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.     

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.     

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.     

Context Affects Scale Selection for Proximity Terms

Abstract

Spatial proximity terms, such as near and far, communicate information regarding the distance in which a “located” object can be found with respect to a “reference” object. The present paper investigates whether people take into account the location of an object extraneous to the located object and reference object pair, when setting the scale for proximity language judgements. Across three experiments participants rated the appropriateness of near and far to describe spatial scenes that included a third (distractor) object positioned the same distance as the located object from the reference object, but at varying distances from the located object. The results show that the presence of other spatial relations affects scale setting, resulting in differences in appropriateness ratings for those spatial terms.     

Interface Familiarity Restores Active Advantage in a Virtual Exploration and Reconstruction Task in Children

Abstract

Active exploration is reportedly better than passive observation of spatial displacements in real environments, for the acquisition of relational spatial information, especially by children. However, a previous study using a virtual environment (VE) showed that children in a passive observation condition performed better than actives when asked to reconstruct in reality the environment explored virtually. Active children were unpractised in using the input device, which may have detracted from any active advantage, since input device operation may be regarded as a concurrent task, increasing cognitive load and spatial working memory demands. To examine this possibility, 7–8-year-old children in the present study were given 5 minutes of training with the joystick input device. When compared with passive participants for spatial learning, active participants gave a better performance than passives, placing objects significantly more accurately. The importance of interface training when using VEs for assessment and training was discussed.     

Spatial Reorientation: Effects of Verbal and Spatial Shadowing

ABSTRACT

Spatially disoriented adults flexibly conjoin geometric information (macroscopic shape) and nongeometric information (e.g., the color of a wall) to re-establish their bearings. It has been proposed that non-geometric information is incorporated into a geometric frame of reference through the use of spatial language. Support for this assumption comes from dual-task studies in which participants failed to use non-geometric features when they shadowed a verbal message concurrent to the reorientation task. These studies were performed in small rectangular spaces. In contrast, our study was performed in a large square room. Experiment 1 showed that verbal shadowing did not disrupt non-geometric feature use in this environment. In Experiment 2, we found that a spatial shadowing task that required the encoding of frequently changing spatial directions impaired reorientation behavior. Our study shows that nongeometric information can be used for reorientation without recourse to linguistic processes, and suggests that the use of non-geometric features is dependent upon a spatial coding process.     

Mining Spatial Associations with Limited Sensory Information

Abstract

Human navigation in an unknown environment requires an understanding of the spatial relationships of the terrain. For example, a soldier who is on a reconnaissance mission in a new city needs to “know” the spatial layout of the surroundings with high confidence. Oftentimes, this understanding must be acquired within a very short amount of time and with limited sensory inputs. The soldier would benefit from a digital avatar that draws inferences about the spatial layout of the city based on an initial set of observations and guides the soldier either in further exploring the environment or in making decisions based on these inferences. In this paper, we present and evaluate an inductive approach to learning spatial associations using sensory data that is available from the simulation environment of a computer game, Unreal Tournament. We study two kinds of spatial relationships between nodes on a level of a game map: nodes that are placed near each other to satisfy some spatial requirement and nodes that are placed near each other to satisfy the design preferences of a level architect. We show that we can infer both kinds of relationships using an association rule mining algorithm. Furthermore, we show how to use an ontology to distinguish between these relationships in order to discover different types of spatial arrangements on a specific map. We discuss how the inferred associations can be used to control an avatar that makes recommendations for navigating unexplored areas on a map. We conclude with some thoughts on the applicability of our methods to scenarios in the real world, beyond the simulation environment of a game, and on how the learned associations can be represented and queried by a simple question-answer type system.     

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.     

空间目标碰撞概率的等效矩形域快速算法

针对线性相对运动假设下的碰撞概率计算问题，提出了等效矩形域方法。利用该方法将概率积分计算进行近似处理，推导出概率密度积分的解析表达式。针对空间目标误差椭球形状固定的情况，给出了最大碰撞概率的计算方法。对目标在交会时刻相距较远和接近碰撞的情况进行了碰撞概率以及最大碰撞概率计算。通过将计算结果与空间压缩无穷级数法的对比，验证了等效矩形域方法近似计算碰撞概率积分的可靠性，同时对于不同的碰撞概率计算情况，等效矩形域方法显示出更高精确度和更好的估计偏差稳定性。     

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.     

Spatio-Temporal Ontologies and Attention

ABSTRACT

This paper presents a new proposal for the design of spatio-temporal ontologies which has its origin in cognitively motivated spatial semantics. It is shown that selective attention not only plays a central role in the characterization of spatial relations but that the representation of attentional aspects also leads to the possibility of defining an ontological upper structure which systematically covers both the spatial and the temporal domain.     

Verb Semantics Affects the Interpretation of Spatial Prepositions

Abstract

Spatial prepositions, more specifically projective prepositions, such as in front of or behind can be interpreted in different ways. Their interpretation depends on the spatial perspective taken as the basis for determining the reference frame's orientation. In 3 series of placement experiments with German speakers, we examined whether the interpretation of projective prepositions in a motion context is affected by the verb used in a spatial instruction. Results suggest that verb semantics is a factor accounting for previously observed seemingly social-situational differences in the interpretation of projective prepositions. Specifically, the findings indicate that, relative to a car as reference object, the semantic aspect of motion interruption associated with some verbs leads to a higher proportion of deictic interpretations determined by the direction from which one is approaching the car. This verb effect on the interpretation of spatial prepositions can be explained by an activation of the temporal dimension through stop-implying verbs, which is integrated into the spatial situation model of the perceived dynamic scene making the deictic frame of reference more compatible. The experimental evidence also shows that verb semantics can account for previously unexplained cross-linguistic differences, and is related to patterns concerning the prepositional inventory of languages.     

An Investigation into Vertical Bias Effects

ABSTRACT

In three experiments, after exploring a virtual environment (VE), adult participants made spatial judgments about the location of target objects that were higher and lower than their perceived test location within the VE. In Experiment 1, the locations of the target objects were inferred from verbal instructions. The main results were a tendency to judge objects as closer to the horizontal plane than their true locations, and more efficient downward than upward judgments. Both effects generally accord with findings reported by Wilson et al. (2004a Wilson, P. N., Foreman, N., Stanton, D. and Duffy, H. 2004a. Memory for targets in a multilevel simulated environment: Evidence for vertical asymmetry in spatial memory. Memory & Cognition, 32: 283–297. [Crossref] , [Google Scholar], 2004b Wilson, P. N., Foreman, N., Stanton, D. and Duffy, H. 2004b. Memory for targets in a multi-level simulated-environment: A comparison between able-bodied and physically disabled children. British Journal of Psychology, 95: 325–338.  [Google Scholar]). In Experiments 2 and 3, which were closely modeled on the design of the Wilson et al. studies, regression to the horizontal plane was noted but no downward bias was observed. A misperception in the viewing height between the floors and ceilings of the virtual rooms was apparent in both experiments. The results from the present study together with earlier investigations suggest different hierarchical encoding of between-axis and within-axis information.     

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.     

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.     

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.     

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.