Qualitative Spatial Reasoning in Interpreting Text and Narrative

Abstract

Simple natural language texts and narratives often raise problems in commonsense spatial knowledge and reasoning of surprising logical complexity and geometric richness. In this article, I consider a dozen short texts—five taken from literature, the remainder contrived as illustrations—and discuss the spatial reasoning involved in understanding them. I conclude by summarizing their common features, and by tentatively drawing some morals for research in this area.     

Modelling Dynamic Spatial Systems in the Situation Calculus

Abstract

We propose and systematically formalise a dynamical spatial systems approach for the modelling of changing spatial environments. The formalisation adheres to the semantics of the situation calculus and includes a systematic account of key aspects that are necessary to realize a domain-independent qualitative spatial theory that may be utilised across diverse application domains. The spatial theory is primarily derivable from the all-pervasive generic notion of “qualitative spatial calculi” that are representative of differing aspects of space. In addition, the theory also includes aspects, both ontological and phenomenal in nature, that are considered inherent in dynamic spatial systems. Foundational to the formalisation is a causal theory that adheres to the representational and computational semantics of the situation calculus. This foundational theory provides the necessary (general) mechanism required to represent and reason about changing spatial environments and also includes an account of the key fundamental epistemological issues concerning the frame and the ramification problems that arise whilst modelling change within such domains. The main advantage of the proposed approach is that based on the structure and semantics of the proposed framework, fundamental reasoning tasks such as projection and explanation directly follow. Within the specialised spatial reasoning domain, these translate to spatial planning/re-configuration, causal explanation and spatial simulation. Our approach is based on the hypothesis that alternate formalisations of existing qualitative spatial calculi using high-level tools such as the situation calculus are essential for their utilisation in diverse application domains such as intelligent systems, cognitive robotics and event-based GIS.     

The Space within Fisherman's Folly: Playing with a Puzzle in Mereotopology

Abstract

In this paper we propose a spatial ontology for reasoning about holes, rigid objects and a string, taking a classical puzzle as a motivating example. In this ontology the domain is composed of spatial regions whereby a theory about holes is defined over a mereotopological basis. Within this theory we define a data structure, named chain, that facilitates a clear and efficient representation of the puzzle states and its solution.     

Localization,Exploration, and Navigation Based on Qualitative Angle Information

Abstract

Three of the major problems in building autonomous mobile robots are localization, exploration, and navigation. This paper investigates how well different qualitative methods based on angle information, most of them originally invented for representation of spatial knowledge, are suited for addressing these problems. It combines results from discrete and computational geometry with methods from qualitative spatial reasoning, gaining some new insights on the complexity of robot navigation. It turns out that essentially only with panoramas (special roundviews) the qualitative localization problem can be solved in a satisfactory manner. The exploration problem (qualitative map building), remains difficult for all considered approaches.     

A Neuro-Cognitive Theory of Deductive Relational Reasoning with Mental Models and Visual Images

Abstract

Many neuro-imaging studies have provided evidence that the parietal cortex plays a key role in reasoning based on mental models, which are supposed to be of abstract spatial nature. However, these studies have also shown concurrent activation in vision-related cortical areas which have often been interpreted as evidence for the role of visual mental imagery in reasoning. The aim of the paper is to resolve the inconsistencies in the previous literature on reasoning and imagery and to develop a neurally and cognitively plausible theory of human relational reasoning. The main assumption is that visual brain areas are only involved if the problem information is easy to visualize and when this information must be processed and maintained in visual working memory. A regular reasoning process, however, does not involve visual images but more abstract spatial representations—spatial mental models—held in parietal cortices. Only these spatial representations are crucial for the genuine reasoning processes.     

Analyzing Qualitative Spatio-Temporal Calculi using Algebraic Geometry

Abstract

Qualitative spatial reasoning is based on calculi which comprise relations and operation tables that encode operations like relation composition. Designing a calculus involves determining these tables and analyzing reasoning properties—a demanding task that is susceptible to errors if performed manually. This paper is concerned with automating computation of operation tables and analysis of qualitative calculi over real-valued domains like the plane ². We present an approach to specify qualitative relations using polynomial equations that allows methods from algebraic geometry to be applied. This paper shows how reasoning with qualitative relations can be posed algebraically and demonstrates algebraic reasoning using Gröbner base analysis. We evaluate this approach and describe our implementation, which is freely available as part of the spatial reasoning toolbox SparQ.     

