Geometric structures of frames of reference and natural language semantics

This article aims at formal specifications of reference systems in spatial cognition. It concentrates on two roles of reference systems connected to spatial language: reference systems resolving ambiguities and reference systems forming a basis for the classification of linguistic terms. Although coordinate systems are often seen as candidates for the geometric structure of reference systems, it is shown here that they do not appear in the explanations that go into the details. An analysis of the German terms vor, hinter, rechts and links (in front of, in back of, right, left) presents an alternative model for the geometric structure of spatial reference systems.     

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).     

Mereological inheritance

In recent investigations of Spatial Reasoning, SpatialKnowledge Representation, and Geographic Information Systems, asignificant effort has been spent by many scholars of the areaabout the problem of representing properties of spatial objects bymeans of logical theories.An analogous effort has been the problem of analyzingthe qualitative relations which can be established between twospace regions. These investigations have led to a generalframework of the field known by the term ``mereo-topology'.Though both the above mentioned approaches have proved to besuccessful in the investigation of formal and practically relevantaspects of spatial objects, no attempt has been carried out in the direction of integrating the approaches and looking at the relationshipbetween a general logical theory of space and mereo-topology from an analytical point of view, in particular for exploiting thecombinatorial behaviour of such an integrated model.This paper intends to fill the gap and analyze the behaviour ofspatial formulae of a logical theory of space as objects which canbe classified based on the behaviour they exhibit with respect tothe parts and supertparts of the regions where they are true. Wename these categories of behaviourinheritance modalities.     

Relation algebras over containers and surfaces: An ontological study of a room space

Recent research in geographic information systems hasbeen concerned with the construction of algebras tomake inferences about spatial relations by embeddingspatial relations within a space in which decisionsabout compositions are derived geometrically. Wepursue an alternative approach by studying spatialrelations and their inferences in a concrete spatialscenario, a room space that contains such manipulableobjects as a box, a ball, a table, a sheet of paper,and a pen. We derive from the observed spatialproperties an algebra related to the fundamentalspatial concepts of containers and surfaces and showthat this container-surface algebra holds allproperties of Tarski's relation algebra, except forthe associativity. The crispness of the compositionscan be refined by considering the relative size of theobjects) and their roles (i.e., whether it isexplicitly known that the objects are containers orsurfaces).     

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.     

Topologically Characterized Movement Patterns: A Cognitive Assessment

Abstract

In this paper, we discuss the role of topology as a predictor for the conceptualization of dynamically changing spatial configurations (referred to as movement patterns). We define meaningful units of movement patterns as paths through a topologically defined conceptual neighborhood graph. Topology plays a central role in formal approaches to human cognition and in predicting cognitive similarity ratings—although primarily for static spatial configurations. Formal specifications of the role of topology for characterizing movement patterns do exist, yet there is paucity of behavioral validation. To bridge this gap, we conducted an experiment based on the grouping paradigm to assess factors that underlie conceptualizations of movement patterns. The experiment was designed such that paths through the conceptual neighborhood graph were distinguished by topologically differentiated ending relations. We believe topology can make an important contribution in explaining movement conceptualizations. One recently formulated topology-based contribution is the endpoint hypothesis, asserting that a cognitive focus is placed on event ending relations. We discuss the results of our experiment in relation to previous experiments targeted toward a framework for modeling the cognitive conceptualization of dynamically changing spatial relations.     

A uniform anthropomorphological approach to the human conception of dimensional relations

Within psycholinguistics, the dimensional conception of space is described through a variety of theoretical constructs, e.g., frames of reference, perspectives, strategies, and patterns. The objective of this paper is to introduce a uniform classification of the alternatives of dimensionally conceiving of object relations, derived from the functional and morphological asymmetries of the human body which define an anthropomorphous Origo, and from our ability to mentally project the Origo into positions and orientations other than we actually occupy. Particularly, the conception of dimensional relations on the first horizontal line is explained through the principle of perceptual accessibility of objects; this allows for the uniform treatment of (almost) all conceptual alternatives from basic psychological principles. Finally, some implications of this anthropomorphological view for the human cognition of dimensional relations are discussed and underpinned with empirical results.     

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.     

