Abstract
AbstractThe calculus of Natural Calculation is introduced as an extension of Natural Deduction by proper term rules. Such term rules provide the capacity of dealing directly with terms in the calculus instead of the usual reasoning based on equations, and therefore the capacity of a natural representation of informal mathematical calculations. Basic proof theoretic results are communicated, in particular completeness and soundness of the calculus; normalisation is briefly investigated. The philosophical impact on a proof theoretic account of the notion of meaning is considered.
Funder
Fundação para a Ciência e a Tecnologia
Deutsche Forschungsgemeinschaft
Fundação Carlos Chagas Filho de Amparo á Pesquisa do Estado do Rio de
Publisher
Springer Science and Business Media LLC
Subject
History and Philosophy of Science,Logic
Reference35 articles.
1. Anellis, I., Forty Years of “Unnatural” Natural Deduction and Quantication: A History of First-order Systems of Natural Deduction, From Gentzen to Copi, Modern Logic 2(2):113–152, 1991.
2. Arana, A., On Formally Measuring and Eliminating Extraneous Notions in Proofs, Philosophia Mathematica (III) 17(2):189–207, 2009.
3. Barendregt, H., The Impact of the Lambda Calculus, Bulletin of Symbolic Logic 3(2):181–215, 1997.
4. Došen, K., Identity of Proofs Based on Normalization and Generality, Bulletin of Symbolic Logic 9:477–503, 2003.
5. Došen, K., and P. Schroeder-Heister, (eds.), Substructural Logics, Studies in Logic and Computation, Oxford University Press, 1993.
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