, Sota Moriyama