Quantified Propositional Gödel Logics

It is shown that Gqp↑, the quantified propositional Gödel logic based on the truth-value set V↑ = {1 - 1/n : n≥1}∪{1}, is decidable. This result is obtained by reduction to Büchi's theory S1S. An alternative proof based on elimination of quantifiers is also given, which yields both an axiomatization and a characterization of Gqp↑ as the intersection of all finite-valued quantified propositional Gödel logics

“TEMPRANDO COL DOLCE L’ACERBO”: INSTRUMENTAL AND VOCAL POLYPHONY IN THE ‘COMMEDIA’

This essay tracks the historical-musicological context of the lemma “organi” / “organo” as it appears in Purg. 9.144 and Par. 17.44. Drawing from medieval treatises and monks’ descriptions such as Raban Maur, Notkerus Balbulus, Baldric of Dol, Aelred of Rievaulx, and Wulstan, the author uses intertextual evidence to show that Purg. 9.144 (“quando a cantar con organi si stea”) evokes a great pipe organ as was found in some medieval churches. The essay also argues that Par. 17.43–44 (“come viene ad orecchia / dolce armonia da organo”) should be understood as a polyphonic organum that serves the two-fold purpose of lending authority to the Commedia’s longest prophecy and of musically representing the harmonious reconciliation of the highs and lows in human life

Il dolce ruggito del tuono : per un'interpretazione di Purgatorio IX, 144 e Paradiso XVII, 44

In questo saggio si esplora il contesto storico-musicologico dell'organo inteso sia come strumento musicale sia come composizione polifonica, al fine di offrire un'interpretazione dei passi della Commedia in cui appare il lemma 'organi' / 'organo' (Purg. IX, 144 e Par. XVII, 44).Il saggio dimostra che nel primo caso, alle porte del purgatorio che si aprono, il poeta fa riferimento alle descrizioni formulaiche dei grandi organi medievali che producevano un suono potente e non privo di asperità dissonanti. Attingendo a fonti trattatistiche e monastiche, si documenta il contesto storico di Purg. IX e Par. XVII leggendo il primo come strumento musicale a canne e il secondo come musica polifonica.This essay explores the historico-musicological context of organum, both as musical instrument and polyphonic song. The essay thus proposes an interpretaion of two passages of the Commedia in which the term 'organi' / 'organo' appears (Purg. IX, 144 e Par. XVII, 44).The essay shows that Dante, in the Purgatorial passage, refers to formulaic descriptions of great church organs, which produced a powerful and disconcerting sound.Drawing from medieval treatises and monastic sources, the article interprets "organi" in Purg. IX as the pipe instrument and "organo" in Par. XVII as vocal polyphony