Conceptual Neighbourhood Diagrams for Representing Moving Objects

Continuously moving objects are prevalent in many domains. Although there have been attempts to combine both spatial and temporal relationships from a reasoning, a database, as well as from a logical perspective, the question remains how to describe motion adequately within a qualitative calculus. In this paper, a Qualitative Trajectory Calculus (QTC) for representing and reasoning about moving objects in two dimensions is presented. Specific attention is given to a central concept in qualitative reasoning, namely the composition of relations. The so-called composition-rule table is presented, which is a neat way of representing a composition table. The usefulness of QTC and the composition-rule table is illustrated by an example.

Representing moving objects in computer-based expert systems: the overtake event example

Knowledge of spatial movement patterns in soccer occurring on a regular basis can give a soccer coach, analyst or reporter insights in the playing style or tactics of a group of players or team. Furthermore, it can support a coach to better prepare for a soccer match by analysing (trained) movement patterns of both his own as well as opponent players. We explore the use of the Qualitative Trajectory Calculus (QTC), a spatiotemporal qualitative calculus describing the relative movement between objects, for spatial movement pattern recognition of players movements in soccer. The proposed method allows for the recognition of spatial movement patterns that occur on different parts of the field and/or at different spatial scales. Furthermore, the Levenshtein distance metric supports the recognition of similar movements that occur at different speeds and enables the comparison of movements that have different temporal lengths. We first present the basics of the calculus, and subsequently illustrate its applicability with a real soccer case. To that end, we present a situation where a user chooses the movements of two players during 20 seconds of a real soccer match of a 2016–2017 professional soccer competition as a reference fragment. Following a pattern matching procedure, we describe all other fragments with QTC and calculate their distance with the QTC representation of the reference fragment. The top-k most similar fragments of the same match are presented and validated by means of a duo-trio test. The analyses show the potential of QTC for spatial movement pattern recognition in soccer.

The analysis and understanding of human-robot joint spatial behaviour (JSB) - such as guiding, approaching, departing, or coordinating movements in narrow spaces - and its communicative and dynamic aspects are key requirements on the road towards more intuitive interaction, safe encounter, and appealing living with mobile robots. This endeavours demand for appropriate models and methodologies to represent JSB and facilitate its analysis. In this paper, we adopt a qualitative trajectory calculus (QTC) as a formal foundation for the analysis and representation of such spatial behaviour of a human and a robot based on a compact encoding of the relative trajectories of two interacting agents in a sequential model. We present this QTC together with a distance measure and a probabilistic behaviour model and outline its usage in an actual JSB study. We argue that the proposed QTC coding scheme and derived methodologies for analysis and modelling are flexible and extensible to be adapted for a variety of other scenarios and studies.

In recent years several qualitative reasoning approaches have been developed in the spatial domain. Although means exists to cope with orientation, position, and topological relations, few of them use the concept of distance. In this paper a new approach is presented that allows to use and to combine knowledge about distances and positions in a qualitative way. It is based on perceptual and cognitive considerations about the capabilities of humans navigating within their environments. The basic spatial reference system, the formalism in which the distance relations are represented, and an implementation that uses multiple domain experts communicating via a black board structure will be described.

This paper describes an Artificial Intelligence (AI) technique called Qualitative Reasoning (QR) for knowledge representation and simulation of organic reaction mechanisms. Even though there are many applications of AI technique in organic chemistry, none has involved QR approach in problem solving. The primary goal of QR research is to understand human-like commonsense reasoning. A software architecture has been designed which consists of two main components, the reasoning and the explanation modules. In qualitative modeling, chemical intuition and chemical commonsense that are required to understand the behavior of reaction mechanisms are represented using the modeling constructs of a QR ontology called Qualitative Process Theory (QPT). Several model fragments have been developed that served as embedded intelligence to the system. A simulation scenario based on these models is presented together with explanation generation for a particular aspect of the system behavior.

Reasoning on the context of human beings is crucial for many real-world applications especially for those deploying autonomous systems (e.g. robots). In this paper, we present a new approach for context reasoning to further advance the field of human motion prediction. We therefore propose a neuro-symbolic approach for human motion prediction (NeuroSyM), which weights differently the interactions in the neighbourhood by leveraging an intuitive technique for spatial representation called Qualitative Trajectory Calculus (QTC). The proposed approach is experimentally tested on medium and long term time horizons using two architectures from the state of art, one of which is a baseline for human motion prediction and the other is a baseline for generic multivariate time-series prediction. Six datasets of challenging crowded scenarios, collected from both fixed and mobile cameras, were used for testing. Experimental results show that the NeuroSyM approach outperforms in most cases the baseline architectures in terms of prediction accuracy.

Plasticity is a central concept in the philosophy of Catherine Malabou and the theory of animation. And yet, the temporal dimension of transformation and mutability that Malabou foregrounds in her philosophy is missing from recent theoretical accounts of plasticity in animation studies​. ​In these accounts, plasticity appears as a mode of spatial extension, conveying the elasticity of form across a Cartesian timeline, whereas Malabou aims to understand time’s own metamorphosis and self-differentiation. This article invokes Malabou’s theorization of plasticity as the becoming of time itself rather than the becoming of things in time to rethink the perception of life-like movement in animation. Reviewing the techniques of animation that Frank Thomas and Ollie Johnston describes in The Illusion of Life as “drawing in the fourth dimension”, I argue that Malabou’s characterization of plasticity as the capacity “to see (what is) coming” ( voir venir) gets to the heart of animation as an art of subjective anticipation. Utilizing the human perceptual system’s tendency to invent new structures and relationships in response to changing inputs from the environment, animation prepares us to anticipate the unforeseeable and to perceive an order of movement typically concealed by the movement of objects in space.

