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.     

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.     

Approximate qualitative spatial reasoning

Qualitative relations between spatial regions play an importantrole in the representation and manipulation of spatial knowledge.The RCC5 and RCC8 systems of relations,used in the Region-Connection Calculus, are of fundamentalimportance. These two systems deal with ideal regions havingprecisely determined location. However,in many practical examples of spatial reasoning,regions are represented by finite approximations rather than known precisely.Approximations may be given by describing how a regionrelates to cells forming a partition of the space underconsideration. Although the RCC5 and RCC8 systems have beengeneralized to ``egg-yolk' regions, in order to modelcertain types of vagueness, their extension to regionsapproximated in this way has not been discussed before.This paper presents two methods, the syntactic and the semantic, by which the RCC5 and RCC8 systemsmay be defined for approximate regions. The syntactic uses algebraicoperations on approximate regions which generalize operations on preciseregions. The semantic method makes use of the set of preciseregions which could be the intended interpretation of anapproximate region. Relationships between these two methods arediscussed in detail.alternative to navigation training with a map.     

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.     

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.     

Spatial updating and common misinterpretations of spatial reference frames

Spatial memory plays an important role in everyday life, and a large amount of research has been devoted to understanding spatial coding and reference frames across many areas. The popular research paradigms to study spatial reference frames include novel shortcut, perspective change, and landmark control tests. However, the growing research on spatial updating challenges the logical foundation of these classical paradigms, and suggests that the experimental findings using these paradigms have usually been misinterpreted. That is, performance in these tasks is generally unrelated to whether the spatial representations themselves are egocentric or allocentric. This article reviews the traditional paradigms and their logic, summarizes the theories of spatial updating, analyzes the logical flaws in these popular paradigms, and discusses their implications.     

Mental representation of spatial cues in microgravity: Writing and drawing tests

Humans have mental representation of their environment based on sensory information and experience. A series of experiments has been designed to allow the identification of disturbances in the mental representation of three-dimensional space during space flight as a consequence of the absence of the gravitational frame of reference. This NASA/ESA-funded research effort includes motor tests complemented by psychophysics measurements, designed to distinguish the effects of cognitive versus perceptual-motor changes due to microgravity exposure. Preliminary results have been obtained during the microgravity phase of parabolic flight. These results indicate that the vertical height of handwritten characters and drawn objects is reduced in microgravity compared to normal gravity, suggesting that the mental representation of the height of objects and the environment change during short-term microgravity. Identifying lasting abnormalities in the mental representation of spatial cues will establish the scientific and technical foundation for development of preflight and in-flight training and rehabilitative schemes, enhancing astronaut performance of perceptual-motor tasks, for example, interaction with robotic systems during exploration-class missions.     

Influences of Form and Function on the Acceptability of Projective Prepositions in Swedish

Abstract

Projective prepositions express the relation between two objects by referring to a direction in space and have traditionally been regarded as expressing purely geometric relations. Recent studies have shown that the appropriateness of English and Spanish projectives also depends on functional relations between objects. This study investigates if the acceptability of the Swedish projectives över, under, ovanför and nedanför are influenced by functional factors as well, and whether över and under are differentially influenced by function than ovanför and nedanför, as has been shown for their English cognates. It also investigates how the shape and parts of the related objects influence their functional interaction, and thereby the acceptability of the prepositions. This is done with respect to the predictions of the AVS-model, a model of the perceptual processes underlying the apprehension of projectives, which takes both the geometric and the functional relation between objects into account. It was found that acceptability judgments about the prepositions are influenced by function as their corresponding English and Spanish prepositions. The acceptability of över was more sensitive to function than ovanför, whereas under and nedanför were not differentially influenced by function, as has been shown for Spanish. It was further found that the shape and parts of both of the related objects influence acceptability regions associated with the prepositions in predictable ways, as functional interactions between objects largely depend on their parts. The results finally show that the AVS-model needs to be further developed in order to account for the form and function of the located object.     

A study of people's sketching habits in GIS

Sketching is traditionally associated withdoodling simple strokes on a piece of paper.Only few professionals outside of design andthe fine arts have recognized the expressivepower of this intuitive modality. However,sketching seems particularly well suited tocapture objects and situations in a spatialenvironment, such as geographic space. To learnmore about the techniques and strategies peopleuse when sketching, a survey of sketching wasconducted. The study showed that paper andpencil sketches contain mostly simple andabstract objects that are composed of only fewstrokes. The spatial configuration of a sceneis primarily expressed through the topologicalordering of objects relative to each other.Metric relationships are used to refine spatialconfigurations. These and other findingssuggest that sketching is an appropriatemodality to interact with a computer where onewants to describe and capture objectconfigurations in a spatial environment, suchas a geographic information system (GIS).     

