Denotational semantics for languages of epistemic grounding based on Prawitz's theory of grounds
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917896493465600 |
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| author | d'Aragona, Antonio Piccolomini |
| author_facet | d'Aragona, Antonio Piccolomini |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10491 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Denotational semantics for languages of epistemic grounding based on Prawitz's theory of grounds d'Aragona, Antonio Piccolomini Logic 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. |
| title | Denotational semantics for languages of epistemic grounding based on Prawitz's theory of grounds |
| topic | Logic |
| url | https://arxiv.org/abs/2501.10491 |