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

TL;DR

This paper develops a denotational semantics framework for epistemic grounding languages inspired by Prawitz's theory, defining denotation functions and exploring properties like closure and expansions, and discusses a ground-theoretic completeness conjecture.

Contribution

It introduces a novel denotational semantics for epistemic grounding languages based on Prawitz's theory, including properties and a version of the completeness conjecture.

Findings

Defined denotation functions relating terms to proof-objects.

Analyzed properties like canonical closure and universal denotation.

Provided a ground-theoretic version of Prawitz's completeness conjecture.

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.