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Proof-Theoretic Semantics and Inquisitive Logic

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Abstract

Prawitz (1971) conjectured that proof-theoretic validity offers a semantics for intuitionistic logic. This conjecture has recently been proven false by Piecha and Schroeder-Heister (2019). This article resolves one of the questions left open by this recent result by showing the extensional alignment of proof-theoretic validity and general inquisitive logic. General inquisitive logic is a generalisation of inquisitive semantics, a uniform semantics for questions and assertions. The paper further defines a notion of quasi-proof-theoretic validity by restricting proof-theoretic validity to allow double negation elimination for atomic formulas and proves the extensional alignment of quasi-proof-theoretic validity and inquisitive logic.

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Correspondence to Will Stafford.

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I would like to thank Sean Walsh, Stella Moon, and Chris Mitsch for their helpful comments and conversations. I would like to thank the anonymous referee for their comments and in particular for pointing me towards generalised inquisitive logic. I would also like to thank the audience at the Tü- bingen 3rd Proof-Theoretic Semantics Workshop, the UC Irvine Logic Seminar, and the UC Irvine Work in Progress Seminar for their helpful questions.

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Stafford, W. Proof-Theoretic Semantics and Inquisitive Logic. J Philos Logic 50, 1199–1229 (2021). https://doi.org/10.1007/s10992-021-09596-7

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