Qualitative Simulation (QS) is a common reasoning technique that represents the system performance based on qualitative reasoning. Reasoning is made to determine qualitative values with changing directions of the system variables. The QS approaches can be implemented with minimal knowledge of system parameters and even when the system model is incomplete, which are common scenarios for most machine users. Bond graph modelling simulates the dynamic systems based on cause and effect reasoning with the help of energy flow. Therefore this paper plans to use bond graph modelling for the purpose of fault detection based on the energy flow without the need for the specific information of machine’s parameters. The bond graph based QS was examined on an AC induction motor (ACIM) which had confirmed the high efficiency of QS based approach in achieving diagnostic results for broken rotor bar. The QS approach uses the temporal causal graph (TCG) and qualitative equations of the system. The applied qualitative analysis predicts the effects of parameter changes (increased-decreased) on the whole system behavior. The results indicate that the proposed QS technique is an effective method for extracting diagnostic information, leading to an accurate diagnosis by combining TCG and qualitative equations with qualitative reasoning.

Hypothesis assessment with qualitative reasoning: Modelling the Fontestorbes fountain

This study aimed to reveal how the Manggarai community used mathematical concepts in making the traditional house (Mbaru Niang) roof of Manggarai people and what were the mathematical concepts contained in it. This research used a qualitative approach with ethnographic methods. The selection of subjects in this study used purposive sampling technique. Data obtained by interviewing, observing and documenting. The validity of the data is supported through theory and facts in the field and also through expert judgment. The results showed that in the stages of the process of making the traditional house roof of Manggarai there were 3 activities that had a mathematical nuance namely designing, numerating and measuring and the mathematical concepts contained in the traditional house roof were the concept of the shapes namely triangles, rectangles, trapezoid and circles, the concept of distance, the concept of parallel lines, and lines and the pyramid.

A new approach to representing qualitative spatial knowledge and to spatial reasoning is presented. This approach is motivated by cognitive considerations and is based on relative orientation information about spatial environments. The approach aims at exploiting properties of physical space which surface when the spatial knowledge is structured according to conceptual neighborhood of spatial relations. The paper introduces the notion of conceptual neighborhood and its relevance for qualitative temporal reasoning. The extension of the benefits to spatial reasoning is suggested. Several approaches to qualitative spatial reasoning are briefly reviewed. Differences between the temporal and the spatial domain are outlined. A way of transferring a qualitative temporal reasoning method to the spatial domain is proposed. The resulting neighborhood-oriented representation and reasoning approach is presented and illustrated. An example for an application of the approach is discussed.

This paper aims to understand the factors that encourage the use of mobile e-books among mathematics postgraduate students. Eight mathematics postgraduate students from a local public university in Malaysia participated in the study. The participants were from Algebra research group. This study employed qualitative case study approach. Data were collected via interview and non-participant observation. Collected data were analysed by using constant comparative analysis. This study used three theoretical frameworks as its guiding theory, namely Technology Acceptance Model, Pleasure, Arousal and Dominance Theory and Diffusion of Innovation Theory to explore the factors that influence the use of mobile e-book among the participants. Findings showed that utilitarian, cognitive, affective, social norm and content qualities were the main factors influencing the use of mobile e-books among the participants. This study also demonstrated that the participants were interested in using mobile e-book and this may assist academicians and mobile e-book designers in improving and understanding the use of mobile e-book among mathematics postgraduate students. This study could contribute in terms of expanding readers’ understanding on the factors that motivate use of mobile e-book among mathematics postgraduate students for their learning activities.

A qualitative reasoning approach is presented for decision support. This approach is initiated with the generation and normalization of a qualitative model including relationship matrix, importance weightings, control limits for decision variables, and specification limits for performance attributes. An extensive Simplex method is then utilized for mapping the global feasibility of the decision problem. Finally, the approach interprets and simplifies the results from the multi-dimensional feasibility space back to the qualitative model. The paper also presents application of the approach to process tuning of multilayer sheet extrusion and concept development of a 2nd generation reusable launch vehicle to orbit. The results indicate that the developed approach is a viable alternative to currently practiced decision analysis methods. Specifically, the approach uses: 1) tightened specification limits rather than a weighted multi-attribute objective relationship, 2) determines global system feasibility from active constraints rather than local parametric optimization, and 3) establishes correlations based on dynamic Pareto-optimal frontiers rather than manual estimations. While the approach is potentially useful, further research is required to extend the methods to non-linear, stochastic, and uncharacterized engineering systems.

Research on qualitative spatial reasoning has produced a variety of calculi for reasoning about orientation or direction relations. Such qualitative abstractions are very helpful for agent control and communication between robots and humans. Conceptual neighborhood has been introduced as a means of describing possible changes of spatial relations which e.g. allows action planning at a high level of abstraction. We discuss how the concrete neighborhood structure depends on application-specific parameters and derive corresponding neighborhood structures for the $\mathcal{OPRA}_m$ calculus. We demonstrate that conceptual neighborhoods allow resolution of conflicting information by model-based relaxation of spatial constraints. In addition, we address the problem of automatically deriving neighborhood structures and show how this can be achieved if the relations of a calculus can be modeled in another calculus for which the neighborhood structure is known.