On Embedding a Qualitative Representation in a Two-Dimensional Plane

Abstract

This paper discusses embedding in a two-dimensional plane a symbolic representation for spatial data using the simple objects, points (P), lines (L), circuits (C), and areas (A). We have proposed PLCA as a new framework for a qualitative spatial reasoning. In a PLCA expression, the entire figure is represented in a form in which all the objects are related. We investigate the conditions for two-dimensional realizability of a PLCA expression, and derive the relation that the numbers of objects in a PLCA expression should have. In this process, we use the well-known Euler's formula. We also give an algorithm for drawing the figure of the PLCA expression that satisfies this condition in a two-dimensional plane and prove its correctness. The algorithm generates a quantitative expression from qualitative expression.     

Managing Temporal Constraints with Preferences

Abstract

Preferences in temporal problems are common but significant in many real world applications. In this paper, we extend our temporal reasoning framework, managing numeric and symbolic information, in order to handle preferences. Unlike the existing models managing single temporal preferences, ours supports four types of preferences, namely: numeric and symbolic temporal preferences, composite preferences and conditional preferences. This offers more expressive power in representing a wide variety of temporal constraint problems. The preferences are considered here as a set of soft constraints using a c-semiring structure with combination and projection operators. Solving temporal constraint problems with preferences consists in finding a solution satisfying all the temporal constraints while optimizing the preference values. This is handled by a variant of the branch and bound algorithm, we propose in this paper, and where constraint propagation is used to improve the time efficiency. Experimental tests, we conducted on randomly generated temporal constraint problems with preferences, favor a variant of MAC as the constraint propagation strategy that should be used within the branch and bound algorithm.     

Qualitative Spatial Reasoning for Topological Map Learning

Abstract

In this paper we investigate the application of qualitative spatial reasoning methods for learning the topological map of an unknown environment. We develop a topological mapping framework that achieves robustness against ambiguity in the available information by tracking all possible graph hypotheses simultaneously. We then exploit spatial reasoning to reduce the space of possible hypotheses. The considered constraints are qualitative direction information and the assumption that the map is planar. We investigate the effects of absolute and relative direction information using two different spatial calculi and combine the approach with a real mapping system based on Voronoi graphs.     

The cognitive adequacy of Allen's interval calculus for qualitative spatial representation and reasoning

Qualitative spatial reasoning (QSR) is often claimed to be cognitively more plausible than conventional numerical approaches to spatial reasoning, because it copes with the indeterminacy of spatial data and allows inferences based on incomplete spatial knowledge. The paper reports experimental results concerning the cognitive adequacy of an important approach used in QSR, namely the spatial interpretation of the interval calculus introduced by Allen (1983). Knauff, Rauh and Schlieder (1995) distinguished between the conceptual and inferential cognitive adequacy of Allen's interval calculus. The former refers to the thirteen base relations as a representational system and the latter to the compositions of these relations as a tool for reasoning. The results of two memory experiments on conceptual adequacy show that people use ordinal information similar to the interval relations when representing and remembering spatial arrangements. Furthermore, symmetry transformations on the interval relations were found to be responsible for most of the errors, whereas conceptualneighborhood theory did not appear to correspond to cognitively relevant concepts. Inferential adequacy was investigated by two reasoning experiments and the results show that in inference tasks where the number of possible interval relations for the composition is more than one, subjects ignore numerous possibilities and interindividually prefer the same relations. Reorientations and transpositions operating on the relations seem to be important for reasoning performance as well, whereas conceptual neighborhood did not appear to affect the difficulty of reasoning tasks based on the interval relations.     

Reasoning about Depth and Motion from an Observer's Viewpoint

ABSTRACT

The goal of this paper is to present a logic-based formalism for representing knowledge about objects in space and their movements, and show how this knowledge could be built up from the viewpoint of an observer immersed in a dynamic world. In this paper space is represented using functions that extract attributes of depth, size and distance from snapshots of the world. These attributes compose a novel spatial reasoning system named Depth Profile Calculus (DPC). Transitions between qualitative relations involving these attributes are represented by an extension of this calculus called Dynamic Depth Profile Calculus (DDPC). We argue that knowledge about objects in the world could be built up via a process of abduction on DDPC relations.     

Taxonomy of Human Wayfinding Tasks: A Knowledge-Based Approach

Abstract

Although the term “Wayfinding” has been defined by several authors, it subsumes a whole set of tasks that involve different cognitive processes, drawing on different cognitive components. Research on wayfinding has been conducted with different paradigms using a variety of wayfinding tasks. This makes it difficult to compare the results and implications of many studies. A systematic classification is needed in order to determine and investigate the cognitive processes and structural components of how humans solve wayfinding problems. Current classifications of wayfinding distinguish tasks on a rather coarse level or do not take the navigator's knowledge, a key factor in wayfinding, into account. We present an extended taxonomy of wayfinding that distinguishes tasks by external constraints as well as by the level of spatial knowledge that is available to the navigator. The taxonomy will help to decrease ambiguity of wayfinding tasks and it will facilitate understanding of the differentiated demands a navigator faces when solving wayfinding problems.     

