Noetherian Gödel logics
| Autor: | Juan Pablo Aguilera, Jan Bydžovský, David Fernández-Duque |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Journal of Logic and Computation. 32:1487-1503 |
| ISSN: | 1465-363X 0955-792X |
| DOI: | 10.1093/logcom/exac064 |
| Popis: | We introduce Noetherian Gödel logics, Gödel logics where the set of truth values is a closed subset of $[0,1]$ containing $0$ and $1$ and without any infinite ascending sequences. There are infinitely many such logics, including the well-known logic $\textsf {G}^\downarrow $ whose set of truth values is $T_\downarrow = \{0\}\cup \{1/n:n\in \mathbb {N}\setminus \{0\}\}$. We compute the complexity of satisfiability and validity for each Noetherian Gödel logic and, in particular, in the logic $\textsf {G}^\downarrow $. This yields optimal strengthening of the results of Baaz–Leitsch–Zach and Hájek |
| Databáze: | OpenAIRE |
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