Algebraic Properties of Qualitative Spatio-Temporal Calculi

Qualitative spatial and temporal reasoning is based on so-called qualitative calculi. Algebraic properties of these calculi have several implications on reasoning algorithms. But what exactly is a qualitative calculus? And to which extent do the qualitative calculi proposed meet these demands? The literature provides various answers to the first question but only few facts about the second. In this paper we identify the minimal requirements to binary spatio-temporal calculi and we discuss the relevance of the according axioms for representation and reasoning. We also analyze existing qualitative calculi and provide a classification involving different notions of a relation algebra.Comment: COSIT 2013 paper including supplementary materia

Qualitative Reasoning with Story-Based Motion Representations: Inverse and Composition

International audienceRepresentations of motion that are story-based constitute a promising tool to categorise the motion of entities, because they can be generated using any qualitative spatial representation, and they consider explicitly the speed of the entities. Up to the present, mainly categorisation properties of the story-based representations have been presented. In this paper we show how story-based representations allow for the reasoning operations that the qualitative calculi possess, namely, inverse and composition—We provide a method to compute the inverse, and a method that notably simplifies the computation of the composition

The Point-Descriptor-Precedence representation for point configurations and movements

In this paper, we represent (moving) point configurations along a curved directed line qualitatively by means of a system of relational symbols based on two distance descriptors: one representing distance along the curved directed line and the other representing signed orthogonal distance to the curved directed line. The curved directed line represents the direction of the movement of interest. For instance, it could be straight as in the case of driving along a highway or could be curved as in the case of an intersection or a roundabout. Inspired by the Point Calculus, the order between the points on the curved directed line is described by means of a small set of binary relations () acting upon the distance descriptors. We call this representation the Point-Descriptor-Precedence-Static (PDPS) representation at a time point and Point-Descriptor-Precedence-Dynamic (PDPD) representation during a time interval. To illustrate how the proposed approach can be used to represent and analyse curved movements, some basic micro-analysis traffic examples are studied. Finally, we discuss some extensions of our work to highlight the practical benefits of PDP in identifying motion patterns that could be useful in GIS, autonomous vehicles, sports analytics, and gait analysis

Smart Sensorization Using Propositional Dynamic Logic

The current high energy prices pose a serious challenge, especially in the domestic economy. In this respect, one of the main problems is obtaining domestic hot water. For this reason, this article develops a heating system applied to a conventional water tank in such a way as to minimize the necessary energy supply by converting it, under certain circumstances, into atmospheric. For this purpose, the domotic system has been equipped with sensors that automate the pressurization of the compartment and solenoid valves that regulate the external water supply. This design, to which different level sensors are applied, sends the information in real time to an artificial intelligence system, by means of deductive control, which recognizes the states of the system. This work shows the introduction of an extension of propositional dynamic logic in the field of energy efficiency. Thanks to this formalism, a qualitative control of the program variables is achieved by incorporating qualitative reasoning tools. On the other hand, it solves preventive maintenance systems through the early detection of faults in the installation. This research has led to the patenting of an intelligent domestic hot water system that considerably reduces energy consumption by setting disjointed heating intervals that, powered by renewable or non-renewable sources, are controlled by a propositional dynamic logic.This research received no external funding. Partial funding for open access charge: Universidad de Málaga

Areas of Same Cardinal Direction

Cardinal directions, such as North, East, South, and West, are the foundation for qualitative spatial reasoning, a common field of GIS, Artificial Intelligence, and cognitive science. Such cardinal directions capture the relative spatial direction relation between a reference object and a target object, therefore, they are important search criteria in spatial databases. The projection-based model for such direction relations has been well investigated for point-like objects, yielding a relation algebra with strong inference power. The Direction Relation Matrix defines the simple region-to-region direction relations by approximating the reference object to a minimum bounding rectangle. Models that capture the direction between extended objects fall short when the two objects are close to each other. For instance, the forty-eight contiguous states of the US are colloquially considered to be South of Canada, yet they include regions that are to the North of some parts of Canada. This research considers the cardinal direction as a field that is distributed through space and may take on varying values depending on the location within a reference object. Therefore, the fundamental unit of space, the point, is used as a reference to form a point-based cardinal direction model. The model applies to capture the direction relation between point-to-region and region-to-region configurations. As such, the reference object is portioned into areas of same cardinal direction with respect to the target object. This thesis demonstrates there is a set of 106 cardinal point-to-region relations, which can be normalized by considering mirroring and 90° rotations, to a subset of 22 relations. The differentiating factor of the model is that a set of base relations defines the direction relation anywhere in the field, and the conceptual neighborhood graph of the base relations offers the opportunity to exploit the strong inference of point-based direction reasoning for simple regions of arbitrary shape. Considers the tiles and pockets of same cardinal direction, while a coarse model provides a union of all possible qualitative direction values between a reference region and a target region