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

Studia Logica 110 (2):355-403 (2021)
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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 and with respect to their 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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2022

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10.1007/s11225-021-09969-8

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References found in this work

The logical basis of metaphysics.Michael Dummett - 1991 - Cambridge: Harvard University Press.
Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
Constructivism in mathematics: an introduction.A. S. Troelstra - 1988 - New York, N.Y.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.. Edited by D. van Dalen.
A natural extension of natural deduction.Peter Schroeder-Heister - 1984 - Journal of Symbolic Logic 49 (4):1284-1300.

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