Three dimensional spatial memory and learning in real and virtual environments

Human orientation and spatial cognition partlydepends on our ability to remember sets ofvisual landmarks and imagine their relationshipto us from a different viewpoint. We normallymake large body rotations only about a singleaxis which is aligned with gravity. However,astronauts who try to recognize environmentsrotated in 3 dimensions report that theirterrestrial ability to imagine the relativeorientation of remembered landmarks does noteasily generalize. The ability of humansubjects to learn to mentally rotate a simplearray of six objects around them was studied in1-G laboratory experiments. Subjects weretested in a cubic chamber (n = 73) and aequivalent virtual environment (n = 24),analogous to the interior of a space stationnode module. A picture of an object waspresented at the center of each wall. Subjectshad to memorize the spatial relationships amongthe six objects and learn to predict thedirection to a specific object if their bodywere in a specified 3D orientation. Percentcorrect learning curves and response times weremeasured. Most subjects achieved high accuracyfrom a given viewpoint within 20 trials,regardless of roll orientation, and learned asecond view direction with equal or greaterease. Performance of the subject group thatused a head mounted display/head tracker wasqualitatively similar to that of the secondgroup tested in a physical node simulator. Body position with respect to gravity had asignificant but minor effect on performance ofeach group, suggesting that results may alsoapply to weightless situations. A correlationwas found between task performance measures andconventional paper-and-pencil tests of fieldindependence and 2&3 dimensional figurerotation ability.     

Environmental reference systems for large-scale spaces

Human navigation in well-known environments is guided by stored memory representations of spatial information. In three experiments (N = 43) we investigated the role of different spatial reference systems when accessing information about familiar objects at different locations in the city in which the participants lived. Our results indicate that two independent reference systems underly the retrieval of spatial knowledge. Environmental characteristics, e.g., the streets at an intersection, determine which headings are easier to imagine at a given location and lead to differences in accessibility of spatial information (orientation-specific behavior). In addition, access to spatial information depends on the relative direction of a location with respect to the imagined heading, such that information about locations imagined in front of oneself is easier to access than about locations towards the back. This influence of an egocentric reference system was found for environmental knowledge as well as map-based knowledge. In light of these reference system effects, position-dependent models of spatial memory for large-scale environments are discussed. To account for the simultaneous effect of an environmental and an egocentric reference system, we present a 2-level model of spatial memory access.     

Learning Spatial Localization: From Rat Studies to Computational Models of the Hippocampus

In his landmark article, Richard Morris (1981) introduced a set of rat experiments intended “to demonstrate that rats can rapidly learn to locate an object that they can never see, hear, or smell provided it remains in a fixed spatial location relative to distal room cues” (p. 239). These experimental studies have greatly impacted our understanding of rat spatial cognition. In this article, we address a spatial cognition model primarily based on hippocampus place cell computation where we extend the prior Barrera–Weitzenfeld model (2008) intended to allow navigation in mazes containing corridors. The current work extends beyond the limitations of corridors to enable navigation in open arenas where a rat may move in any direction at any time. The extended work reproduces Morris's rat experiments through virtual rats that search for a hidden platform using visual cues in a circular open maze analogous to the Morris water maze experiments. We show results with virtual rats comparing them to Morris's original studies with rats.     

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.     

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.     

SNAP and SPAN: Towards Dynamic Spatial Ontology

This paper presents the results from an experimental framework developed to extract topological and geometrical indicators for geographic concepts. The overall purpose is to demonstrate the usefulness of conceptual cognitive schemas for defining relationships and ontological distinctions between vague geographic concepts. In doing so, the problems in formal specifications arising due to semantic overlaps and ambiguity in geographic concepts, especially ones that have cognitive anchoring, is resolved. The results from the experiment described in this paper have significant implications for the way formal models of place can be developed that encapsulate representational configuration informed by commonsense knowledge.     

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.     

Path visualization: a method for objective measurement of spatial visualization

ABSTRACT

The ability to mentally represent spatial information is a fundamental cognitive process. To many people, this process feels a bit like visual perception, hence the term ‘spatial visualization’. In this paper, we describe a method for measuring the accuracy of spatial visualization, specifically visualization of a complex path in imaginary space. A critical feature of this method (called Path Visualization) is that it relies on the detection of intersections in a visualized path. Intersection detection is an inherently spatial task that requires a spatial representation. In this paper, we show how the Path Visualization method works, and how it can be customized to address several key research issues in human spatial cognition.     

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.