Unlike repetitions in Western Chess where all repetitions are draws, repetitions in Chinese Chess could result in a win, draw, or loss depending on the kind of repetition being made by both players. One of the biggest hurdles facing Chinese Chess application development is a proper system for judging games correctly. This paper introduces a complete algorithm for ruling the WXF rules correctly in all 110 example cases found in the WXF manual. We introduce several novel optimizations for speeding up the repetition handling without compromising the program correctness. This algorithm is usable in engines, and we saw a total increase in playing strength by +10 point rating increase, or an increased 5% winrate when integrating this approach into our prototype engine.

To operate autonomously, such systems and agents often rely on automated controllers, which are designed to translate a stream of sensor observations or system states into a stream of commands (controls) to execute, in order to maintain a safe behavior, or robustly perform a specified task. Traditionally, controllers had to be expertly designed, e.g., by meticulously considering physical and mechanical aspects of the system. In recent years, however, computational Neural-Network (NN) controllers have been experiencing tremendous popularity. These can handle complex, highdimensional sensor observations, such as images, and enable effective control of highly-complex dynamical systems, such as racing cars, snake robots, high Degree-of-Freedom (DoF) manipulators, and dexterous robot hands, which have been a great challenge in the controls and robotics communities. Such controllers are typically built ("trained") by compressing numerous examples ("training data") using statistical machine learning techniques, in an attempt to yield a certain behavior. Common techniques include Reinforcement Learning (RL) [2], from repeated trial-and-error control attempts, until apparent convergence to a desired behavior, and Imitation Learning [3], from demonstrations of either a human operator or a traditional controller. Unfortunately, such learning methods generally do not provide a guarantee that the resulting controller will robustly exhibit the desired behavior; hence, relying on these controllers can cause the system to suffer from unpredictable or unsafe behavior on edge cases. While there has been a recent efforts to advance controller synthesis [4-6]--that is, the automated creation of controllers that are guaranteed to comply to given specification by design--these usually fail to scale beyond simple scenarios; and, more importantly, are only certified in relation to the assumed (and often simplified) system models.

DatalogMTL is a powerful rule-based language for temporal reasoning. Due to its high expressive power and flexible modeling capabilities, it is suitable for a wide range of applications, including tasks from industrial and financial sectors. However, due its high computational complexity, practical reasoning in DatalogMTL is highly challenging. To address this difficulty, we introduce a new reasoning method for DatalogMTL which exploits the magic sets technique -- a rewriting approach developed for (non-temporal) Datalog to simulate top-down evaluation with bottom-up reasoning. We implement this approach and evaluate it on several publicly available benchmarks, showing that the proposed approach significantly and consistently outperforms performance of the state-of-the-art reasoning techniques.

Conservation is a critical milestone of cognitive development considered to be supported by both the understanding of quantitative concepts and the reversibility of mental operations. To assess whether this critical component of human intelligence has emerged in Vision Language Models, we have curated the ConserveBench, a battery of 365 cognitive experiments across four dimensions of physical quantities: volume, solid quantity, length, and number. The former two involve only transformational tasks, whereas the latter two involve non-transformational tasks assessing the understanding of quantitative concepts alone. Surprisingly, we find that while Vision Language Models are generally capable of conserving, they tend to fail at non-transformational tasks whose successes are typically considered to be evidence of the ability to conserve. This implies that the law of conservation, at least in concrete domains, may exist without corresponding conceptual understanding of quantity.

Recently, slow-thinking reasoning systems, such as o1, have demonstrated remarkable capabilities in solving complex reasoning tasks. These systems typically engage in an extended thinking process before responding to a query, allowing them to generate more thorough, accurate, and well-reasoned solutions. These systems are primarily developed and maintained by industry, with their core techniques not publicly disclosed. In response, an increasing number of studies from the research community aim to explore the technical foundations underlying these powerful reasoning systems. Building on these prior efforts, this paper presents a reproduction report on implementing o1-like reasoning systems. We introduce an ``imitate, explore, and self-improve'' framework, denoted as \textbf{STILL-2}, as our primary technical approach to train the reasoning model. In the initial phase, we use distilled long-form thought data to fine-tune the reasoning model, enabling it to invoke a slow-thinking mode. The model is then encouraged to explore challenging problems by generating multiple rollouts, which can result in increasingly more high-quality trajectories that lead to correct answers. Furthermore, the model undergoes self-improvement by iteratively refining its training dataset. To verify the effectiveness of this approach, we conduct extensive experiments on three challenging benchmarks. The experimental results demonstrate that our approach achieves competitive performance compared to industry-level reasoning systems on these benchmarks.

