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From proof-theoretic validity to base-extension semantics for intuitionistic propositional logic

From proof-theoretic validity to base-extension semantics for intuitionistic propositional logic
From proof-theoretic validity to base-extension semantics for intuitionistic propositional logic

Proof-theoretic semantics (P-tS) is the approach to meaning in logic based on proof (as opposed to truth). There are two major approaches to P-tS: proof-theoretic validity (P-tV) and base-extension semantics (B-eS). The former is a semantics of arguments, and the latter is a semantics of logical constants. This paper demonstrates that the B-eS for intuitionistic propositional logic (IPL) encapsulates the declarative content of a version of P-tV based on the elimination rules. This explicates how the B-eS for IPL works, and shows the completeness of this version of P-tV.

Intuitionistic logic, Logic, Proof, Proof-theoretic semantics, Semantics
0039-3215
Gheorghiu, Alexander V.
4569dbd7-8426-4631-80a1-424e922436da
Pym, David J.
dcd2c0b6-80dd-4486-9649-8f0ee547d110
Gheorghiu, Alexander V.
4569dbd7-8426-4631-80a1-424e922436da
Pym, David J.
dcd2c0b6-80dd-4486-9649-8f0ee547d110

Gheorghiu, Alexander V. and Pym, David J. (2025) From proof-theoretic validity to base-extension semantics for intuitionistic propositional logic. Studia Logica. (doi:10.1007/s11225-024-10163-9).

Record type: Article

Abstract

Proof-theoretic semantics (P-tS) is the approach to meaning in logic based on proof (as opposed to truth). There are two major approaches to P-tS: proof-theoretic validity (P-tV) and base-extension semantics (B-eS). The former is a semantics of arguments, and the latter is a semantics of logical constants. This paper demonstrates that the B-eS for intuitionistic propositional logic (IPL) encapsulates the declarative content of a version of P-tV based on the elimination rules. This explicates how the B-eS for IPL works, and shows the completeness of this version of P-tV.

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e-pub ahead of print date: 9 January 2025
Keywords: Intuitionistic logic, Logic, Proof, Proof-theoretic semantics, Semantics
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Identifiers

Local EPrints ID: 502230
URI: http://eprints.soton.ac.uk/id/eprint/502230
DOI: doi:10.1007/s11225-024-10163-9
ISSN: 0039-3215
PURE UUID: f11f625b-b4da-485f-8d72-bc5b73686d1d
ORCID for Alexander V. Gheorghiu: ORCID iD orcid.org/0000-0002-7144-6910

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Date deposited: 18 Jun 2025 16:45
Last modified: 22 Aug 2025 02:47

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Contributors

Author: Alexander V. Gheorghiu ORCID iD
Author: David J. Pym

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