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.     

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 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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Spatial Influence of Environmental Axes in a Baseball Field

Abstract

We investigated the influence of environmental axes in a baseball field. In Experiment 1, participants walked either a path in the prototypical orientation (home plate to second base) or one which was rotated 225°. Recall for object locations was best when participants imagined themselves aligned with axes salient from the experienced orientation. In Experiment 2, when learning was through a route text, there was less of an influence of environmental axes. In Experiment 3, when participants walked both paths, memories were good for the atypical orientation, suggesting that task-specific spatial cues can be more influential than a prior conceptual north.     

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.     

Combining Locations from Working Memory and Long-Term Memory into a Common Spatial Image

Abstract

This research uses a novel integration paradigm to investigate whether target locations read in from long-term memory (LTM) differ from perceptually encoded inputs in spatial working-memory (SWM) with respect to systematic spatial error and/or noise, and whether SWM can simultaneously encompass both of these sources. Our results provide evidence for a composite representation of space in SWM derived from both perception and LTM, albeit with a loss in spatial precision of locations retrieved from LTM. More generally, the data support the concept of a spatial image in working memory and extend its potential sources to representations retrieved from LTM.     

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.     

Tractable Fragments of Fuzzy Qualitative Algebra

Abstract

In this paper we study the computational complexity of Fuzzy Qualitative Temporal Algebra (QA ^fuz ), a framework that combines qualitative temporal constraints between points and intervals, and allows modelling vagueness and uncertainty. Its tractable fragments can be identified by generalizing the results obtained for crisp Constraint Satisfaction Problems (CSPs) to fuzzy CSPs (FCSPs); to do this, we apply a general methodology based on the notion of α-cut. In particular, the results concerning the tractability of Qualitative Algebra QA, obtained in a recent study by different authors, can be extended to identify the tractable algebras of the fuzzy Qualitative Algebra QA ^fuz in such a way that the obtained set is maximal, namely any maximal tractable fuzzy algebra belongs to this set.