Current research on qualitative spatial representation and reasoning mainly focuses on one single aspect of space. In real world applications, however, multiple spatial aspects are often involved simultaneously.
This paper investigates problems arising in reasoning with combined topological and directional information. We use the RCC8 algebra and the Rectangle Algebra (RA) for expressing topological and directional information respectively. We give examples to show that the bipath-consistency algorithm BIPATH is incomplete for solving even basic RCC8 and RA constraints. If topological constraints are taken from some maximal tractable subclasses of RCC8, and directional constraints are taken from a subalgebra, termed DIR49, of RA, then we show that BIPATH is able to separate topological constraints from directional ones. This means, given a set of hybrid topological and directional constraints from the above subclasses of RCC8 and RA, we can transfer the joint satisfaction problem in polynomial time to two independent satisfaction problems in RCC8 and RA. For general RA constraints, we give a method to compute solutions that satisfy all topological constraints and approximately satisfy each RA constraint to any prescribed precision.
Topology of Reasoning: Retrieved Cell Complex-Augmented Generation for Textual Graph Question Answering
Academy of Advanced Interdisciplinary Studies, Chongqing University of Posts and Telecommunications（重庆邮电大学先进交叉学科研究院）；School of Computer Science and Technology, Chongqing University of Posts and Telecommunications（重庆邮电大学计算机科学与技术学院）；Intelligent System Department, Zhongxing Telecom Equipment (ZTE)（中兴电信设备智能系统部）
GALAX: Graph-Augmented Language Model for Explainable Reinforcement-Guided Subgraph Reasoning in Precision Medicine
I2DB, Washington University School of Medicine（I2DB，华盛顿大学医学学院）；Department of Computer Science and Engineering, Washington University in St. Louis（计算机科学与工程系，华盛顿大学圣路易斯分校）；Department of Genetics, Washington University School of Medicine（遗传学系，华盛顿大学医学学院）
RAGNav: A Retrieval-Augmented Topological Reasoning Framework for Multi-Goal Visual-Language Navigation
Southwestern University of Finance（西南财经大学）；Department of Informatics,Universitat Hamburg, Hamburg, Germany（汉堡大学信息学院）；University of Electronic Science（电子科技大学）
Reasoning about Cardinal Directions between Extended Objects
Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology, Sydney（悉尼科技大学工程与信息技术学院量子计算与智能系统中心）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）
TopoBench: Benchmarking LLMs on Hard Topological Reasoning
Intercom Research（Intercom研究院）；University College Dublin（都柏林大学）；University of Galway（Galway大学）；Salk Institute（Salk研究所）；Dublin City University（都柏林城市大学）；Trinity College Dublin（都柏林三一学院）
Foundation Models for Geospatial Reasoning: Assessing Capabilities of Large Language Models in Understanding Geometries and Topological Spatial Relations
GeoDS Lab, Department of Geography, University of Wisconsin-Madison, USA（威斯康星大学麦迪逊分校地理系GeoDS实验室）；Department of Geography and Regional Research, University of Vienna, Austria（维也纳大学地理与区域研究系）；Department of Geography, University of California-Santa Barbara, USA（加州大学圣塔芭芭拉分校地理系）
TDA-RC: Task-Driven Alignment for Knowledge-Based Reasoning Chains in Large Language Models
School of Information and Software Engineering, University of Electronic Science and Technology of China（电子科技大学信息与软件工程学院）；School of Computer Science and Engineering, University of Electronic Science and Technology of China（电子科技大学计算机科学与工程学院）；College of Professional and Continuing Education, The Hong Kong Polytechnic University（香港理工大学专业及持续教育学院）；School of Robotics and Advanced Manufacture, Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳）机电工程与自动化学院）；School of Computing, Kyung Hee University（庆熙大学计算机学院）；School of Computer Science and Technology, Tongji University（同济大学计算机科学与技术学院）
