Spatio-Temporal Continuity

We want to formalize the intuitive notion of spatio-temporal continuity for a qualitative theory of motion. Describing how the relationships between regions change with time is necessary for modelling real-world processes. We have generated a continuity network that demonstrates the allowed transitions between spatial relationships for the basic eight relation of RCC logic. This is shown in the figure on the left. Similar networks for extended forms of RCC have also been developed. The image on the right is actually a 3-dimensional depiction of a continuity network for an extended 15 relation form of RCC.

Intuitive spatio-temporal continuity is temporal continuity without spatial leaps. However, such a notion of continuity allows temporal pinching i.e., a history is allowed to disappear and re-appear instantaneously and weird transitions are possible. To avoid temporal pinching, we have introduced a notion of firm-connectedness and define firm continuity. We have investigate the different notions of spatio-temporal continuity and transitions possible under distinct notions and provide a hierarchy of conceptual neighbourhood diagrams.

We characterize transitions in pure mereotopology over space-time regions. In order to identify an instantaneous relation occurring during a transition between histories we have developed a exhaustive categorization of relationships between adjacent parts of histories. Under the strongest notion of spatio-temporal continuity, we axiomatize continuous transitions for maximal firmly-connected space-time histories. We are working on how to use the formulation to recover the RCC-8 conceptual neighbourhood.

Qualitative Spatio-Temporal Continuity
S. M. Hazarika and A. G. Cohn
LNCS -- Spatial Information Theory, COSIT-01, 2001.
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Qualitative Modelling

An important application of RCC has been to produce a Qualitative Spatial Simulation program (QSSIM) for modelling physical and biological systems. The components of a device and their initial spatial inter-relationships are described using RCC. Constraints on the possible behaviours of these components are expressed using a simple meta-language. QSSIM is then able to generate successive `envisionments' of the stages of the device's operation. The program has been used to simulate the operation of a force pump and the feeding habits of an amoeba. The figure is a pictorial representation of the amoeba simulation.
Spatial simulation: the phagocytosis-exocytosis cycle of an amoeba.
Key: a=amoeba; n=nucleus; f=food; e=enzyme-packet; v=vacuole; nt=nutrients; w=waste-matter

Spatio-Temporal Ontology

Taking space-time as primitive, we are working on an axiomatic theory for physical objects. We introduce and characterize by means of logical axioms the basic ontological distinctions needed to reason about physical objects. The main distinction we make is between objects and their substrates. In addition, the expressivity restrictions which follow from use of mereological and topological primitives alone are overcome by introduction of the morphological primitive of congruence .

Under a notion of strong space-time continuity, we identify distinct motion classes for a subset of physical objects: the shape invariant rigid bodies. Combined with relations from the qualitative spatial representation language RCC-8 the expressive power of the theory allows for location description amongst physical objects. Further with space-time as the ontological primitive and using distinct spatio-temporal patterns for categories of objects, self-localization (correlation of current and former impressions of the world for a mobile agent) within an integrated spatio-temporal framework is investigated. Given a record of local surveys, we are investigating how space-time history descriptions might be abduced from local surveys and spatio-temporal patterns. The qualitative mereo-topological world model so constructed would form a basis for self-localization.

The issue of inferring complete spatio-temporal information given partial spatial knowledge over a complete time interval is being investigated; the dual problem of inferring complete spatio-temporal information from complete spatial knowledge at specific times only (such as from time-lapse photography, or annual geographic surveys for instance) also deserves investigation. This would form part of our future research under spatio-temporal reasoning.