This paper provides a logic framework for investigations of game theoretical problems. We adopt an infinitary extension of classical predicate logic as the base logic of the framework. The reason for an infinitary extension is to express the common knowledge concept explicitly. Depending upon the choice of axioms on the knowledge operators, there is a hierarchy of logics. The limit case is an infinitary predicate extension of modal propositional logic KD4, and is of special interest in applications. In Part I, (...) we develop the basic framework, and show some applications: an epistemic axiomatization of Nash equilibrium and formal undecidability on the playability of a game. To show the formal undecidability, we use a term existence theorem, which will be proved in Part II. (shrink)

dai 1-kan. Kōshitsu hen. Kokka shakai hen. Gunji hen. Shisō hen. Kyōkun hen. Shūkyō hen -- dai 2-kan. Gakugei hen. Keizai sangyō hen. Shūyō hen. Ningen hen -- dai 3-kan. Undō kyōgi shumi hen. Katei hen. Daihyō ijin jūninin kun.

This paper provides a Genzten style formulation of the game logic framework GLm (0 m ), and proves the cut-elimination theorem for GLm. As its application, we prove the term existence theorem for GL used in Part I.

Kaneko-Suzuki developed epistemic logics of shallow depths with multiple players for investigations of game theoretical problems. By shallow depth, we mean that nested occurrences of belief operators of players in formulae are restricted, typically to be of finite depths, by a given epistemic structure. In this paper, we develop various methods of surgical operations (cut and paste) of epistemic world models. An example is a bouquet-making, i.e., tying several models into a bouquet. Another example is to engraft a model to (...) some branches of another model. By these methods, we obtain various meta-theorems on semantics and syntax on epistemic logics. To illustrate possible uses of our meta-theorems, we present one game theoretical theorem, which is also a meta-theorem in the sense of logic. (shrink)

We show the faithful embedding of common knowledge logic CKL into game logic GL, that is, CKL is embedded into GL and GL is a conservative extension of the fragment obtained by this embedding. Then many results in GL are available in CKL, and vice versa. For example, an epistemic consideration of Nash equilibrium for a game with pure strategies in GL is carried over to CKL. Another important application is to obtain a Gentzen-style sequent calculus formulation of CKL and (...) its cut-elimination. The faithful embedding theorem is proved for the KD4-type propositional CKL and GL, but it holds for some variants of them. (shrink)

In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as fixed-point ones and infinitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among them are still unclear. The purpose of this paper is to draw a map showing the relationships among them. In the propositional case, these extensions turn out to be all Kripke complete and can be comparable in a meaningful manner. F. Wolter (...) showed that the predicate extension of the Halpern-Moses fixed-point type common knowledge logic is Kripke incomplete. However, if we go further to an infinitary extension, Kripke completeness would be recovered. Thus there is some gap in the predicate case. In drawing the map, we focus on what is happening around the gap in the predicate case. The map enables us to better understand the common knowledge logics as a whole. (shrink)

日本人は「死」にどう向き合うべきなのか。西洋との違い、仏教の影響、私たちの古層にある死生観―社会思想の大家による渾身の論考.

We develop a series of small infinitary epistemic logics to study deductive inference involving intra-/interpersonal beliefs/knowledge such as common knowledge, common beliefs, and infinite regress of beliefs. Specifically, propositional epistemic logics GL are presented for ordinal α up to a given αo so that GL is finitary KDn with n agents and GL allows conjunctions of certain countably infinite formulae. GL is small in that the language is countable and can be constructive. The set of formulae Lα is increasing up (...) to α = ω but stops at ω We present Kripke-completeness for GL for each α ≤ ω, which is proved using the Rasiowa–Sikorski lemma and Tanaka–Ono lemma. GL has a sufficient expressive power to discuss intra-/interpersonal beliefs with infinite lengths. As applications, we discuss the explicit definability of Axioms T, 4, 5, and of common knowledge in GL Also, we discuss the rationalizability concept in game theory in our framework. We evaluate where these discussions are done in the series GL, α ≤ ω. (shrink)

The neuromodulatory effects of brain stimulation therapies notably involving repetitive transcranial magnetic stimulation on nocturnal sleep, which is critically disturbed in major depression and other neuropsychiatric disorders, remain largely undetermined. We have previously reported in major depression patients that prefrontal rTMS sessions enhanced their slow wave activity power, but not their sigma power which is related to sleep spindle activity, for electrodes located nearby the stimulation site. In the present study, we focused on measuring the spindle density to investigate cumulative (...) effects of prefrontal rTMS sessions on the sleep spindle activity. Fourteen male inpatients diagnosed with medication-resistant unipolar or bipolar depression were recruited and subjected to 10 daily rTMS sessions targeting the left dorsolateral prefrontal cortex. All-night polysomnography data was acquired at four time points: Adaptation, Baseline, Post-1, and Post-2. Clinical and cognitive evaluations were longitudinally performed at Baseline, Post-1, and Post-2 time points to explore associations with the spindle density changes. The PSG data from 12 of 14 patients was analyzed to identify sleep spindles across the sleep stages II–IV at four electrode sites: F3, F4, P3, and P4. Statistical analysis by two-way ANOVA revealed that spindle density at F3 increased at Post-1 but decreased at Post-2 time points. Moreover, the local and transient increase of spindle density at F3 was associated with the previously reported SWA power increase at F3, possibly reflecting a shared mechanism of thalamocortical synchronization locally enhanced by diurnal prefrontal rTMS sessions. Clinical and cognitive correlations were not observed in this dataset. These findings suggest that diurnal rTMS sessions transiently modulate nocturnal sleep spindle activity at the stimulation site, although clinical and cognitive effects of the local changes warrant further investigation. (shrink)

