Function,geometry and spatial prepositions: Three experiments

In this paper the results of three experiments are reported whichaddress the issue of the relative extent to which functionalrelations versus geometric relations affect spatial language. Theexperiments examine the role of a discourse context on the useand rating of the preposition in to describe a visual scenewhere the constraint of spatial containment between figure(object located) and ground (reference object) does not hold. Allthree experiments demonstrate that in is used more andrated to be significantly more appropriate in a functionalcontext than in a no context condition. The implications of thesestudies for spatial language and spatial representation arediscussed.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Heading south with a north-up map: A choice processing analysis of map alignment effects

This study employed an information accumulation model of choice reaction times to investigate alignment effects in mental representations of maps. University students studied a map from a single orientation (with north at the top). In a subsequent two-choice reaction time task, the students’ spatial knowledge of the map was assessed employing spatial left/right judgments, which were made from imagined perspectives that were either north-aligned or south-aligned. Data showed a standard alignment effect, favoring north- over south-aligned trials. To examine the locus of this effect, data were fit using the Linear Ballistic Accumulator (LBA) model of speeded decisions (Brown & Heathcote, 2008). Of interest were three model parameters: drift rate, the speed at which evidence accumulates toward a response; response threshold, the amount of evidence demanded from the decision maker before selecting a response; and non-decision time, the time consumed by pre- and postdecisional processes. The best-fitting model suggested that non-decision time accounted for the alignment effect. The difference in non-decision time between north and south-aligned judgments suggests a mental alignment stage on south-aligned trials, accounting for the longer reaction times for judgements misaligned with the presented north orientation of the map.     

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.     

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.     

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.     

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.     

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.