### Dr Peter Chapman

Senior Lecturer

**contact:**

Computing, Engineering and Mathematics

W422 Watts Building

Moulsecoomb

Brighton

BN2 4GJ

Telephone: +44 (0)1273 642531

Email: P.B.Chapman@brighton.ac.uk

#### Quick Links:

**Teaching:**

I have experience of teaching the following topics:

- Logic,
- Foundations of Mathematics,
- Univariate calculus,
- Multivariate calculus,
- Partial differential equations,
- Real analysis,
- Complex analysis,
- Probability,
- Elementary statistics,
- History of mathematics,
- Remedial/service mathematics

**Research Interests:**

My research interests are in the field of logic, specifically proof theory and visual representations of logic.

My interests in proof theory lie in formalisation of results (using proof assistants, such as Isabelle for sequent calculi. These results include Cut admissibility and invertibility.

I am interested in the visual representations of logic, specifically using diagrammatic notations to encode logical propositions and proofs. In particular, my work is focused on providing visualisations of ontologies. [top]

I am also doing some work in mathematics in Higher Education, specifically how students interact with mathematical proof. [top]

- 3rd International Workshop on Euler Diagrams, General co-Chair (with Luana Micallef). Held in conjunction with Diagrams 2012, Canterbury, UK, July 2012. CEUR, vol. 854.

*Journal of Visual Languages and Computing*,

*Cognitive Science*,

*Notre Dame Journal of Formal Logic*and

*Computer Science and Infromation Structures*. [top]

**Publications:**

**Publications (peer reviewed):**

- “
*A Locally Nameless Visual λ-calculus*” Peter Chapman, in Visual Languages and Computing 2013, Knowledge Systems Institute, pages 188-193, 2013. - “
*Formalizing Concept Diagrams*” Gem Stapleton, John Howse, Peter Chapman, Aidan Delaney, Jim Burton and Ian Oliver, in Visual Languages and Computing 2013, Knowledge Systems Institute, pages 182-187, 2013. - “
*On the Expressiveness of Second-Order Spider Diagrams*” Peter Chapman, Gem Stapleton and Aidan Delaney, Journal of Visual Languages and Computing 24 (5), Elsevier, pages 327-349, 2013. - “
*On the Completeness of Spider-diagrams Augmented with Constants*” Gem Stapleton, John Taylor, John Howse, Simon Thompson and Peter Chapman, Chapter 7 of Visual Reasoning with Diagrams, Birkhäuser, pages 101-134, 2013. - “
*What Can Concept Diagrams Say?*” Gem Stapleton, John Howse, Peter Chapman, Ian Oliver and Aidan Delaney, 7th International Conference of Diagrammatic Representation and Inference, 2012, in Lecture Notes in Artificial Intelligence no. 7352, Springer, pages 291-293. - “
*Visualizing Ontologies: A Case Study*” John Howse, Gem Stapleton, Kerry Taylor and Peter Chapman, International Semantic Web Conference, 2011, in Lecture Notes in Computer Science no. 7031, Springer, pages 257-272. - “
*Defining Sound Inference Rules for Concept Diagrams*” Peter Chapman, Gem Stapleton, John Howse and Ian Oliver, IEEE Symposium on Visual Languages and Human-Centric Computing, 2011, in VL/HCC 2011, pages 87-94. *“On the Relative Expressiveness of Second-Order Spider Diagrams and Regular Expressions”★*Peter Chapman and Gem Stapleton, International Workshop on Visual Languages and Computing, in Distributed Multimedia Systems, pages 283-288, 2010.*“Introducing Second-Order Spider Diagrams for Defining Regular Languages”★*Peter Chapman and Gem Stapleton, IEEE Symposium on Visual Languages and Human-Centric Computing, 2010, in VL/HCC 2010, pages 159-167.*“Creating a Second-Order Diagrammatic Logic”*Peter Chapman and Gem Stapleton, 6th International Conference on Diagrammatic Representation and Inference, 2010, in Lecture Notes in Artificial Intelligence no. 6170, Springer, pages 298-300.- “
*Syntactic Invertibility in Sequent Calculi*” Peter Chapman, Archive of Formal Proofs, available at “AFP”, 2009. *“Mechanising a Proof of Craig's Interpolation Theorem for Intuitionistic Logic in Nominal Isabelle”★*Peter Chapman, James McKinna and Christian Urban, 9th International Conference on Artificial Intelligence and Symbolic Computation, 2008, in Lecture Notes in Artificial Intelligence no. 5144, Springer, pages 38-52.

**Talks given (in addition to those marked with a ★ above):**

*“Syntactic Invertibility in Sequent Calculi”*Workshop on Structural Proof Theory, Paris, November 2008.- “
*Formalising Gentzen-style Proof Theory in Isabelle*” Gentzen Centenary Symposium, St Andrews, November 2009. *“Sequent Calculi and Isabelle”*Seminar series, University of Brighton, December 2009.*“The role of diagrams in proof”*Seminar series, University of Uppsala, Uppsala, September 2010.

**Brief academic biography:**

My undergraduate degree was in Mathematics and Economics from the London School of Economics. I have a Masters degree, in Mathematics and the Foundations of Computer Science, from the University of Oxford, and a PhD from the University of St Andrews, entitled “Tools and Techniques for Formalising Structural Proof Theory” (supervised by Roy Dyckhoff). From January 2010 to January 2011, I was employed on the EPSRC grant “Defining Regular Languages with Diagrams” [EP/H012311/1]. In 2011-2012, I completed the Postgraduate Certificate in Teaching and Learning in Higher Education at the University of Brighton, and am currently enrolled on the MA Education (Higher Education) course. [top]

**6**.

CHAPMAN, PETER, STAPLETON, GEM and DELANEY, AIDAN
(2013)
*On the expressiveness of second-order spider diagrams*
Journal of Visual Languages and Computing, 24 (5).
pp. 327-349.
ISSN 1045-926X

CHAPMAN, PETER, STAPLETON, GEM, HOWSE, JOHN and Oliver, Ian
(2011)
*Deriving sound inference rules for concept diagrams*
In: Proceedings of the IEEE symposium on visual languages and human-centric computing 2011, 18-22 September 2011, Pittsburgh, PA, USA, 18-22 September, 2011.

HOWSE, JOHN, STAPLETON, GEM, Taylor, Kerry and CHAPMAN, PETER
(2011)
*Visualizing ontologies: a case study*
In: Proceedings of the 10th International Semantic Web Conference, Part I, Bonn, Germany, October 23-27, 2011.

CHAPMAN, PETER and STAPLETON, GEM
(2010)
*Creating a second order diagrammatic logic*
In: 6th International Conference on the Theory and Application of Diagrams, 9-11 August 2010, Portland, OR, USA.

CHAPMAN, PETER and STAPLETON, GEM
(2010)
*Introducing second order spider diagrams for defining regular languages*
In: 2010 IEEE Symposium on Visual Languages and Human-Centric Computing, 21 - 25 Sep 2010, Universidad Carlos III de Madrid.

CHAPMAN, PETER, McKinna, James and Urban, Christian
(2008)
*Mechanising a proof of Craig's Interpolation Theorem for intuitionistic logic in nominal isabelle*
In: Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics, 31 July - 1 August, 2011, Birmingham, UK, July 28 - August 1, 2008.