BackgroundBoth impairment and sex differences in social cognition and neurocognition have been documented in schizophrenia. However, whether sex differences exist in the association between social cognition and neurocognition are not known. We aimed to investigate the contribution of areas of neurocognition to theory of mind and hostility bias, representing social cognition, according to sex in early course schizophrenia.MethodsIn this cross-sectional study, we assessed neurocognition using the Japanese version of the Brief Assessment of Cognition in Schizophrenia and assessed the ToM and (...) hostility bias subdomains of social cognition using the Social Cognition Screening Questionnaire in 131 participants diagnosed with schizophrenia within 5 years of onset. Sex differences were analyzed using t-tests. The associations of neurocognitive subdomains with ToM and hostility bias according to sex were analyzed using multiple regression analysis. Results were adjusted by age, estimated premorbid intelligence quotient, and symptomatology.ResultsNo sex differences were found in ToM or hostility bias. Higher verbal fluency was significantly associated with higher ToM in females, whereas higher executive function was significantly associated with higher ToM in males. Higher verbal fluency was significantly associated with lower hostility bias in females, whereas neurocognition and hostility bias were not significantly associated in males.ConclusionThe results suggest that neurocognition associated with social cognition differ according to sex. These differences should be considered for more effective treatment of social cognition. (shrink)

Nowadays virtual reality has gained extreme popularity among adolescents around the world, thanks to the possibility they offer to create a new life for their users. Especially for teenagers affected by the hikikomori syndrome, who experience struggles in establishing communication with others, virtual reality has become a tool to forsake their “adverse” reality, shaping fictitious safe environments and creating relationships with similar-minded users. This issue of virtual reality has been depicted in recent Japanese animation, whose country is mostly affected by (...) this issue. I will show mainly two approaches to the phenomenon: the one given in the anime series Sword Art Online (2012), in which virtual reality is perceived as the only place where true communication can happen; the second is the interpretation given by director Hosoda Mamoru in his animated features Summer Wars (2009) and Belle (2021), where virtual reality is a tool to support real life’s difficulties. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Fabuler la fin du monde: La puissance critique des fictions d’apocalypse by Jean-Paul EngélibertCyril CamusJean-Paul Engélibert. Fabuler la fin du monde: La puissance critique des fictions d’apocalypse [Fabulating the end of the world: The critical power of apocalypse fiction]. Paris: Éditions La Découverte, 2019. 239 pp. Print. 20€. ISBN 978-2-348-03719-1.Jean-Paul Engélibert is a well-established expert on apocalyptic and postapocalyptic fiction. His exploration of the genre thus far includes (...) the monograph Apocalypses sans royaume: Politique des fictions de la fin du monde, XX–XXIe siècles (2013), numerous articles, as well as the essay collection L’Apocalypse: Une imagination politique, XIXe–XXIe siècles (2018), which he co-edited. In his latest book, Fabuler la fin du monde, he returns to several texts and aspects of the genre previously covered, delving deeper into what he calls “fictions of the end of the world.” In the ten chapters, gathered in five parts, he approaches his subject as a seasoned scholar in the field of comparative literature, and his analysis draws from comparisons between modern fiction’s representation of apocalypse and biblical literature’s visions of apocalypse and messianism. The book also offers ecocritical insights into the specter of Anthropocenic manifestations in fiction, with reflections on the interrelated genres of utopia and dystopia, theories of cinema, and philosophical writings on the catastrophic history of the twentieth and twenty-first centuries.The range of fictional works discussed is wide, including Jean-Baptiste Cousin de Grainville’s Le dernier homme (1805); Mary Shelley’s Frankenstein (1818); Émile Souvestre’s Le monde tel qu’il sera (1846); Didier de Chousy’s Ignis (1883); Robert Merle’s Malevil (1972); José Saramago’s Blindness (1995); Antoine Volodine’s Minor Angels (1999); Don DeLillo’s Cosmopolis (2003); Cormac McCarthy’s The Road (2006); Céline Minard’s Le dernier monde (2007); Davide [End Page 163] Longo’s The Last Man Standing (2010); and Margaret Atwood’s MaddAddam trilogy (Oryx and Crake [2003], The Year of the Flood [2009], and MaddAddam [2013]). Engélibert also touches on feature-length movies such as Stanley Kramer’s On the Beach (1959), Lars von Trier’s Melancholia (2011), Abel Ferrara’s 4:44 Last Day on Earth (2012), and Mamoru Oshii’s Ghost in the Shell (1995), as well as on other literary and audiovisual fictions, such as E. M. Forster’s short story “The Machine Stops” (1909), Edward Bond’s dramatic trilogy The War Plays (1985), and the first season (2014) of Damon Lindelof and Tom Perrotta’s TV series The Leftovers (2014–17).Engélibert’s exegeses of the genre build around two aspects of the evolving relationship of apocalyptic narratives to the context of their production. Apocalypse (in the sense of “the end of the world” rather than the etymological sense of “revelation”) is no longer primarily a religious myth: the creation and use of the atomic bomb during the Second World War, the theorization of the Anthropocene, and the mainstreaming of concerns over climate change have made the term “apocalypse” a very real, tangible prospect for the future. Engélibert relies on Günther Anders’s Die atomare Drohung (1981) to highlight the importance of the A-bomb in bringing home the reality of potential annihilation to people’s collective consciousness. Yet his second contextual/historical point is that the Anthropocene (albeit unnamed at the time) actually started with the Industrial Revolution, and that thinkers and polemicists such as Charles Fourier or Eugène Huzar, as well as contemporary fiction writers, were already acknowledging the environmental impact of humans and their economic/industrial/technological activity as threats to human and nonhuman life, and to the health of the planetary system itself.1Citing the work of Jean-Baptiste Fressoz and Christophe Bonneuil on the history of climate science, Engélibert analyzes in detail several nineteenth-century novels (namely Le Dernier homme, Frankenstein, Le monde tel qu’il sera, and Ignis) and one early-twentieth-century story (Forster’s “The Machine Stops”) that denounce the harm that the idol of the time, Progress, was already wreaking on nature and human life... (shrink)

