Qualitative spatial reasoning about directions in a corridor containing a single turn

An experiment was conducted to investigate the process of reasoning about directions in an egocentric space. Each participant walked through a corridor containing an angular turn ranging in size from 0° to 90°, in 15° increments. A direction was given to participants at the entrance of the corridor and they were asked to answer this direction at the end of this corridor. Considering the fact that participants had to reason the direction in the featureless corridor, two hypotheses were proposed: (i) reasoning about directions falls into qualitative reasoning by using a small number of coarse angular categories (four 90° categories or eight 45° categories: 90° categories consist of front, back, left, right; 45° categories consist of 90° categories and the four intermediates) that reference axes generate; (ii) reasoning about directions would be done by recalling the rotation angle from the traveling direction to the direction that participants tried to answer. In addition, the configuration of reference axes that participants employed was examined. Both hypotheses were supported, and the data designated that reference axes consisted of eight directions: a pair of orthogonal axes and diagonals.

Generating Relation Algebras for Qualitative Spatial Reasoning

Basic relationships between certain regions of space are formulated in natural language in everyday situations. For example, a customer specifies the outline of his future home to the architect by indicating which rooms should be close to each other. Qualitative spatial reasoning as an area of artificial intelligence tries to develop a theory of space based on similar notions. In formal ontology and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts. We shall introduce abstract relation algebras and present their structural properties as well as their connection to algebras of binary relations. This will be followed by details of the expressiveness of algebras of relations for region based models. Mereotopology has been the main basis for most region based theories of space. Since its earliest inception many theories have been proposed for mereotopology in artificial intelligence among which Region Connection Calculus is most prominent. The expressiveness of the region connection calculus in relational logic is far greater than its original eight base relations might suggest. In the thesis we formulate ways to automatically generate representable relation algebras using spatial data based on region connection calculus. The generation of new algebras is a two pronged approach involving splitting of existing relations to form new algebras and refinement of such newly generated algebras. We present an implementation of a system for automating aforementioned steps and provide an effective and convenient interface to define new spatial relations and generate representable relational algebras.

A knowledge-based system to represent spatial reasoning for fire modelling

This paper describes the architecture of the knowledge based system (KBS) component of Smartfire, a fire field modelling tool for use by members of the fire safety engineering community who are not expert in modelling techniques. The KBS captures the qualitative reasoning of an experienced modeller in the assessment of room geometries, so as to set up the important initial parameters of the problem. Fire modelling expertise is an example of geometric and spatial reasoning, which raises representational problems. The approach taken in this project is a qualitative representation of geometric room information based on Forbus’ concept of a metric diagram. This takes the form of a coarse grid, partitioning the domain in each of the three spatial dimensions. Inference over the representation is performed using a case-based reasoning (CBR) component. The CBR component stores example partitions with key set-up parameters; this paper concentrates on the key parameter of grid cell distribution.

IQ and aptitude tests : assess your verbal, numerical and spatial reasoning skills.

El libro presenta un conjunto de tests de aptitud (para medir el potencial de éxito de una persona) y tests de inteligencia normalizados, cada vez más utilizados en procesos de contratación, selección y evaluación de personal. Organizados en cuatro apartados, tests de aptitud verbal, espacial, numérica y tests de inteligencia, permiten trabajar distintas áreas (significado de palabras, gramática y comprensión, aptitud verbal avanzada, análisis lógico, cálculo mental, secuencias numéricas y problemas numéricos) para mejorar las habilidades verbales, numéricas y de razonamiento del lector.

Reasoning about shadows in a mobile robot environment

This paper describes a logic-based formalism for qualitative spatial reasoning with cast shadows (Perceptual Qualitative Relations on Shadows, or PQRS) and presents results of a mobile robot qualitative self-localisation experiment using this formalism. Shadow detection was accomplished by mapping the images from the robot’s monocular colour camera into a HSV colour space and then thresholding on the V dimension. We present results of selflocalisation using two methods for obtaining the threshold automatically: in one method the images are segmented according to their grey-scale histograms, in the other, the threshold is set according to a prediction about the robot’s location, based upon a qualitative spatial reasoning theory about shadows. This theory-driven threshold search and the qualitative self-localisation procedure are the main contributions of the present research. To the best of our knowledge this is the first work that uses qualitative spatial representations both to perform robot self-localisation and to calibrate a robot’s interpretation of its perceptual input.

A blackboard architecture for a hybrid CBR system for scientific software

This paper describes the use of a blackboard architecture for building a hybrid case based reasoning (CBR) system. The Smartfire fire field modelling package has been built using this architecture and includes a CBR component. It allows the integration into the system of qualitative spatial reasoning knowledge from domain experts. The system can be used for the automatic set-up of fire field models. This enables fire safety practitioners who are not expert in modelling techniques to use a fire modelling tool. The paper discusses the integrating powers of the architecture, which is based on a common knowledge representation comprising a metric diagram and place vocabulary and mechanisms for adaptation and conflict resolution built on the Blackboard.

Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.

A Study of Qualitative and Geometric Knowledge in Reasoning about Motion

Reasoning about motion is an important part of our commonsense knowledge, involving fluent spatial reasoning. This work studies the qualitative and geometric knowledge required to reason in a world that consists of balls moving through space constrained by collisions with surfaces, including dissipative forces and multiple moving objects. An analog geometry representation serves the program as a diagram, allowing many spatial questions to be answered by numeric calculation. It also provides the foundation for the construction and use of place vocabulary, the symbolic descriptions of space required to do qualitative reasoning about motion in the domain. The actual motion of a ball is described as a network consisting of descriptions of qualitatively distinct types of motion. Implementing the elements of these networks in a constraint language allows the same elements to be used for both analysis and simulation of motion. A qualitative description of the actual motion is also used to check the consistency of assumptions about motion. A process of qualitative simulation is used to describe the kinds of motion possible from some state. The ambiguity inherent in such a description can be reduced by assumptions about physical properties of the ball or assumptions about its motion. Each assumption directly rules out some kinds of motion, but other knowledge is required to determine the indirect consequences of making these assumptions. Some of this knowledge is domain dependent and relies heavily on spatial descriptions.

Modeling and measuring the spatial relation "along": Regions, contours and fuzzy sets

The analysis of spatial relations among objects in an image is an important vision problem that involves both shape analysis and structural pattern recognition. In this paper, we propose a new approach to characterize the spatial relation along, an important feature of spatial configurations in space that has been overlooked in the literature up to now. We propose a mathematical definition of the degree to which an object A is along an object B, based on the region between A and B and a degree of elongatedness of this region. In order to better fit the perceptual meaning of the relation, distance information is included as well. In order to cover a more wide range of potential applications, both the crisp and fuzzy cases are considered. In the crisp case, the objects are represented in terms of 2D regions or ID contours, and the definition of the alongness between them is derived from a visibility notion and from the region between the objects. However, the computational complexity of this approach leads us to the proposition of a new model to calculate the between region using the convex hull of the contours. On the fuzzy side, the region-based approach is extended. Experimental results obtained using synthetic shapes and brain structures in medical imaging corroborate the proposed model and the derived measures of alongness, thus showing that they agree with the common sense. (C) 2011 Elsevier Ltd. All rights reserved.

Preschooler’s Comprehension of Spatial Terms

This study aims to understand individual differences in preschooler’s early comprehension of spatial language. Spatial language is defined as terms describing location, direction, shape, dimension, features, orientation, and quantity (e.g location, shape). Spatial language is considered to be one of the important factors in the development of spatial reasoning in the preschool years (Pruden, Levine, & Huttenlocher, 2011). In recent years, research has shown spatial reasoning is an important predictor of successes in STEM (Science, Technology, Engineering, and Mathematics) fields (e.g. Shea, Lubinski & Benbow, 2001; Wai, Lubinksi &Benbow, 2009). The current study focuses on when children begin to comprehend spatial terms, while previous work has mainly focused on production of spatial language. Identifying when children begin to comprehend spatial terms could lead to a better understanding of how spatial reasoning develops. We use the Intermodal Preferential Looking paradigm (IPLP) to examine three-year-old children’s ability to map spatial terms to visual representations. Fourteen spatial terms were used to test these abilities (e.g. bottom, diamond, longer). For each test trial children were presented with two different stimuli simultaneously on the left and right sides of a television screen. A female voice prompted the child to find the target spatial relation (e.g. “can you find the boy pointing to the bottom of the window”; Figure 1). A Tobii X60 eye-tracker was used to record the child’s eye gaze for each trial. For each child the proportion of looking to the target image divided by their total looking during the trial was calculated; this served as the dependent variable. Proportions above .50 indicated that the child had correctly mapped the spatial term to the target image. Preliminary data shows that the number of words comprehended in the IPLP task is correlated to parental report of the child’s comprehension of spatial terms (r[14]=.500, p<.05).

