From Proof-theoretic Validity to Base-extension Semantics for Intuitionistic Propositional Logic
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909312055508992 |
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| author | Gheorghiu, Alexander V. Pym, David J. |
| author_facet | Gheorghiu, Alexander V. Pym, David J. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_05344 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | From Proof-theoretic Validity to Base-extension Semantics for Intuitionistic Propositional Logic Gheorghiu, Alexander V. Pym, David J. Logic in Computer Science 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. |
| title | From Proof-theoretic Validity to Base-extension Semantics for Intuitionistic Propositional Logic |
| topic | Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2210.05344 |