# Spatio-Temporal Domains: An Overview

• David Janin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11187)

## Abstract

We consider the possibility of defining a general mathematical framework for the homogeneous modeling and analysis of heterogeneous spatio-temporal computations as they occur more and more in modern computerized systems of systems. It appears that certain fibrations of posets into posets, called here spatio-temporal domains, eventually provide a fully featured category that extends to space and time the category of cpos and continuous functions, aka Scott Domains, used in classical denotational semantics.

## Notes

### Acknowledgment

The author wishes to express his deep gratitude to Gordon Plotkin and Phil Scott for their early advice to look at the notion of presheaves, to Marek Zawadowski for his help in understanding Grothendieck topologies and sheaves, to referees for their numerous suggestions of improvement, and to Simon Archipoff, Michail Raskin and Bernard Serpette for many fruitful discussions on various aspects of this work.

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## Authors and Affiliations

1. 1.LaBRI, Bordeaux INP, Université de BordeauxTalence CedexFrance