A Partial Calculus for Dag Prawitz’s Theory of Grounds and a Decidability Issue

  • Antonio Piccolomini d’Aragona
Part of the European Studies in Philosophy of Science book series (ESPS, volume 9)


We consider Dag Prawitz’s theory of grounds and suggest a formal apparatus for it. On its basis we show that the account faces a decidability issue similar to one that is often associated with BHK semantics, and propose different readings of the issue that involve different consequences.


Decidability Grounding Operation Proof Typing 



This work has been carried out thanks to the support of the A*MIDEX grant (n ANR-11-IDEX-0001-02) funded by the French Government “Investissement d’Avenir” program.


  1. Cozzo, C. 2015. Necessity of thought. In Dag Prawitz on proofs and meaning, ed. H. Wansing, 101–120. Heidelberg: Springer.Google Scholar
  2. Cozzo, C. 2016. Inference and compulsion. In Second pisa colloquium in logic, language and epistemology, ed. E. Moriconi. Pisa: ETS, forthcoming.Google Scholar
  3. Crocco, G., and E. Audureau 2003. Intuitionisme et Constructivisme chez Brouwer. In Calcul et formes de l’activité mathématique, ed. J. Boniface, 190–217. Paris: Ellipses.Google Scholar
  4. Díez, G.F. 2000. Five observations concerning the intended meaning of the intuitionistic logical constants. Journal of Philosophical Logic 29(4): 409–424.CrossRefGoogle Scholar
  5. Došen, K. 2015. Inferential semantics. In Dag Prawitz on proofs and meaning, ed. H. Wansing, 147–162. Heidelberg: Springer.Google Scholar
  6. Gentzen, G. 1934–1935. Untersuchungen über das logische Schließen. Matematische Zeitschrift XXXIX: 176–210, 405–431.Google Scholar
  7. Heyting, A. 1956. Intuitionism. An Introduction. Amsterdam: North-Holland.Google Scholar
  8. Howard, W. 1980. The formula-as-types notion of construction. In To H. B. Curry: Essays on combinatoriy logic, lambda calculus and formalism, ed. J. R. Hindley and J. P. Seldin, 479–490. London: Academic.Google Scholar
  9. Kreisel, G. 1962. Foundations of intuitionistic logic. In Logic methodology and philosophy of science, ed. E. Nagel, 198–212. Stanford: Stanford University Press.Google Scholar
  10. Prawitz, D. 1973. Towards a foundation of a general proof-theory. In Logic methodology and philosophy of science IV, ed. P. Suppes, 225–307. Amsterdam: North-Holland.Google Scholar
  11. Prawitz, D. 1977. Meaning and proofs: On the conflict between classical and intuitionistic logic. Theoria 43: 2–40.CrossRefGoogle Scholar
  12. Prawitz, D. 2006. Natural deduction. A proof theoretical study. New York: Dover Publications.Google Scholar
  13. Prawitz, D. 2009. Inference and knowledge. In The Logica Yearbook 2008, ed. M. Pelis, 175–192. London: College Publications.Google Scholar
  14. Prawitz, D. 2012. The epistemic significance of valid inference. Synthese 187(3): 887–898.CrossRefGoogle Scholar
  15. Prawitz, D. 2013. Validity of inferences. In M. Frauchiger, Reference, rationality, and phenomenology: Themes from Føllesdal, 179–204. Ontos Verlag: Dordrecht.Google Scholar
  16. Prawitz, D. 2014. An approach to general proof theory and a conjecture of a kind of completeness of intuitionistic logic revisited. In Advances in natural deduction, ed. L. C. Pereira, E. H. Haeusler, and V. de Paiva, 269–279. Heidelberg: Springer.CrossRefGoogle Scholar
  17. Prawitz, D. 2015. Explaining deductive inference. In Dag Prawitz on proofs and meaning, ed. H. Wansing, 65–100. Heidelberg: Springer.Google Scholar
  18. Schroeder-Heister, P. 2006. Validity concepts in proof-theoretic semantics. Synthese 148(3): 525–571.CrossRefGoogle Scholar
  19. Tranchini, L. 2014. Proof-theoretic semantics, proofs and the distinction between sense and denotation. In Journal of Logic and Computation.
  20. Usberti, G. 2015. A notion of C-justification for empirical statements. In Dag Prawitz on proofs and meaning, ed. H. Wansing, 415–450. Heidelberg: Springer.Google Scholar
  21. Usberti G. 2017. Inference and epistemic transparency. In “Inferences and proofs”, special issue of TOPOI, ed. G. Crocco, and A. Piccolomini d’Aragona,

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CNRS, CEPERCAix Marseille UniversityAix en ProvenceFrance
  2. 2.“La Sapienza” University of RomeRomeItaly

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