Preschooler’s Comprehension of Spatial Terms

This study aims to understand individual differences in preschooler’s early comprehension of spatial language. Spatial language is defined as terms describing location, direction, shape, dimension, features, orientation, and quantity (e.g location, shape). Spatial language is considered to be one of the important factors in the development of spatial reasoning in the preschool years (Pruden, Levine, & Huttenlocher, 2011). In recent years, research has shown spatial reasoning is an important predictor of successes in STEM (Science, Technology, Engineering, and Mathematics) fields (e.g. Shea, Lubinski & Benbow, 2001; Wai, Lubinksi &Benbow, 2009). The current study focuses on when children begin to comprehend spatial terms, while previous work has mainly focused on production of spatial language. Identifying when children begin to comprehend spatial terms could lead to a better understanding of how spatial reasoning develops. We use the Intermodal Preferential Looking paradigm (IPLP) to examine three-year-old children’s ability to map spatial terms to visual representations. Fourteen spatial terms were used to test these abilities (e.g. bottom, diamond, longer). For each test trial children were presented with two different stimuli simultaneously on the left and right sides of a television screen. A female voice prompted the child to find the target spatial relation (e.g. “can you find the boy pointing to the bottom of the window”; Figure 1). A Tobii X60 eye-tracker was used to record the child’s eye gaze for each trial. For each child the proportion of looking to the target image divided by their total looking during the trial was calculated; this served as the dependent variable. Proportions above .50 indicated that the child had correctly mapped the spatial term to the target image. Preliminary data shows that the number of words comprehended in the IPLP task is correlated to parental report of the child’s comprehension of spatial terms (r[14]=.500, p<.05).

Primary students’ interpretation of maps : gesture use and mapping knowledge

Maps are used to represent three-dimensional space and are integral to a range of everyday experiences. They are increasingly used in mathematics, being prominent both in school curricula and as a form of assessing students understanding of mathematics ideas. In order to successfully interpret maps, students need to be able to understand that maps: represent space, have their own perspective and scale, and their own set of symbols and texts. Despite the fact that maps have an increased prevalence in society and school, there is evidence to suggest that students have difficulty interpreting maps. This study investigated 43 primary-aged students’ (aged 9-12 years) verbal and gestural behaviours as they engaged with and solved map tasks. Within a multiliteracies framework that focuses on spatial, visual, linguistic, and gestural elements, the study investigated how students interpret map tasks. Specifically, the study sought to understand students’ skills and approaches used to solving map tasks and the gestural behaviours they utilised as they engaged with map tasks. The investigation was undertaken using the Knowledge Discovery in Data (KDD) design. The design of this study capitalised on existing research data to carry out a more detailed analysis of students’ interpretation of map tasks. Video data from an existing data set was reorganised according to two distinct episodes—Task Solution and Task Explanation—and analysed within the multiliteracies framework. Content Analysis was used with these data and through anticipatory data reduction techniques, patterns of behaviour were identified in relation to each specific map task by looking at task solution, task correctness and gesture use. The findings of this study revealed that students had a relatively sound understanding of general mapping knowledge such as identifying landmarks, using keys, compass points and coordinates. However, their understanding of mathematical concepts pertinent to map tasks including location, direction, and movement were less developed. Successful students were able to interpret the map tasks and apply relevant mathematical understanding to navigate the spatial demands of the map tasks while the unsuccessful students were only able to interpret and understand basic map conventions. In terms of their gesture use, the more difficult the task, the more likely students were to exhibit gestural behaviours to solve the task. The most common form of gestural behaviour was deictic, that is a pointing gesture. Deictic gestures not only aided the students capacity to explain how they solved the map tasks but they were also a tool which assisted them to navigate and monitor their spatial movements when solving the tasks. There were a number of implications for theory, learning and teaching, and test and curriculum design arising from the study. From a theoretical perspective, the findings of the study suggest that gesturing is an important element of multimodal engagement in mapping tasks. In terms of teaching and learning, implications include the need for students to utilise gesturing techniques when first faced with new or novel map tasks. As students become more proficient in solving such tasks, they should be encouraged to move beyond a reliance on such gesture use in order to progress to more sophisticated understandings of map tasks. Additionally, teachers need to provide students with opportunities to interpret and attend to multiple modes of information when interpreting map tasks.

Co-thought gestures : supporting students to successfully navigate map tasks

This study considers the role and nature of co-thought gestures when students process map-based mathematics tasks. These gestures are typically spontaneously produced silent gestures which do not accompany speech and are represented by small movements of the hands or arms often directed toward an artefact. The study analysed 43 students (aged 10–12 years) over a 3-year period as they solved map tasks that required spatial reasoning. The map tasks were representative of those typically found in mathematics classrooms for this age group and required route finding and coordinate knowledge. The results indicated that co-thought gestures were used to navigate the problem space and monitor movements within the spatial challenges of the respective map tasks. Gesturing was most influential when students encountered unfamiliar tasks or when they found the tasks spatially demanding. From a teaching and learning perspective, explicit co-thought gesturing highlights cognitive challenges students are experiencing since students tended to not use gesturing in tasks where the spatial demands were low.