CINECA IRIS Institutional Research Information System
IRIS è la piattaforma adottata dall’Università degli Studi di Udine per gestire l’archivio aperto dei prodotti della ricerca. L’archivio contiene articoli, contributi in volume, monografie, interventi pubblicati in atti di convegno, Tesi di dottorato e altri materiali.
EnglishIn classical propositional logic, a theory T is prime (i.e., for every pair of formulas F,G, either T⊢F→G or T⊢G→F) iff it is complete. In Lukasiewicz infinite-valued logic the two notions split, completeness being stronger than primeness. Using toric desingularization algorithms and the fine structure of prime ideal spaces of free ℓ-groups, in this paper we shall characterize prime theories in infinite-valued logic. We will show that recursively enumerable (r.e.) prime theories over a finite number of variables are decidable, and we will exhibit an example of an undecidable r.e. prime theory over countably many variables.
| Titolo: | Decidable and undecidable prime theories in infinite-valued logic | |
| Autori: | ||
| Data di pubblicazione: | 2001 | |
| Rivista: | ||
| Abstract: | In classical propositional logic, a theory T is prime (i.e., for every pair of formulas F,G, either T⊢F→G or T⊢G→F) iff it is complete. In Lukasiewicz infinite-valued logic the two notions split, completeness being stronger than primeness. Using toric desingularization algorithms and the fine structure of prime ideal spaces of free ℓ-groups, in this paper we shall characterize prime theories in infinite-valued logic. We will show that recursively enumerable (r.e.) prime theories over a finite number of variables are decidable, and we will exhibit an example of an undecidable r.e. prime theory over countably many variables. | |
| Handle: | http://hdl.handle.net/11390/674315 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
http://hdl.handle.net/11390/674315
Copyright © 2022