Wednesday, June 29, 2016

Natural Deduction for the Working Logician: a reader

A preliminary Reader for  the course.

[1]Francis Jeffry Pelletier, A Brief History of Natural Deduction, History and Philosophy of Logic 20 (1): 1-31, 1999

[2] Gerhrad Gentzen, Untersuchungen über das logische Schließen.I. Mathematische Zeitschrift [S.l.:s.n.] 39 (2): 176–210. 1934
 Untersuchungen über das logische Schließen. II. Mathematische Zeitschrift[S.l.: s.n.] 39 (3): 405–431. 1935

English translation in M. E. Szabo: Collected Papers of Gerhard Gentzen. North-Holland, 1969. Investigations into Logical Deduction

[3] Dag Prawitz, Natural Deduction: A Proof-Theoretical Study (Dover Books on Mathematics, 2006) original publication, Stockholm, 1965

[4] Sara Negri and Jan von Plato, Structural Proof Theory, CUP, 2001. Also Jan von Plato, Natural Deduction: Some Recent Developments 2003, from Negri's webpage.

[5] Jean-Yves Girard, Yves Lafont and Paul Taylor,  Proofs and Types, CUP, 1989.

[6]   Manipulating Proofs, Jonathan P. Seldin's manuscript, available from his publications page.

[7]  Curry’s anticipation of the types used inprogramming languages, Jonathan P. Seldin, Proceedings of the Annual Meeting of the Canadian Society for History and Philosophy of Mathematics, 2002. There are also slides available in his publications page.

[8] Propositional Logics Complexity and the Sub-Formula Property, Edward Hermann Haeusler, Proceedings Tenth International Workshop on Developments in Computational Models, Vienna, Austria, 13th July 2014,  Electronic Proceedings in Theoretical Computer Science, 179, pages 1-16, 2015.

No comments:

Post a Comment