In the context of large language models (LLMs), current advanced reasoning methods have made impressive strides in various reasoning tasks. However, when it comes to logical reasoning tasks, major challenges remain in both efficacy and efficiency. This is rooted in the fact that these systems fail to fully leverage the inherent structure of logical tasks throughout the reasoning processes such as decomposition, search, and resolution. To address this, we propose a logic-complete reasoning framework, Aristotle, with three key components: Logical Decomposer, Logical Search Router, and Logical Resolver. In our framework, symbolic expressions and logical rules are comprehensively integrated into the entire reasoning process, significantly alleviating the bottlenecks of logical reasoning, i.e., reducing sub-task complexity, minimizing search errors, and resolving logical contradictions. The experimental results on several datasets demonstrate that Aristotle consistently outperforms state-of-the-art reasoning frameworks in both accuracy and efficiency, particularly excelling in complex logical reasoning scenarios. We will open-source all our code at https://github.com/Aiden0526/Aristotle.

Direction reasoning is essential for intelligent systems to understand the real world. While existing work focuses primarily on spatial reasoning, compass direction reasoning remains underexplored. To address this, we propose the Compass Direction Reasoning (CDR) benchmark, designed to evaluate the direction reasoning capabilities of multimodal language models (MLMs). CDR includes three types images to test spatial (up, down, left, right) and compass (north, south, east, west) directions. Our evaluation reveals that most MLMs struggle with direction reasoning, often performing at random guessing levels. Experiments show that training directly with CDR data yields limited improvements, as it requires an understanding of real-world physical rules. We explore the impact of mixdata and CoT fine-tuning methods, which significantly enhance MLM performance in compass direction reasoning by incorporating diverse data and step-by-step reasoning, improving the model's ability to understand direction relationships.

Reasoning future unknowable facts on temporal knowledge graphs (TKGs) is a challenging task, holding significant academic and practical values for various fields. Existing studies exploring explainable reasoning concentrate on modeling comprehensible temporal paths relevant to the query. Yet, these path-based methods primarily focus on local temporal paths appearing in recent times, failing to capture the complex temporal paths in TKG and resulting in the loss of longer historical relations related to the query. Motivated by the Dual Process Theory in cognitive science, we propose a \textbf{Cogn}itive \textbf{T}emporal \textbf{K}nowledge \textbf{E}xtrapolation framework (CognTKE), which introduces a novel temporal cognitive relation directed graph (TCR-Digraph) and performs interpretable global shallow reasoning and local deep reasoning over the TCR-Digraph. Specifically, the proposed TCR-Digraph is constituted by retrieving significant local and global historical temporal relation paths associated with the query. In addition, CognTKE presents the global shallow reasoner and the local deep reasoner to perform global one-hop temporal relation reasoning (System 1) and local complex multi-hop path reasoning (System 2) over the TCR-Digraph, respectively. The experimental results on four benchmark datasets demonstrate that CognTKE achieves significant improvement in accuracy compared to the state-of-the-art baselines and delivers excellent zero-shot reasoning ability. \textit{The code is available at https://github.com/WeiChen3690/CognTKE}.

AI for Mathematics (AI4Math) is not only intriguing intellectually but also crucial for AI-driven discovery in science, engineering, and beyond. Extensive efforts on AI4Math have mirrored techniques in NLP, in particular, training large language models on carefully curated math datasets in text form. As a complementary yet less explored avenue, formal mathematical reasoning is grounded in formal systems such as proof assistants, which can verify the correctness of reasoning and provide automatic feedback. In this position paper, we advocate for formal mathematical reasoning and argue that it is indispensable for advancing AI4Math to the next level. In recent years, we have seen steady progress in using AI to perform formal reasoning, including core tasks such as theorem proving and autoformalization, as well as emerging applications such as verifiable generation of code and hardware designs. However, significant challenges remain to be solved for AI to truly master mathematics and achieve broader impact. We summarize existing progress, discuss open challenges, and envision critical milestones to measure future success. At this inflection point for formal mathematical reasoning, we call on the research community to come together to drive transformative advancements in this field.

Despite recent advances in large language models, open-source models often struggle to consistently perform well on complex reasoning tasks. Existing ensemble methods, whether applied at the token or output levels, fail to address these challenges. In response, we present Language model Ensemble with Monte Carlo Tree Search (LE-MCTS), a novel framework for process-level ensembling of language models. LE-MCTS formulates step-by-step reasoning with an ensemble of language models as a Markov decision process. In this framework, states represent intermediate reasoning paths, while actions consist of generating the next reasoning step using one of the language models selected from a predefined pool. Guided by a process-based reward model, LE-MCTS performs a tree search over the reasoning steps generated by different language models, identifying the most accurate reasoning chain. Experimental results on five mathematical reasoning benchmarks demonstrate that our approach outperforms both single language model decoding algorithms and language model ensemble methods. Notably, LE-MCTS improves performance by 3.6% and 4.3% on the MATH and MQA datasets, respectively, highlighting its effectiveness in solving complex reasoning problems.