Fully funded PhD studentship: Computational Logic of Euclidean Spaces
Institution: School of Computer Science, University of Manchester

Start date for project: September 1st, 2007 Closing date for
applications: May 31st, 2007

The School of Computer Science at the University of Manchester is
offering a fully funded PhD position as part of a 3-year research
project jointly undertaken with Birkbeck College, London and the
University of Hasselt (Belgium) on the subject of "Computational
Geometry of Euclidean Spaces". The Principal Investigators of the
Project are Dr. Ian Pratt-Hartmann (http://www.cs.man.ac.uk/~ipratt/)
and Prof. Michael Zakharyaschev (http://www.dcs.bbk.ac.uk/~michael/).

By a "spatial logic", we understand any formal language interpreted
over a class of geometrical structures (broadly construed). Thus,
spatial logic is concerned with the interface between logic and
geometry (including topology). In recent years, substantial progress
has been made in analysing of the computational and mathematical
properties of various spatial logics. However, most of this progress
has centred on logics of very abstract "spaces", having little
practical significance.  The aim of this research project is to
investigate the computational properties of practically applicable
spatial and spatio-temporal logics interpreted over 2- and
3-dimensional Euclidean spaces, and to develop and implement
algorithms for reasoning with them. The concrete objectives are as
follows:

1. Analyse the computational complexity of decidable topological
representation formalisms over well-behaved regions in the Euclidean
plane. Identify tractable fragments. Develop and implement reasoning
procedures.

2. Analyse the computational complexity of decidable metric
representation formalisms over well-behaved regions in the Euclidean
plane. Develop and implement reasoning procedures.

3. Investigate topological and metrical representation formalisms over
well-behaved regions in 3-dimensional Euclidean space and
3-dimensional spatio-temporal structures. Identify decidable
fragments.

The successful candidate will have the opportunity to contribute to
any of these objectives.  Applicants should have a 1st class or good
2.1 honours degree (or equivalent) or Master's degree in either
Mathematics (with good knowledge of computing) or Computer Science
(with a firm mathematical background). Strong candidates with other
backgrounds (e.g. in the physical sciences) who can demonstrate the
requisite background knowledge and interests will also be considered.

Studentships are open to UK/EU residents and will pay fees together
with a maintenance award of UKP 12,300 per annum for the duration of
the programme.

Contact for further information: Dr. Ian Pratt-Hartmann:
ipratt@cs.man.ac.uk

How to apply: In the first instance please send detailed curriculum
vitae including at least two referees (email address preferred) to:

      Dr Ian Pratt-Hartmann 
      School of Computer Science
      Manchester University
      Manchester M13 9PL
      UK
      ipratt@cs.man.ac.uk 

as soon as possible.

Formal application to be admitted by the PhD program in the School of
Computer Science at the University of Manchester needs to be made
separately. See

http://www.cs.manchester.ac.uk/Study_subweb/PhDWeb/PhDApplication.php