Modeling visuospatial reasoning

I apply my proposed modification of Soar/Spatial/Visual System and Kosslyn’s (1983) computational operations on images to problems within a 2 × 2 taxonomy that classifies research according to whether the coding involves static or dynamic relations within an object or between objects (Newcombe & Shipley, 2015). I then repeat this analysis for problems that are included in mathematics and science curricula. Because many of these problems involve reasoning from diagrams Hegarty’s (2011) framework for reasoning from visual-spatial displays provides additional support for organizing this topic. Two more relevant frameworks specify reasoning at different levels of abstraction (Reed, 2016) and with different combinations of actions and objects (Reed, 2018). The article concludes with suggestions for future directions.     

Space,Language and Ontology: A Response to Davis

Abstract

Ernest Davis' article “Qualititative Spatial Reasoning in Interpreting Text and Narrative” discusses challenges that the interpretation of natural language appears to raise for the formalization of commonsense spatial reasoning. Davis finds these to be of “surprising logical complexity,” but also “erratic” in that they do not show a logical structuring of the problem space that could guide productive research. In this response I argue that much of the apparent lack of structure Davis laments is due to the very style of formal modeling he pursues. By augmenting logical considerations with substantial input from other disciplines and by adopting a heterogeneous and modular approach to formalization, I suggest that the problem space is by no means as ill-structured as Davis presents it.     

基于XML的知识获取工具研究与实现

知识获取(KA)是专家系统研究的重点之一.而知识获取工具是沟通领域专家和知识应用开发人员的桥梁.为了解决专家系统中的知识获取问题,基于XML(eXtensible Markup Language)开发了一种方便的知识获取工具,通过生成知识获取模板来辅助实现知识的获取,领域专家通过该模板表达自己所掌握的领域知识,而开发人员根据该模板建立行为模型.以虚拟战场环境中CGF(Computer Generated Force)实体的行为知识获取为例,说明了基于XML的知识获取工具开发过程,这种方法同样适合于其它领域的知识表达和知识获取.     

空间飞行器推进系统的故障检测

文中采用基于人工智能条件下的专家系统知识，应用门限算法进行故障特性提取和相应的故障推理机制研究，在由大量小发动机组成的空间飞行器推进系统实验中进行应用，通过已有的实验数据，离线回放表明此方法具有实时检测功能，可以解决工程实际问题。     

Learning to Reach to Locations Encoded from Imaging Displays

We examined the use of hand gestures while people solved spatial reasoning problem in which they had to infer motion from static diagrams (mental animation problems). In Experiment 1, participants were asked to think aloud while solving mental animation problems. They gestured on more than 90% of problems, and most gestures expressed information about the component motions that was not stated in words. Two further experiments examined whether the gestures functioned in the mechanical inference process, or whether they merely served functions of expressing or communicating the results of this process. In these experiments, we examined the effects of instructions to think aloud, restricting participants' hand motions, and secondary tasks on mental animation performance. Although participants who were instructed to think aloud gestured more than control groups, some gestures occurred even in control conditions. A concurrent spatial tapping task impaired performance on mechanical reasoning, whereas a simple tapping task and restricting hand motions did not. These results indicate that gestures are a natural way of expressing the results of mental animation processes and suggest that spatial working memory and premotor representations are involved in mental animation. They provide no direct evidence that gestures are functional in the thought process itself, but do not rule out a role for overt gestures in this type of spatial thinking.     

The Influence of Landmarks and Pre-exposure to a Structural Map During the Process of Spatial Knowledge Acquisition: A Study with Children and Adults in a Virtual Environment

ABSTRACT

This study investigated the effects of featural information (landmarks) and geometric information (pre-exposure to a structural map) and their possible interaction during the process of spatial knowledge acquisition of 8- and 11-year-old children and adults in a virtual environment. The study confirmed the well-known result of a developmental achievement in spatial cognition from childhood to adulthood. Although landmarks and the pre-exposure to a structural map did not affect the time to learn a specific route, they influenced the use of behavior in spatial learning and eased the acquisition of spatial knowledge measured by a route reversal and map-drawing tasks. Children and adults are able to integrate featural and geometric information in the spatial knowledge acquisition process in an environmental space, but their integration depends on the spatial processing stages that are investigated. Moreover, it was successfully demonstrated that the use of desktop virtual environments seems to be appropriate to investigate the development of spatial cognition.