Noetherian Godel logics

Autoři: David Fernández-Duque
Rok vydání: 2022
Typ publikace: Článek v odborném periodiku
Periodikum: Journal of Logic and Computation
Bibliografická citace: AGUILERA, J. P., BYDŽOVSKÝ, J., FERNÁNDEZ-DUQUE, David. Noetherian Godel logics. Journal of Logic and Computation. 2022, 32(8), 1487-1503. ISSN 0955-792X. E-ISSN 1465-363X
Dostupné z: doi:10.1093/logcom/exac064.
DOI: 10.1093/logcom/exac064
ID: 568283
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Abstrakt

We introduce Noetherian Godel logics, Godel 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 G(down arrow) whose set of truth values is T-down arrow = {0} boolean OR {1/n : n is an element of N\{0}. We compute the complexity of satisfiability and validity for each Noetherian Godel logic and, in particular, in the logic G(down arrow). This yields optimal strengthening of the results of Baaz-Leitsch-Zach and Hajek.