The Integration and Interaction of Multiple Mathematical Reasoning Processes

我们在DReaM小组的工作涉及人工智能和理论计算机科学技术的独特融合，使我们能够在自动推理和数学发现方面采取独特的整体视角。拟议的平台授权更新将用于提供必要的基础设施，并使探索性活动能够支持一系列项目，这些项目将重点放在数学推理过程的自动化上，包括它们的分析、开发和交互。根据我们对自动推理的整体看法，我们可以大致分类。这个主题的核心是表征和推理之间的相互作用。也就是说，发现正确的表示通常可以极大地简化解决问题所需的推理，相反，元级推理，特别是证明-失败分析，通常可以为发展正确的表示提供指导。平台补助金的续期将使我们能够在基础研究和应用方面保持和加强围绕这一主题建立的势头。前者涵盖了一系列主题，包括：理论形成的认知方面；数学发现与自动定理生成；本体的创造、修复与演化；证明过程;可计算性;证明规划;人工智能问题重构；量子计算;计算的创造力;以及推理过程的可视化。后者涵盖了广泛的应用，例如：软件验证；软件密集型系统的形式化建模；安全与隐私分析与设计；平面设计;游戏设计;灾难恢复计划；医疗保健过程的建模;诗歌和艺术。我们目前的平台资助资金的积极效果可以在我们研究的各个方面看到-它使我们能够：与世界上最好的研究人员合作和交流思想；探索和测试新想法；制定大胆的拨款建议并赢得资金；巩固我们的研究项目的成果，并确保后续资金，使我们的研究的影响充分实现；并帮助培养我们领域的下一代研究明星和领导者。更新的平台补助金将使我们能够继续成长为一个研究小组，在我们的研究人员的职业发展方面，我们研究的深度和广度，以及它对社会更广泛方面的影响。

Our work in the DReaM group involves a unique blend of the techniques of artificial intelligence and theoretical computer science, enabling us to take a uniquely holistic perspective on automated reasoning and mathematical discovery.The proposed Platform Grant renewal will be used to provide essential infrastructure and to enable exploratory activities that will support a portfolio of projects which focus on the automation of mathematical reasoning processes, including their analysis, development and interaction. We can be broadly classified by our holistic perspective on automated reasoning. Central to this theme is the interplay between representation and reasoning. That is, discovering the right representation can often dramatically simplify the reasoning required in solving a problem, and conversely, meta-level reasoning, and in particular proof-failure analysis, can often provide guidance in evolving the right representations.The renewal of the Platform Grant will enable us to maintain and strengthen the momentum that has been built up around this theme - in terms of basic research as well as applications. The former covers a spectrum of topics, including: cognitive aspects of theory formation; mathematical discovery and automatic theorem generation; ontology creation, repair and evolution; proof procedures; computability; proof planning; AI problem reformulation; quantum computation; computational creativity; and the visualisation of reasoning processes. The latter covers wide ranging applications such as: software verification; formal modelling of software intensive systems; security and privacy analysis and design; graphic design; videogame design; disaster recovery planning; and the modelling of healthcare processes; poetry and art.The positive effective of our current Platform Grant funding can be seen across all aspects of our research - it enables us to: collaborate and exchange ideas with the best researchers in the world; explore and test new ideas; develop adventurous grant proposals and win funding; consolidate the results of our research projects and secure the follow-on funding that enables the impact of our research to be fully realised; and help develop the next generation of research stars and leaders in our field. A renewed Platform Grant would enable us to continue to grow as a research group, in terms of the career development of our researchers, the depth and breadth of our research, and the impact it has on wider aspects of society.