David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Logic Journal of the IGPL 10 (3):299-337 (2002)
The system of natural deduction that originated with Gentzen , and for which Prawitz proved a normalization theorem, is re-cast so that all elimination rules are in parallel form. This enables one to prove a very exigent normalization theorem. The normal forms that it provides have all disjunction-eliminations as low as possible, and have no major premisses for eliminations standing as conclusions of any rules. Normal natural deductions are isomorphic to cut-free, weakening-free sequent proofs. This form of normalization theorem renders unnecessary Gentzen's resort to sequent calculi in order to establish the desired metalogical properties of his logical system.Ultimate normal forms are well-adapted to the needs of the computational logician, affording valuable constraints on proof-search. They also provide an analysis of deductive relevance. There is a deep isomorphism between natural deductions and sequent proofs in the relevantized system
|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
Peter Schroeder-Heister (2014). The Calculus of Higher-Level Rules, Propositional Quantification, and the Foundational Approach to Proof-Theoretic Harmony. Studia Logica 102 (6):1185-1216.
Nissim Francez (2015). On the Notion of Canonical Derivations From Open Assumptions and its Role in Proof-Theoretic Semantics. Review of Symbolic Logic 8 (2):296-305.
Similar books and articles
Maria Da Paz N. Medeiros (2006). A New S4 Classical Modal Logic in Natural Deduction. Journal of Symbolic Logic 71 (3):799 - 809.
Takahito Aoto (1999). Uniqueness of Normal Proofs in Implicational Intuitionistic Logic. Journal of Logic, Language and Information 8 (2):217-242.
Hartley Slater (2008). Harmonising Natural Deduction. Synthese 163 (2):187 - 198.
Sara Negri (2002). Varieties of Linear Calculi. Journal of Philosophical Logic 31 (6):569-590.
Mirjana Borisavljevi (2008). Normal Derivations and Sequent Derivations. Journal of Philosophical Logic 37 (6):521 - 548.
Kosta Došen (2003). Identity of Proofs Based on Normalization and Generality. Bulletin of Symbolic Logic 9 (4):477-503.
Wilfried Sieg & John Byrnes (1998). Normal Natural Deduction Proofs (in Classical Logic). Studia Logica 60 (1):67-106.
Roy Dyckhoff & Luis Pinto (1998). Cut-Elimination and a Permutation-Free Sequent Calculus for Intuitionistic Logic. Studia Logica 60 (1):107-118.
A. S. Troelstra (1999). Marginalia on Sequent Calculi. Studia Logica 62 (2):291-303.
David J. Pym (1995). A Note on the Proof Theory the λII-Calculus. Studia Logica 54 (2):199 - 230.
Added to index2009-01-28
Total downloads26 ( #142,097 of 1,789,836 )
Recent downloads (6 months)9 ( #93,120 of 1,789,836 )
How can I increase my downloads?