1.

Allwein, G., and J. Barwise (eds.), *Logical Reasoning with Diagrams*, Oxford Studies in Logic and Computation Series, 1996.

2.

Barwise, J., and J. Seligman, *Information Flow: The Logic of Distributed Systems*, Cambridge University Press, 1997.

3.

Buss, S. R., Propositional proof complexity: an introduction, in U. Berger and H. Schwichtenberg (eds.), *Computational Logic*, Springer, Berlin, 1999 pp. 127–178.

4.

Gentzen, G., Untersuchungen über das logische Schließen, Mathematische Zeitschrift 39:176–210, 405–431, 1934. English Translation: Investigations into logical deduction, in M. E. Szabo (ed.), *The collected Papers of Gerhard Gentzen*, 1969.

5.

Howse, J., G. Stapleton, and J. Taylor, Spider diagrams, *LMS Journal of Computation and Mathematics* 8:145–194, 2005, London Mathematical Society.

6.

Mineshima, K., M. Okada, and R. Takemura, Conservativity for a hierarchy of Euler and Venn reasoning systems, *Proceedings of Visual Languages and Logic 2009*, CEUR Series 510:37–61, 2009.

7.

Mineshima, K., M. Okada, and R. Takemura, A diagrammatic inference system with Euler circles, accepted for publication in *Journal of Logic, Language and Information*.

8.

Mineshima, K., M. Okada, and R. Takemura, Two types of diagrammatic inference systems: natural deduction style and resolution style, in *Diagrammatic Representation and Inference: 6th International Conference, Diagrams 2010*, Lecture Notes In Artificial Intelligence, Springer, 2010, pp. 99–114.

9.

Mossakowski T., Diaconescu R., Tarlecki A.: What is a logic translation?. Logica Universalis

**3**(1), 95–124 (2009)

CrossRef10.

Negri, S., and J. von Plato, *Structural Proof Theory*, Cambridge, UK, 2001.

11.

von Plato, J., Proof theory of classical and intuitionistic logic, in L. Haaparanta (ed.), *History of Modern Logic*, Oxford University Press, 2009, pp. 499–515.

12.

Prawitz, D., *Natural Deduction*, Almqvist & Wiksell, 1965 (Dover, 2006).

13.

Prawitz, D., Ideas and results in proof theory, in *Proceedings 2nd Scandinavian Logic Symposium*, 1971, pp. 237–309.

14.

Shimojima, A., On the efficacy of representation, Ph.D thesis, Indiana University, 1996.

15.

Shin, S.-J., *The Logical Status of Diagrams*, Cambridge University Press, 1994.

16.

Stapleton G.: A survey of reasoning systems based on Euler diagrams, in Proceedings of Euler 2004. Electronic Notes in Theoretical Computer Science

**134**(1), 127–151 (2005)

CrossRef17.

Stapleton G., Howse J., Rodgers P., Zhang L.: ZhangGenerating Euler Diagrams from existing layouts, Layout of (Software) Engineering Diagrams 2008. Electronic Communications of the EASST **13**, 16–31 (2008)