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arXiv · 2501.10491

Denotational semantics for languages of epistemic grounding based on Prawitz's theory of grounds

Antonio Piccolomini d'Aragona
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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 (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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Antonio Piccolomini d'Aragona. 2025-01-17. Denotational semantics for languages of epistemic grounding based on Prawitz's theory of grounds. https://arxiv.org/abs/2501.10491

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