Dr Peter Fletcher
- JOB TITLE: Lecturer (in the
School of Computing and
Mathematics)
- ROOM: MacKay Building 2.36
- ADDRESS: School of Computing and Mathematics, Keele University, Keele,
Staffordshire, ST5 5BG, U.K.
- PHONE: +44 (0)1782 733260
- FAX: +44 (0)1782 734268
- E-MAIL: X@Y, where X = p.fletcher and Y = keele.ac.uk
- ORCID: 0000-0002-6183-0265
My research interests are in artificial intelligence (especially
connectionism and syntactic pattern recognition) and
the philosophy of mathematics (especially intuitionism).
(Note: please e-mail me if you would like a copy of any of the papers listed
below.)
Artificial Intelligence
- 1. Syntactic pattern recognition.
- I have developed self-configuring connectionist networks for unsupervised
learning of recursive graph grammars. The 1991 and 1992 papers below describe a
network that can learn simple (non-recursive) geometric structure from example
patterns. The 2001 paper shows how the method can be extended to handle
iterative structure. See the 1993 conference paper for a broader perspective on
this project.
- Fletcher, P. (1991) A self-configuring network.
Connection Science, 3, no. 1, 35-60.
- Fletcher, P. (1992) Principles of node growth and
node pruning. Connection Science, 4, no. 2, 125-141.
- Fletcher, P. (1993) Neural networks for learning
grammars.
In Grammatical Inference: Theory, Applications and Alternatives. First
International Colloquium on Grammatical Inference, Essex, U.K., 22nd-23rd April
1993. IEE Digest no. 1993/092. Also available as Technical Report 93.07, Keele
University, Computer Science Department.
- Fletcher, P. (2001) Connectionist learning
of regular graph grammars. Connection Science, 13, no. 2,
127-188. (See EXAMPLES.)
Work in progress: robust symbol processing, recognition of
noisy, vague, distorted, recursively structured patterns, in an inherently
affine-invariant way. See
EXAMPLES
involving recognising several overlapping patterns. The following two papers
refer to this work.
- Fletcher, P. (2004) Mathematical Theory
of Recursive Symbol Systems. Technical Report GEN-0401, Keele
University, Computer Science Department. (This paper sets out the underlying
mathematical theory.)
- Lam, K.P. & Fletcher, P. (2009)
Concurrent grammar inference machines for 2-D pattern recognition: a comparison
with the level set approach. In Image Processing: Algorithms and
Systems VII, edited by J.T. Astola, K.O. Egiazarian, N.M. Nasrabadi &
S.A. Rizvi. Proceedings of SPIE-IS&T Electronic Imaging 2009, published by
SPIE-IS&T, SPIE vol. 7245, article no. 724515. DOI 10.1117/12.806035.
- 2. Foundations of connectionist computation.
- This is an investigation of the conceptual foundations of connectionism
and its relation to other models of parallel processing. The result of this work
is a general formal definition and semantics for connectionism, which is
somewhat broader than the usual `weighted sum' models derived from McCulloch
and Pitts.
Philosophy of Mathematics
I am an intuitionist. Fundamental to intuitionism are the notions of a
mathematical construction and a constructive proof; I am
working on clarifying these basic notions and the way they are used to provide
an interpretation of predicate logic, number theory and analysis. I am also
concerned to reconcile the intuitionistic view with important insights from
Hilbert's formalism and logicism.
Full details are available in the following monograph:
For a broader perspective, including the implications for mathematical physics,
see
- Fletcher, P. (2002) A constructivist perspective on
physics. Philosophia Mathematica, Series III, 10, 26-42.
- Fletcher, P. (2007) Infinity. In D.
Jacquette (ed.) Philosophy of Logic, vol. 5 of the Handbook of the
Philosophy of Science, pp. 523-585. Amsterdam: Elsevier. ISBN
0-444-51541-0.
- Just published: Fletcher, P. (2020) Brouwer's weak counterexamples and the creative subject: a critical
survey. Journal of Philosophical Logic, DOI:
10.1007/s10992-020-09551-y,
open
access.
I am also interested in nonstandard analysis; see
- Fletcher, P. (1989) Nonstandard set theory.
Journal of Symbolic Logic, 54, 1000-1008.
- Fletcher, P., Hrbacek, K., Kanovei, V., Katz, M.G., Lobry, C. &
Sanders, S. (2017) Approaches to analysis
with infinitesimals following Robinson, Nelson, and others. Real
Analysis Exchange, 42, no. 2, 1-59.
My current topics of interest are
- intuitionistic choice sequences - my student, James Appleby, has
just completed a PhD on this, entitled Choice sequences and knowledge states:
extending the notion of finite information to produce a clearer foundation for
intuitionistic analysis;
- constructivist axiomatic geometry - deriving three-dimensional
geometry from axioms similar to Hilbert's, within the framework of
Bishop-style constructive mathematics.
Last updated 10th May 2020.