EAGER: Robust Reasoning using a Geometric Approach to SAT and PSAT

EAGER：使用几何方法进行 SAT 和 PSAT 的稳健推理

• 批准号: 2152454
• 负责人: Thomas Henderson
• 金额: $ 9.92万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-04-01 至 2023-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2152454&HistoricalAwards=false
• 关键词: EAGER; Robust; Reasoning; using; Geometric

The overarching goal of this EAGER project is to develop efficient and reliable methods for autonomous agents to produce plans for their safe operation in complex situations. For example, the development of large-scale unmanned aircraft system operation in urban areas for package delivery depends on such a capability. The fundamental issue is to determine if there is a viable solution in a specific situation; at the present time the complexity of this problem is too high to guarantee that a solution can be found. The team of researchers is developing a lower complexity approach with wide application in artificial intelligence. The project engages student researchers from underrepresented groups in computer science, and the research results are integrated into the classroom through courses like artificial intelligence, theory of computation, and autonomous agent systems.The project provides a new approach to agent planning at the cognitive level. The basic innovation is to convert the satisfiability problem into a geometric setting; in particular, the models of an n-variable logical sentence are viewed as the corners of an n-D hypercube, and interior points assign probabilities to the variables. Each conjunct in the conjunctive normal form sentence reduces the convex feasible solution region. Any non-empty feasible region indicates the existence of a solution to the probabilistic satisfiability problem and can also be probed with linear programming methods in polynomial time to seek an answer to the satisfiability problem. Particular approaches to be explored include: (1) modifications to the interior point method using barrier methods, (2) finding linear programming solutions in a non-Euclidean geometry, (3) applying random rotations to the feasible region to allow coordinate projects to determine if there is a solution, and (4) using Markov Chain Monte Carlo to get a point near a corner. Applications include probabilistic satisfiability inference, reinforcement policy optimization for autonomous agents, and probabilistic temporal logic.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这个渴望的项目的总体目标是为自主代理开发有效且可靠的方法，以在复杂情况下制定其安全操作计划。例如，在城市地区开发大规模无人飞机系统以进行包装交付取决于这种能力。基本问题是确定在特定情况下是否有可行的解决方案；目前，此问题的复杂性太高，无法确保可以找到解决方案。研究人员团队正在开发较低的复杂方法，并在人工智能中广泛应用。该项目与计算机科学中代表性不足的小组的学生研究人员参与，研究结果通过人工智能，计算理论和自主代理系统等课程整合到课堂上。该项目为认知水平的代理计划提供了一种新的方法。基本的创新是将满足性问题转换为几何环境。特别是，N-变量逻辑句子的模型被视为N-D HyperCube的角落，并且内部点为变量分配了概率。连词正常形式句子中的每个连词都会降低凸的可行解区域。任何非空的可行区域都表明存在解决概率令人满意问题的解决方案，也可以在多项式时间内使用线性编程方法来探测，以寻求解决可满足性问题的答案。要探索的特定方法包括：（1）使用屏障方法对内点方法进行修改，（2）在非欧几里得几何形状中找到线性编程解决方案，（3）（3）将随机旋转应用于可行区域以允许坐标项目允许坐标项目以确定是否存在解决方案，（4）使用Markov Chain Monte Carlo来靠近角度。申请包括概率的满足性推断，对自主代理的强化政策优化以及概率的时间逻辑。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子和更广泛影响的评估来评估值得支持的。