David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Bulletin of Symbolic Logic 9 (4):477-503 (2003)
Some thirty years ago, two proposals were made concerning criteria for identity of proofs. Prawitz proposed to analyze identity of proofs in terms of the equivalence relation based on reduction to normal form in natural deduction. Lambek worked on a normalization proposal analogous to Prawitz's, based on reduction to cut-free form in sequent systems, but he also suggested understanding identity of proofs in terms of an equivalence relation based on generality, two derivations having the same generality if after generalizing maximally the rules involved in them they yield the same premises and conclusions up to a renaming of variables. These two proposals proved to be extensionally equivalent only for limited fragments of logic. The normalization proposal stands behind very successful applications of the typed lambda calculus and of category theory in the proof theory of intuitionistic logic. In classical logic, however, it did not fare well. The generality proposal was rather neglected in logic, though related matters were much studied in pure category theory in connection with coherence problems, and there are also links to low-dimensional topology and linear algebra. This proposal seems more promising than the other one for the general proof theory of classical logic
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
L. Mehats & Sergei Soloviev (2007). Coherence in SMCCs and Equivalences on Derivations in IMLL with Unit. Annals of Pure and Applied Logic 147 (3):127-179.
Kosta Dosen & Zoran Petric (2012). Isomorphic Formulae in Classical Propositional Logic. Mathematical Logic Quarterly 58 (1):5-17.
Willem Heijltjes (2010). Classical Proof Forestry. Annals of Pure and Applied Logic 161 (11):1346-1366.
Similar books and articles
Roy Dyckhoff & Luis Pinto (1998). Cut-Elimination and a Permutation-Free Sequent Calculus for Intuitionistic Logic. Studia Logica 60 (1):107-118.
Vincent Danos, Jean-Baptiste Joinet & Harold Schellinx (1997). A New Deconstructive Logic: Linear Logic. Journal of Symbolic Logic 62 (3):755-807.
Ken-etsu Fujita (1998). On Proof Terms and Embeddings of Classical Substructural Logics. Studia Logica 61 (2):199-221.
Ulrich Berger, Stefan Berghofer, Pierre Letouzey & Helmut Schwichtenberg (2006). Program Extraction From Normalization Proofs. Studia Logica 82 (1):25 - 49.
Sachio Hirokawa, Yuichi Komori & Izumi Takeuti (1996). A Reduction Rule for Peirce Formula. Studia Logica 56 (3):419 - 426.
G. E. Mint͡s (2000). A Short Introduction to Intuitionistic Logic. Kluwer Academic / Plenum Publishers.
Marie-Renée Fleury & Myriam Quatrini (2007). A Mixed Λ-Calculus. Studia Logica 87 (2-3):269 - 294.
Kosta Došen & Zoran Petrić (2003). Generality of Proofs and its Brauerian Representation. Journal of Symbolic Logic 68 (3):740-750.
Added to index2009-01-28
Total downloads17 ( #105,341 of 1,140,266 )
Recent downloads (6 months)1 ( #142,694 of 1,140,266 )
How can I increase my downloads?