Positions, Regions, and Clusters: Strata of Granularity in Location Modelling

Abstract. Location models are data structures or knowledge bases used in Ubiquitous Computing for representing and reasoning about spatial relationships between so-called smart objects, i.e. everyday objects, such as cups or buildings, containing computational devices with sensors and wireless communication. The location of an object is in a location model either represented by a region, by a coordinate position, or by a cluster of regions or positions. Qualitative reasoning in location models could advance intelligence of devices, but is impeded by incompatibilities between the representation formats: topological reasoning applies to regions; directional reasoning, to positions; and reasoning about set-membership, to clusters. We present a mathematical structure based on scale spaces giving an integrated semantics to all three types of relations and representations. The structure reflects concepts of granularity and uncertainty relevant for location modelling, and gives semantics to applications of RCC-reasoning and projection-based directional reasoning in location models

A model for ternary projective relations between regions

peer reviewe

Formalizing Context for Domain Ontologies in Coq

International audienceWhile context is crucial for reasoning about ontologies as well as for conceptual modeling, its formal definition is often imprecise and its implementation in standard classical logic-based theories suffers from a lack of expressiveness and leads to ambiguities. In this chapter, it is shown that a two-layered language using the Calculus of Inductive Constructions (i.e., the Coq language) as a lower layer, and an ontological upper layer for giving types their meaning is able to support a clear and expressive semantics for context specification