Logical implications are closely related to modal operators. Lattice-valued logic LL and quantum logic QL were formulated in Titani S (1999) Lattice Valued Set Theory. Arch Math Logic 38:395–421, Titani S (2009) A Completeness Theorem of Quantum Set Theory. In: Engesser K, Gabbay DM, Lehmann D (eds) Handbook of Quantum Logic and Quantum Structures: Quantum Logic. Elsevier Science Ltd., pp. 661–702, by introducing the basic implication → which represents the lattice order. In this paper, we fomulate a predicate orthologic provided (...) with the basic implication, which corresponds to complete ortholattices, and then formulate a quantum logic which is equivalent to QL, by using a modal operator instead of the basic implication. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Awesome Nightfall: The Life, Times, and Poetry of SaigyōMichiko YusaAwesome Nightfall: The Life, Times, and Poetry of Saigyō. By William R. LaFleur. Boston: Wisdom Publications, 2003. Pp. ix + 173. Paper $14.95.A quarter of a century ago William LaFleur published his book on Saigyō, Mirror for the Moon, which the present work, Awesome Nightfall: The Life, Times, and Poetry of Saigyō, thoughtfully and masterfully supersedes. In this connection (...) I may mention the philosopher, Nishida Kitarō, whose Zen no kenkyū (An inquiry into the good) was reprinted in 1936, twenty-five years after its first publication. On that occasion Nishida, deeply moved by the thought that his earliest work was still being read, expressed his sentiment by quoting the last two lines of one of Saigyō's poems: [End Page 270]Toshitaketemata koyubeshitoomoikiyaInochi narikeriSaya no NakayamaDid I ever imagineIn my advanced ageI should cross once againThis mountain pass of Saya-no-Nakayama?Ah, it is all thanks to having lived a long life!1(Saigyō composed this poem on going for the second time to Mutsu, the northern region of Japan, forty-two years after his first visit there.)As LaFleur notes, a number of important works on Saigyō's life and his times have been published in Japan in the last two decades, which these offer us more complete sketches of his life and allow an appreciation of his poetry to a greater depth. In the first part of the book, "The Life and Times of Saigyō," the author succinctly incorporates many of these findings and relates Saigyō's poems both to historical events and to his personal life experience (pp. 1-70). The second half of the book contains LaFleur's translation of over 150 poems by Saigyō, all of which appear to be taken from his earlier book (pp. 73-152).LaFleur shows how Saigyō's life (1118-1190) was closely linked to the historical context. The time was fast changing from the insei system (political administration run by the court of the retired emperor) to the Hōgen and Heiji Disturbances, the fierce power struggle between the Taira and the Minamoto military clans, with the dramatic demise of the former and the end of the Heian period. Saigyō's path crossed with such eminent political figures as Taira no Kiyomori in 1172 and Minamoto no Yoritomo in 1186. By juxtaposing historical events with Saigyō's poems, which often bear headnotes describing the circumstances under which he composed them, a full-fledged biography of Saigyō promises to be in the offing.In the present work, LaFleur sketches Saigyō's life in bold strokes and introduces new findings for the English-reading audience, such as the homoeroticism that dominated the court of the retired Emperor Toba (1103-1156)—although Saigyō himself does not appear to have been a member of this coterie.2 LaFleur also draws our attention to the fact that Saigyō practiced religious austerities at Mt. Kōya and Ōmine (pp. 20-21). Going beyond a rather two-dimensional image of Saigyō as a nature-loving poet of the moon and the flowers, the present study presents a picture of a man caught in an impossible love affair; a highly skilled equestrian, archer, and kemari (a sort of kickball) player; and a man who caused a sensation by renouncing the world at the young age of twenty-three despite his promising career as an imperial guard. Saigyō's mental and physical strength, honed by his mountain asceticism, no doubt was essential in his making extensive journeys far and wide. We also see that the distance Saigyō created from the political arena by becoming a monk gave him a keener eye to assess the fundamental political changes that were then taking [End Page 271] place. The full import of his poems, dealing with warfare, emperors, and the court, cannot be understood when separated from the political events of the day, although Saigyō himself maintained his cool objectivity and distanced himself from them.The tantalizing speculation that Saigyō was infatuated with Empress Taikenmon'in, Emperor Toba's consort and Emperor Sutoku's mother, is highly probable... (shrink)