In Japan during the 1980s, there was an interesting debate about how to teach the area of a parallelogram effectively to primary school children. Yutaka Saeki criticized the standard method, which relies on a cut-and-paste procedure. He argued that the standard method inevitably failed to convince children because it does not provide any cogent reason for them to accept that the formula ‘base x height’ is indeed true. Saeki proposed his own method using a bundle of paper. This (...) method, however convincing at first glance, was totally dismissed by Akira Nakagaki based on his orthodox scientific methodology. There emerged a lively debate between the two. By means of a reconstruction of this debate, this paper will show how the materiality of a thing can scaffold the process of gaining understanding of the concept of geometrical space. Although Saeki and Nakagaki were both unaware of the fact, the debate between them shows clearly that the convincing points of Saeki’s method rely on its material basis. The materiality of a thing can serve as a common basis, in which acquaintance in the context of everyday life is transgressed to the mathematical context. With this transgressive structure entailed in the materiality of a thing, children can be led to understand the spatial logic of the parallelogram, while they themselves make their own reasoning and judgement based on the context of their everyday lives. (shrink)

A post-photographic cinema. The myth of "the myth of total cinema" -- The matrix: "a prison for your mind" -- The new realness -- Quid est veritas: the reality ofunspeakable suffering -- Social network -- Postscript: total cinema redux -- A chronicle of theBush years. 2001: after September 11 -- 2002: the war on terror begins -- 2003: invading Iraq-- 2004: Bush's victory -- 2005: looking for the Muslim world -- 2006: September 11, theanniversary -- 2007: what was Iraq and (...) where? -- 2008: the election -- Notes toward a syllabus.In praise of love (Jean-Luc Godard, 2001) -- Avalon (Mamoru Oshii, 2001) -- Avant-garde goesdigital: Corpus callosum, Cotton Candy, and Razzle Dazzle -- Russian ark (AlexanderSokurov,2002) -- Ten (Abbas Kiarostami, 2002) -- Goodbye Dragon Inn (Tsai Ming-Liang,2002) -- Dogville (Lars Von Trier, 2003) -- The world (Jia Zhangke, 2004) -- Battle in heaven(Carlos Reygadas, 2005) -- The death of Mr. Lazarescu (Cristi Puiu, 2005) -- Day night daynight (Julia Loktev, 2006) -- Southland tales (Richard Kelly, 2006) -- Inland empire (DavidLynch, 2006) -- Between darkness and light (after William Blake) (Douglas Gordon, 1997/2006)-- Lol (Joe Swanberg, 2006) -- Flight of the red balloon (Hou Hsiao-Hsien, 2007) -- Hunger(Steve McQueen, 2008) -- Opening ceremonies, Beijing Olympics (August 8, 2008) -- Carlos(Olivier Assayas, 2010) -- The strange case of Angelica (Manoel de Oliveira, 2010) -- Onceupon a time in Anatolia (Nuri Bilge Ceylan, 2011). (shrink)