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Denotational Semantics for Languages of Epistemic Grounding Based on Prawitz’s Theory of Grounds

Abstract

We outline a class of term-languages for epistemic grounding inspired by Prawitz’s theory of grounds. We show how denotation functions can be defined over these languages, relating terms to proof-objects built up of constructive functions. We discuss certain properties that the languages may enjoy both individually (canonical closure and universal denotation) and with respect to their expansions (primitive/non-primitive and conservative/non-conservative expansions). Finally, we provide a ground-theoretic version of Prawitz’s completeness conjecture, and adapt to our framework a refutation of this conjecture due to Piecha and Schroeder-Heister.

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Acknowledgements

I am grateful to Cesare Cozzo, Gabriella Crocco, Ansten Klev, Dag Prawitz and Peter Schroeder-Heister for helpful suggestions. I am also grateful to the anonymous reviewers, whose comments helped me to improve an earlier draft of this paper.

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Correspondence to Antonio Piccolomini d’Aragona.

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d’Aragona, A.P. Denotational Semantics for Languages of Epistemic Grounding Based on Prawitz’s Theory of Grounds. Stud Logica 110, 355–403 (2022). https://doi.org/10.1007/s11225-021-09969-8

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Keywords

  • Grounding
  • Canonicity
  • Primitiveness
  • Conservativity
  • Completeness