Human Four-Dimensional Spatial Judgments of Hyper-Volume

The dimensionality limitation of human spatial representations has been a long-lasting, unsolved issue in psychology, mathematics, and philosophy. The present study examined the possibility of human four-dimensional spatial representations using a spatial judgment task on hyper-volume, a novel property unique to higher dimensional space. Observers studied visual simulations of random wireframe hyper-tetrahedrons (4-simplexes) rotating around the y-z plane and judged their hyper-volume by adjusting the size of a 4-D block. Multiple regression analyses showed a significant correlation between the responses and the actual hyper-volume but not the definition-based, lower-dimensional cues such as the mean 3-D volume, providing empirical evidence of human 4-D spatial representations that can support judgments of certain novel, high-dimensional properties.     

Children's control of reference systems in spatial tasks: Foundations of spatial cognitive skill?

Two experiments are presented, one that focused on the abilities of 3- through 8-year-old children to use frames of reference as means for solving a search task in a small-scale perceived space and one that focused on the abilities of 8- through 11-year-old children to use different frames of reference to answer questions about the locations of objects in an environment they had read about. Experiment 1 revealed developmental improvement in the consistent application of object-, place-, and viewer-based frames of reference, with scale of space impacting the pattern of age-related improvement. Experiment 2 showed that young readers' first successes with switching from one reference system to another in representational space involved a vantage point perspective, a viewer-based ``gaze tour' of a small-scale area. Although disparate in focus and method, the studies point to the need for a new theoretical framework for examining developmental issues in the application of spatial frames of reference.     

Registration of space objects: ESA member states’ practice

The registration of space objects is indispensable for the orderly administration of outer space. Most states recognize this and comply with the instruments—the Registration Convention and the UN General Assembly Resolution—set up to permit registration, but they display different approaches to and interpretations of the concept of registration. This article examines the registration practices of various European Space Agency (ESA) member states and of ESA itself. It finds that, despite varied policies, the system seems to be working well. However, there has been a worrying rise in non-registrations over the past few years, perhaps linked to the growth in the number of, especially commercial, entities engaging in space activities.     

Geometric problem solving with strings and pins

Humans solve spatial and abstract problems more easily if these can be visualized and/or physically manipulated. We analyze the domain of geometric problem solving from a cognitive perspective and identify several levels of domain abstraction that interact in the problem solving process. We discuss the roles of physical manifestations of spatial configurations, their manipulation, and their perception for understanding problem solving processes. We propose an extension of the classical problem solving repertoire of constructive geometry to approach certain problems more directly than under the compass-and-straightedge paradigm. Specifically, we introduce strings and pins as helpful metaphors for a generalization of the constructive geometry approach. We present classical problems from spatial problem solving to illustrate the ‘strings and pins’ paradigm. Three case studies are discussed: strings-and-pins solutions to (i) the ellipse construction problem; (ii) the shortest path problem; and (iii) the angle trisection problem. Comparisons to formal solutions are drawn. Differences and similarities between the compass-and-straightedge paradigm and the strings-and-pins paradigm are analyzed. Features and limitations of constructive and depictive geometry as well as implications for computational approaches are discussed. The strings-and-pins domain is shown to be more general and less restrictive than the compass-and-straightedge domain.     

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.     

Selecting a reference frame

Reference frames are representations that parse space. In the case of spatial terms, reference frames mediate the mapping of linguistic expressions onto spatial configurations of objects. In the sentence ``The fly is above the cat,' ``above' is defined with respect to a reference frame that is imposed on the cat. Different types of reference frames can be used to define spatial terms, each based on a different source of information. For example, gravity, the orientation of objects in the scene or the orientation of the viewer can all be used to set the orientation of a reference frame. When these reference frames disagree (because the viewer is reclining or because the objects in the scene are overturned), there are competing definitions for the spatial term, resulting in the need for reference frame selection. The purpose of this paper is to review a line of research that examines reference frame selection in the context of spatial language. This work shows that all reference frames are initially active and assign a direction to a spatial term. Moreover, this activation is automatic, and is followed by the selection of a single reference frame, with selection accompanied by inhibition of the non-selected frames. Parallels between reference frame selection in language and in perception and attention are discussed.