- 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.)

- 1.
**Connectionist symbol processing.** - I am working on self-configuring 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, and a full account will be published shortly.- 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.

- Fletcher, P. (1991) A self-configuring network.
- 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.
- Fletcher, P. (2000) The foundations of
connectionist computation.
*Connection Science*,**12**, no. 2, 163-196.

- Fletcher, P. (2000) The foundations of
connectionist computation.

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:

- Fletcher, P. (1998)
*Truth, Proof and Infinity: A Theory of Constructions and Constructive Reasoning*. Synthese Library (Studies in Epistemology, Logic, Methodology and Philosophy of Science), vol. 276. Dordrecht: Kluwer Academic Publishers. 480 pp. ISBN 0-7923-5262-9.

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.

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*
and *constructivist axiomatic geometry*.

Last updated 17th February 2017.