Abstract
The 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.
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The slides of the talk given at the conference “Advances in Proof-Theoretic Semantics” in Tübingen can be found in the online proceedings [8].
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Acknowledgements
This work was supported by the French-German ANR-DFG project “Beyond Logic” (DFG Grant Schr275/17-1), by the Portuguese Science Foundation (FCT) through the Grant SFRH/BI/33955/2009 in the project LogiCCC (the ESF EUROCORES project “Dialogical Foundations of Semantics”) and by the science foundation FAPERJ of the state Rio de Janeiro, Brazil, through the Grant E-26/101.254/2014.
The results of this work have been presented in part at the conferences PCC 2013 (Toulouse, France, 2013), NAT@Logic 2015 (Natal, Brazil, 2015), “Beyond Logic” (Cerisy-la-Salle, France, 2017) and “Advances in Proof-Theoretic Semantics” (Tübingen, Germany, 2019).Footnote 1
I would like to thank Andrzej Indrzejczak, Reinhard Kahle, Luiz Carlos Pereira and Peter Schroeder-Heister not only for their helpful comments and suggestions, but also for encouraging me to write this article. I am grateful to the two anonymous reviewers for many helpful comments and suggestions.
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Gazzari, R. The Calculus of Natural Calculation. Stud Logica 109, 1375–1411 (2021). https://doi.org/10.1007/s11225-020-09938-7
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DOI: https://doi.org/10.1007/s11225-020-09938-7