Modelling spatio-temporal relationships in object-oriented applications ISABEL BESEMBEL-CARRERA Data and Knowledge Engineering Research Group (GIDyC). Department of Computer Science. School of System Engineering. University of Los Andes. Mérida-5101. Venezuela. Email: ibc@ing.ula.ve JONÁS MONTILVA-CALDERÓN Data and Knowledge Engineering Research Group (GIDyC). Department of Computer Science. School of System Engineering. University of Los Andes. Mérida-5101. Venezuela. Email: jonas@ing.ula.ve ABSTRACT The D/K data model is an integrated object-oriented data and knowledge model. In particular, D/K data model uses the vector representation to model spatial objects and relationships, defining a spatial graph. We extend D/K data model to support temporal objects and relationships by including new classes named TemporalObject, TemporalRepresentation, and TemporalGraph. The temporal model is based on the mixed model, which consider a linear, totally ordered and discrete time line, where intervals are its primitives. We define a spatio-temporal object as an object that has at least one spatial and one temporal property. These properties are represented by spatial and temporal data, respectively. It can be represented by a four-tuple (objId, geom, t, att) where objId is the object identifier, geom is the geometry that indicates the spatial location and shape of that object, t is the description of the temporal characteristics of that object, and att is a set of other attributes that describes the object. We consider three groups of relationships, namely: spatio-temporal, spatial, and temporal. In the spatio-temporal, we only consider the topological relationships among d-dimensional rectangles, called here hyper-rectangles, where spatial and temporal dimensions are treated homogeneously. An object instance of the spatio-temporal object (STObject) inherits spatial and temporal representation, but internally is stored in a uniform manner by appliying transformation functions to it. Thus, a STObject has a unique representation, which unifies its representation. A spatio-temporal graph is a graph composed of nodes which are spatio-temporal objects and arcs (edges) that are spatio-temporal relationships other than topological ones. KEYWORDS: Spatio-temporal object-oriented models, spatio-temporal and knowledge bases, spatio-temporal object-oriented techniques. 1. INTRODUCTION In this paper we propose an extension to an integrated data and knowledge model, called D/K model, which is an object-oriented data model that provides knowledge representation capabilities [1]. In many engineering applications, the representation of the spatial and temporal properties and relationships of domain entities is an important aspect of the process of data modelling and knowledge representation. In transportation systems, for instance, route planning can be modeled by using a directed graph whose nodes represent domain entities (e.g. airports, underground stations and road intersections) and whose edges capture the connections between the nodes. On the other hand, moving from one node to another demands some form of temporal representation, such as timetables. The spatial extension of the D/K model uses the vector representation to model spatial objects and relationships. A set of classes, including SpatialObject, SpatialRepresentation and SpatialGraph, are provided. Similarly, temporal objects and relationships are supported by including a set of classes such as TemporalObject, TemporalRepresentation, and TemporalGraph. The temporal extension is based on the mixed model [2, 3], which considers a linear, totally ordered and discrete time line, where intervals are its primitives. It also permits both time points and intervals by considering time points as zero length intervals. The rest of this paper is organized as follows: Section 2 is devoted to define spatio-temporal objects, section 3 presents the main spatio-temporal relationships considered by us in this work, the extension of the D/K model is presented in section 4 to support spatio-temporal objects, relationships, and graphs; section 5 illustrated how can be implemented the mentioned classes by following the UML notation [4]. Finally, we include some concluding remarks in section 6. 2. SPATIO-TEMPORAL OBJECTS A spatio-temporal object is defined as an object that has at least one spatial and one temporal property [5]. An object instance of the spatio-temporal object class (STObject)