The fields of modal logics, table intelligence, and large language models are experiencing significant developments, driven by the need for more expressive, flexible, and robust frameworks. A common theme among these areas is the integration of defeasibility, density notions, and innovative semantic and calculi techniques to enable more nuanced and context-dependent reasoning. Notably, the development of new frameworks and methods, such as preferential semantics and tableau-based methods, is facilitating the analysis and computation of these enhanced logical frameworks. For instance, the introduction of defeasible propositional standpoint logic and the corrected proof of the decidability of quasi-dense modal logics are noteworthy advancements in modal logics. In table intelligence, the integration of large language models into table reasoning frameworks has enabled holistic understanding and efficient processing of complex tabular data. Novel approaches, such as TableReasoner and TableCopilot, have achieved state-of-the-art results in table question answering tasks and set new standards for interactive table assistants. The field of large language models is witnessing significant advancements in reasoning and mathematics capabilities, with a focus on improving accuracy and efficiency through innovative training methods. The combination of supervised fine-tuning and reinforcement learning has led to state-of-the-art performance on challenging benchmarks, including mathematical Olympiad competitions. Moreover, the development of novel frameworks, such as Review, Remask, Refine (R3), and TruthTorchLM, has enabled models to efficiently identify and correct their own errors and predict truthfulness in outputs. The introduction of cache steering methods and bi-level frameworks for structured reasoning has also improved the qualitative structure of model reasoning and quantitative task performance. The field of neurosymbolic AI is integrating learning and reasoning to exploit the strengths of both large-scale learning and robust, verifiable reasoning. Novel frameworks, such as ChainEdit and KELPS, have proposed methods for improving the scalability and expressiveness of neurosymbolic models. Overall, these innovations are poised to significantly improve the capabilities of large language models and related fields, enabling more effective and efficient reasoning, problem-solving, and decision-making in complex and uncertain environments.