Complexity in Spatial Reasoning
Complexity in Spatial Reasoning
复制标题
空间推理的复杂性
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
L. Webber
中科院分区：
文献类型：
--
作者：
T. Fangmeier;M. Knauff;Marco Ragni;L. Webber
空间推理的复杂性 Marco Ragni (ragni@informatik.uni-freiburg.de) 计算机科学系，Georges-Kohler-Allee 79110 Freiburg, 德国 Thomas Fangmeier (thomas.fangmeier@cognition.uni-freiburg.de) 认知科学中心，Friedrichstrase 50 79098 Freiburg, 德国 Lara Webber (lara.webber@cognition.uni-freiburg.de) 认知科学中心，Friedrichstrase 50 79098 Freiburg, 德国 Markus Knauff (knauff@cognition.uni-freiburg.de) 认知科学中心，Friedrichstrase 50 79098 Freiburg, 德国 锤子位于钳子的右侧。螺丝刀位于钳子的左侧。扳手位于螺丝刀的前面。锯子位于钳子的前面。摘要 我们引入了一种统一的方法来解决人们在空间推理中遇到的问题。这种方法结合了两种理论：心智模型理论，旨在解释演绎过程；关系复杂性理论，解释概念化推理问题所需的空间关系的处理复杂性。我们建议这两种理论的结合可以解释空间推理中发现的一些各种错误。我们提出了两个实验，证明参与者使用第一自由适应原则来构建首选的心理模型。然后，我们在模型空间推理计算框架中正式实施这些发现。扳手和锯子之间存在什么关系？关键词：空间推理；心理模型；复杂;计算框架 简介 日常空间推理与空间关系的广泛使用密切相关，空间关系定位一个对象相对于其他对象的位置。此类关系的示例包括二元关系，例如“在...的左边”或“在...前面”，甚至更复杂的关系，例如“在中间”的三元关系。处理此类空间关系的典型推理问题是从对象的空间配置的不完整描述来推断对象之间的关系。因此，在演绎推理过程中，一系列对象之间的隐含关系将从描述空间配置的断言中推断出来。下面的问题提供了一个简单的例子：前四个断言称为前提，而问题指的是可以从前提得出的可能结论。 Johnson-Laird 和 Byrne (1991) 提出的心智模型理论 (MMT) 表明，人们通过构建和检查代表前提中描述的事态的空间阵列来得出结论。这个推理过程由三个不同的阶段组成：理解、描述和验证（请参阅下一节的解释）。根据 MMT，语言过程仅与将信息从前提转移到空间阵列并再次返回相关，但推理过程本身仅依赖于非语言过程。迄今为止，现代货币理论的局限性在于该理论无法解释人类处理复杂关系时遇到的困难。 MMT解释了推理问题的复杂性，但忽略了模型构建的复杂性。我们相信，这正是 Halford (1993) 提出的关系复杂性理论 (RCT) 发挥作用的地方。代表空间描述的不同模型可以根据认知经济性来衡量（Halford，1993；Goodwin & Johnson-Laird，2005）。但 RCT 的一个弱点是它没有解释推理过程本身是如何运作的。换句话说，随机对照试验和现代货币理论这两种理论在某种程度上都有局限性，或者更积极地说可以相互补充。本文建议通过提供一个基于 MMT 特定规范（即偏好理论）的正式框架来整合 RCT 和 MMT。
Complexity in Spatial Reasoning Marco Ragni (ragni@informatik.uni-freiburg.de) Department of Computer Science, Georges-Kohler-Allee 79110 Freiburg, Germany Thomas Fangmeier (thomas.fangmeier@cognition.uni-freiburg.de) Center for Cognitive Science, Friedrichstrase 50 79098 Freiburg, Germany Lara Webber (lara.webber@cognition.uni-freiburg.de) Center for Cognitive Science, Friedrichstrase 50 79098 Freiburg, Germany Markus Knauff (knauff@cognition.uni-freiburg.de) Center for Cognitive Science, Friedrichstrase 50 79098 Freiburg, Germany The hammer is to the right of the pliers. The screwdriver is to the left of the pliers. The wrench is in front of the screwdriver. The saw is in front of the pliers. Abstract We introduce a unified approach to account for the problems people have in spatial reasoning. This approach combines two theories: the mental model theory which aims to explain the deduction process, and the relational complexity theory which explains the processing complexity of the spatial relations needed in order to conceptualize the reasoning problem. We propose that a combination of these two theories can account for some of various errors found in spatial reasoning. We present two experiments in which we demonstrate that participants use the principle of first free fit to construct preferred mental models. We then formally implement these findings in the Spatial Reasoning by Models computational framework. Which relation holds between the wrench and the saw? Keywords: Spatial reasoning; Mental Models; complexity; computational framework Introduction Everyday spatial reasoning is strongly connected to the extensive use of spatial relations which locate one object with respect to others. Examples of such relations include binary relations such as “to the left of”, or “in front of”, and even more complex relations like the ternary relation “in- between”. A typical reasoning problem dealing with such spatial relations is to infer relations between objects from an incomplete description of a spatial configuration of objects. Hence, in the deductive reasoning process implicit relations between a series of objects are to be inferred from assertions describing the spatial configuration. An easy example is provided by the following problem: The first four assertions are called premises, while the question refers to a possible conclusion that can be drawn from the premises. The mental model theory (MMT), proposed by Johnson-Laird and Byrne (1991), suggests that people draw conclusions by constructing and inspecting a spatial array that represents the state of affairs described in the premises. This reasoning process consists of three distinct stages: comprehension, description, and validation (see next section for explanation). According to the MMT, linguistic processes are only relevant to transfer the information from the premises into a spatial array and back again, but the reasoning process itself relies only on non- linguistic processes. A limitation of the MMT so far is that this theory does not explain the difficulty humans have with complex relations. The MMT explains the complexity of reasoning problems, but neglects the construction complexity of the models. This is, we believe, where the relational complexity theory (RCT) introduced by Halford (1993) comes into play. Different models representing a spatial description can be measured in terms of cognitive economicity (Halford, 1993; Goodwin & Johnson-Laird, 2005). But a weakness of the RCT is that it does not explain how the reasoning process itself works. In other words both theories, RCT and MMT are limited to some extent, or—more positively—can complement each other. This paper suggests an integration of RCT and MMT by providing a formal framework which is based on a particular specification of the MMT, namely the theory of preferred
影响因子：
1.9
作者：
R. Rauh;C. Hagen;M. Knauff;Thomas Kuss;C. Schlieder;G. Strube
通讯作者：
R. Rauh;C. Hagen;M. Knauff;Thomas Kuss;C. Schlieder;G. Strube