Graduate studies at Western
|Abstract||The system of natural deduction that originated with Gentzen (1934–5), and for which Prawitz (1965) 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.|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Only published papers are available at libraries|
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 downloads10 ( #114,476 of 739,357 )
Recent downloads (6 months)2 ( #37,287 of 739,357 )
How can I increase my downloads?