Inferentialist Public Announcement Logic: Base-extension Semantics
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912511275565056 |
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| author | Eckhardt, Timo Pym, David J. |
| author_facet | Eckhardt, Timo Pym, David J. |
| contents | Proof-theoretic semantics, and base-extension semantics in particular, can be seen as a logical realization of inferentialism, in which the meaning of expressions is understood through their use. We present a base-extension semantics for public announcement logic, building on earlier work giving a base-extension semantics for the modal logic $S5$, which in turn builds on earlier such work for $K$, $KT$, $K4$, and $S4$. These analyses rely on a notion of `modal relation' on bases. The main difficulty in extending the existing B-eS for $S5$ to public announcement logic is to account announcements of the form $[ψ]ϕ$, which, in this setting, update the modal relations on bases. We provide a detailed analysis of two classical examples, namely the three-player card game and the muddy children puzzle. These examples illustrate how the inferentialist perspective requires fully explicit information about the state of the participating agents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15775 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inferentialist Public Announcement Logic: Base-extension Semantics Eckhardt, Timo Pym, David J. Logic Proof-theoretic semantics, and base-extension semantics in particular, can be seen as a logical realization of inferentialism, in which the meaning of expressions is understood through their use. We present a base-extension semantics for public announcement logic, building on earlier work giving a base-extension semantics for the modal logic $S5$, which in turn builds on earlier such work for $K$, $KT$, $K4$, and $S4$. These analyses rely on a notion of `modal relation' on bases. The main difficulty in extending the existing B-eS for $S5$ to public announcement logic is to account announcements of the form $[ψ]ϕ$, which, in this setting, update the modal relations on bases. We provide a detailed analysis of two classical examples, namely the three-player card game and the muddy children puzzle. These examples illustrate how the inferentialist perspective requires fully explicit information about the state of the participating agents. |
| title | Inferentialist Public Announcement Logic: Base-extension Semantics |
| topic | Logic |
| url | https://arxiv.org/abs/2411.15775 |