CRII: III: RI: Empowering Multi-Conceptual Spatial Reasoning with a Repository of Qualitative and Quantitative Spatial Ontologies

人们有多种方式来表达和处理空间信息。根据需要，他们使用空间的概念化，即所谓的认知地图，在粒度、范围和精确度上有所不同。基于语境，人们使用不同的隐含假设来解释空间关系，如“A包含在B中”。不同的概念所作的假设或暗示的假设甚至常常与另一个概念相矛盾(例如，在“湖中有海湾”中，海湾是湖泊的一个分区，而在“湖中有一个岛”中，岛屿被湖包围)。这对人们来说不是问题：我们能够快速而可靠地决定哪种概念化最适合特定情况，通常选择最简单、适用的概念化。例如，人们可以快速做出导航决策(“我需要在州际公路上向北还是向南旅行？”)或者回答简单的空间查询(“海洋是从这里向东还是向西？”)。灵活利用多种概念的类似能力将使记录和处理空间信息的计算工具更加强大和用户友好。为了实现这一目标，拟议的研究将调查自动选择最适合于解决特定任务的空间表示的形式和基本程序，例如寻找具有某些定性特征的数据、回答空间查询或检验空间假设。这项研究将有助于在信息系统中以更自然的方式收集、访问和处理空间信息，而不会阻碍其有效处理。在这个项目中，不同的空间概念化将被编码为机器可解释的空间本体，并被放置在利用数学逻辑关系的结构化本体库中。使用可定义性的数学概念比较本体的表达能力的形式基础将被开发出来，并用于通过本体假设和表达能力的差异来组织储存库。这种结构将被用于自动选择最适合特定空间任务的本体的程序利用。此外，将研究将空间信息从一个本体论转换为另一个本体论所需知识的正式编码，并伴随着利用这些信息自动识别和转换与特定空间任务相关的几何背景知识的程序。该项目的研究将有助于更好地理解如何利用逻辑关系来正式比较两个空间本体的表达能力，以及如何通过允许基于不同本体的知识自动转换的信息来补充空间本体库。有关更多信息，请参阅项目网页：http://www.spatial.maine.edu/~torsten/projects/QQSOR.shtml

People have manifold ways to express and process spatial information. As needed, they employ conceptualizations of space, so-called cognitive maps, that differ in granularity, scope, and precision. Based on the context, people use different implicit assumptions to interpret a spatial relation such as "A is contained in B." The assumptions made or implied by different conceptualizations often even contradict another (e.g., in "the lake contains a bay" the bay is a subregion of the lake while in "the lake contains an island" the island is surrounded by the lake). This is not an issue for people: we are able to quickly and reliably decide which conceptualization is most suitable in a specific situation, often choosing the simplest applicable conceptualization. For instance, people can quickly make navigation decisions ("Do I need to travel north or south on the Interstate?") or answer simple spatial queries ("Is the ocean east or west from here?"). Similar capabilities for flexibly utilizing multiple conceptualizations would make computational tools for recording and processing spatial information much more powerful and user-friendly. Towards this goal, the proposed research will investigate a formalism and basic procedures for automatically choosing a spatial representation best suited to solve a specific task, such as finding data with certain qualitative characteristics, answering a spatial query, or testing a spatial hypothesis. The research will contribute to a theoretical foundation for collecting, accessing, and manipulating spatial information in more natural ways without impeding its efficient processing in information systems. It will lower the barrier of entry for interacting with and analyzing spatial information and promotes technologies to cut time and costs typically spent on transforming diverse spatial data sets into a coherent model.In this project, the different spatial conceptualizations will be encoded as machine-interpretable spatial ontologies and placed in a structured ontology repository that leverages relationships from mathematical logic. The formal foundation for comparing the expressivity of ontologies using the mathematical notion of definability will be developed and used to organize the repository by differences in ontological assumptions and expressivity. This structure will be exploited by procedures for automatically selecting an ontology that best fits a specific spatial task. In addition, formal encodings of the knowledge necessary to convert spatial information from one ontology to another will be investigated, accompanied by procedures that utilize this information for automatically identifying and converting pieces of geometric background knowledge relevant to a specific spatial task. The research in this project will contribute to a better understanding of how logical relationships can be utilized to formally compare the expressiveness of two spatial ontologies, and how a spatial ontology repository can be supplemented by information that allows automated conversion of knowledge based on different ontologies. For further information see the project web page: http://www.spatial.maine.edu/~torsten/projects/QQSOR.shtml