Artificial Intelligence (AI) has achieved remarkable success in specialized tasks but struggles with efficient skill acquisition and generalization. The Abstraction and Reasoning Corpus (ARC) benchmark evaluates intelligence based on minimal training requirements. While Large Language Models (LLMs) have recently improved ARC performance, they rely on extensive pre-training and high computational costs. We introduce MADIL (MDL-based AI), a novel approach leveraging the Minimum Description Length (MDL) principle for efficient inductive learning. MADIL performs pattern-based decomposition, enabling structured generalization. While its performance (7% at ArcPrize 2024) remains below LLM-based methods, it offers greater efficiency and interpretability. This paper details MADIL's methodology, its application to ARC, and experimental evaluations.

Autonomous robots must operate in diverse environments and handle multiple tasks despite uncertainties. This creates challenges in designing software architectures and task decision-making algorithms, as different contexts may require distinct task logic and architectural configurations. To address this, robotic systems can be designed as self-adaptive systems capable of adapting their task execution and software architecture at runtime based on their context.This paper introduces ROSA, a novel knowledge-based framework for RObot Self-Adaptation, which enables task-and-architecture co-adaptation (TACA) in robotic systems. ROSA achieves this by providing a knowledge model that captures all application-specific knowledge required for adaptation and by reasoning over this knowledge at runtime to determine when and how adaptation should occur. In addition to a conceptual framework, this work provides an open-source ROS 2-based reference implementation of ROSA and evaluates its feasibility and performance in an underwater robotics application. Experimental results highlight ROSA's advantages in reusability and development effort for designing self-adaptive robotic systems.

This article deals with the description and recognition of fiber bundles, in particular nerves, in medical images, based on the anatomical description of the fiber trajectories. To this end, we propose a logical formalization of this anatomical knowledge. The intrinsically imprecise description of nerves, as found in anatomical textbooks, leads us to propose fuzzy semantics combined with first-order logic. We define a language representing spatial entities, relations between these entities and quantifiers. A formula in this language is then a formalization of the natural language description. The semantics are given by fuzzy representations in a concrete domain and satisfaction degrees of relations. Based on this formalization, a spatial reasoning algorithm is proposed for segmentation and recognition of nerves from anatomical and diffusion magnetic resonance images, which is illustrated on pelvic nerves in pediatric imaging, enabling surgeons to plan surgery.

We present a lattice-based scheme for homomorphic evaluation of quantum programs and proofs that remains secure against quantum adversaries. Classical homomorphic encryption is lifted to the quantum setting by replacing composite-order groups with Module Learning-With-Errors (MLWE) lattices and by generalizing polynomial functors to bounded natural super functors (BNSFs). A secret depolarizing BNSF mask hides amplitudes, while each quantum state is stored as an MLWE ciphertext pair. We formalize security with the qIND-CPA game that allows coherent access to the encryption oracle and give a four-hybrid reduction to decisional MLWE. The design also covers practical issues usually left open. A typed QC-bridge keeps classical bits produced by measurements encrypted yet still usable as controls, with weak-measurement semantics for expectation-value workloads. Encrypted Pauli twirls add circuit privacy. If a fixed knowledge base is needed, its axioms are shipped as MLWE "capsules"; the evaluator can use them but cannot read them. A rho-calculus driver schedules encrypted tasks across several QPUs and records an auditable trace on an RChain-style ledger. Performance analysis shows that the extra lattice arithmetic fits inside today's QPU idle windows: a 100-qubit, depth-10^3 teleportation-based proof runs in about 10 ms, the public key (seed only) is 32 bytes, and even a CCA-level key stays below 300 kB. A photonic Dirac-3 prototype that executes homomorphic teleportation plus knowledge-base-relative amplitude checks appears feasible with current hardware. These results indicate that fully homomorphic, knowledge-base-aware quantum reasoning is compatible with near-term quantum clouds and standard post-quantum security assumptions.

