Computability in Europe 2008
Logic and Theory of Algorithms

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Invited Plenary Talk:
Domain theory and the causal structure of space-time

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Speaker: Prakash Panangaden
Author(s): Keye Martin and Prakash Panangaden


Domain theory was developed by Dana Scott, Gordon Plotkin, Mike Smyth and others
as a tool for understanding recursive programs and reflexive types in
computation.  Mathematically it is a theory of topological order structures: the
order captures the notion of approximation while the topology captures the
notion of limit.  There is an intimate tie-up between the order and the topology
which was explored by Scott, Lawson, Keimel and many others.  This continues to
be an active area of research especially in the context of probabilistic

In general relativity the causal structure of space time is also modelled by a
partial order.  Surprisingly, the mathematics of domain theory fits in a very
pleasing manner with the theory of causal structure.  Keye Martin and I were
able to show how to reconstruct the topology of space-time from the causal order
alone. Furthermore, we were able to show the existence of natural domain
theoretic structures leading to a notion of "approximate points" in
space-time.  In this talk I will give an overview of these results.

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