We study a variant of LTLf synthesis that synthesizes adaptive strategies for achieving a multi-tier goal, consisting of multiple increasingly challenging LTLf objectives in nondeterministic planning domains. Adaptive strategies are strategies that at any point of their execution (i) enforce the satisfaction of as many objectives as possible in the multi-tier goal, and (ii) exploit possible cooperation from the environment to satisfy as many as possible of the remaining ones. This happens dynamically: if the environment cooperates (ii) and an objective becomes enforceable (i), then our strategies will enforce it. We provide a game-theoretic technique to compute adaptive strategies that is sound and complete. Notably, our technique is polynomial, in fact quadratic, in the number of objectives. In other words, it handles multi-tier goals with only a minor overhead compared to standard LTLf synthesis.

This paper seeks to apply categorical logic to the design of artificial intelligent agents that reason symbolically about objects more richly structured than sets. Using Johnstone's sequent calculus of terms- and formulae-in-context, we develop forward chaining and normal form algorithms for reasoning about objects in cartesian categories with the rules for Horn logic. We also adapt first-order unification to support multi-sorted theories, contexts, and fragments of first-order logic. The significance of these reformulations rests in the fact that they can be applied to reasoning about objects in semantic categories that do not support classical logic or even all its connectives.

Large language models (LLMs) have shown promise in formal theorem proving, but their token-level processing often fails to capture the inherent hierarchical nature of mathematical proofs. We introduce \textbf{Hierarchical Attention}, a regularization method that aligns LLMs' attention mechanisms with mathematical reasoning structures. Our approach establishes a five-level hierarchy from foundational elements to high-level concepts, ensuring structured information flow in proof generation. Experiments demonstrate that our method improves proof success rates by 2.05\% on miniF2F and 1.69\% on ProofNet while reducing proof complexity by 23.81\% and 16.50\% respectively. The code is available at https://github.com/Car-pe/HAGBP.

Program synthesis is an umbrella term for generating programs and logical formulae from specifications. With the remarkable performance improvements that GPUs enable for deep learning, a natural question arose: can we also implement a search-based program synthesiser on GPUs to achieve similar performance improvements? In this article we discuss our insights on this question, based on recent works~. The goal is to build a synthesiser running on GPUs which takes as input positive and negative example traces and returns a logical formula accepting the positive and rejecting the negative traces. With GPU-friendly programming techniques -- using the semantics of formulae to minimise data movement and reduce data-dependent branching -- our synthesiser scales to significantly larger synthesis problems, and operates much faster than the previous CPU-based state-of-the-art. We believe the insights that make our approach GPU-friendly have wide potential for enhancing the performance of other formal methods (FM) workloads.

Current text-to-video (T2V) generation models are increasingly popular due to their ability to produce coherent videos from textual prompts. However, these models often struggle to generate semantically and temporally consistent videos when dealing with longer, more complex prompts involving multiple objects or sequential events. Additionally, the high computational costs associated with training or fine-tuning make direct improvements impractical. To overcome these limitations, we introduce NeuS-E, a novel zero-training video refinement pipeline that leverages neuro-symbolic feedback to automatically enhance video generation, achieving superior alignment with the prompts. Our approach first derives the neuro-symbolic feedback by analyzing a formal video representation and pinpoints semantically inconsistent events, objects, and their corresponding frames. This feedback then guides targeted edits to the original video. Extensive empirical evaluations on both open-source and proprietary T2V models demonstrate that NeuS-E significantly enhances temporal and logical alignment across diverse prompts by almost 40%

Modern society is full of computational challenges that rely on probabilistic reasoning, statistics, and combinatorics. Interestingly, many of these questions can be formulated by encoding them into propositional formulas and then asking for its number of models. With a growing interest in practical problem-solving for tasks that involve model counting, the community established the Model Counting (MC) Competition in fall of 2019 with its first iteration in 2020. The competition aims at advancing applications, identifying challenging benchmarks, fostering new solver development, and enhancing existing solvers for model counting problems and their variants. The first iteration, brought together various researchers, identified challenges, and inspired numerous new applications. In this paper, we present a comprehensive overview of the 2021-2023 iterations of the Model Counting Competition. We detail its execution and outcomes. The competition comprised four tracks, each focusing on a different variant of the model counting problem. The first track centered on the model counting problem (MC), which seeks the count of models for a given propositional formula. The second track challenged developers to submit programs capable of solving the weighted model counting problem (WMC). The third track was dedicated to projected model counting (PMC). Finally, we initiated a track that combined projected and weighted model counting (PWMC). The competition continued with a high level of participation, with seven to nine solvers submitted in various different version and based on quite diverging techniques.