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)

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.

古代西洋より伝わったとされる対称美の分析―黄金比。しかし、本書では葛飾北斎、歌川広重など偉大な日本の先人たちはすでに、黄金比を会得していたことを証明しています。なぜ、北斎がすばらしいのか?なぜ、俳句は 5・7・5なのか?富士山はどの角度から眺めるのが一番美しいのか?すべては黄金比を使い、美の世界を数値化することで見える新たな世界。初めて黄金比を用い、実例を分析した本書は日本初の試み。.

Collection of texts published previously.

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)

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)

Heterogeneous beliefs and decision processes generate positive externalities for social and economic systems, analogous to biodiversity in biological systems. Although some aspects of biodiversity (e.g., pests, parasites and bacteria) can lead to ecological and economic problems, biodiversity provides flows of beneficial ecological services and is widely regarded as a valuable natural resource and informational asset, whose value increases as we learn more and science progresses (Wilson in Bioscience 35(11):700–706, 1985). Heterogeneous beliefs and decision processes (and heterogeneous behaviors they generate) similarly (...) provide flows of beneficial economic services. Behavioral diversity should therefore be seen as a natural resource and informational asset likely to improve human wellbeing in surprising ways in the future. Paternalistic policies motivated by the goal of “correcting” allegedly suboptimal beliefs and behavior that diverge from expert recommendations jeopardize behavioral diversity at a substantial cost to social welfare. The risk of encroaching on this beneficial behavioral heterogeneity with policies that aim to induce behavioral and belief monocultures should be included explicitly as costs when evaluating nudges and other paternalistic policies. (shrink)

Ashok Aklujkar, Indian Sanskritist and Indologist; contributed articles.

This chapter contains section titled: Looking at the Text (T 1.3.14) Three Readings Reconstructions and Speculations References Further Reading.

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)

Actions shape what we see and memorize. A previous study suggested the interaction between motor and memory systems by showing that memory encoding for task-irrelevant items was enhanced when presented with motor-response cues. However, in the studies on the attentional boost effect, it has been revealed that detection of the target stimulus can lead to memory enhancement without requiring overt action. Thus, the direct link between the action and memory remains unclear. To exclude the effect of the target detection process (...) as a potential confounder, this study assessed the benefit of action for memory by separating items from the response cue in time. In our pre-registered online experiment, participants responded to visual Go cues by pressing a key or counting while ignoring No-go cues. In each trial, two task-irrelevant images were sequentially presented after the cue disappearance. After encoding the Go/No-go tasks, participants performed a surprise recognition memory test for those images. Importantly, we quantified the impact of overt execution of the action by comparing memories with and without motor response and the impact of covert motor processes by comparing memory between the motor and cognitive tasks. The results showed no memory differences between Go and No-go trials in the motor task. This means that the execution itself was not critical for memory enhancement. However, the memory performance in the motor No-go trials was higher than that in the cognitive No-go trials, only for the items presented away from the cues in time. Therefore, engaging the motor task itself could increase incidental memory for the task-irrelevant items compared to a passive viewing situation. We added empirical evidence on the online interaction between action and memory encoding. These memory advantages could be especially brought in action preparation and planning. We believe this fact may expand our present understanding of everyday memory, such as active learning. (shrink)

We examined amygdala subregion volumes in patients with a first episode of major depression and in healthy subjects. Covariate-adjusted linear regression was performed to compare the MD and healthy groups, and adjustments for age, gender, and total estimated intracranial volume showed no differences in amygdala subregion volumes between the healthy and MD groups. Within the MD group, we examined the association between amygdala subregion volume and the 17-item Hamilton Rating Scale for Depression score and the HAMD subscale score, and found (...) no association in the left amygdala. In the right amygdala, however, there was an inverse linear association between the HAMD total and the HAMD core and lateral nucleus and anterior-amygdaloid-regions. Furthermore, an inverse linear association was seen between the HAMD psychic and the lateral nucleus, anterior-amygdaloid-regions, transition, and whole amygdala. The findings of this study suggest that the severity of MD and some symptoms of MD are associated with right amygdala volume. There have been few reports on the relationship between MD and amygdala subregional volume, and further research is needed to accumulate more data for further validation. (shrink)

A demanding introduction to logic and critical thinking, this book offers more traditional means of teaching the art of reasoning at a time when the field has become almost mathematical. Francis Dauer has rethought the framework for teaching reasoning in general and formal logic in particular, the desired epistemological context, and the role of the fallacies. The result is a coherent and very readable work, informed by Dauer's extensive experience teaching and writing on the subject.

Some spatio-temporal structures are easier to transfer implicitly in sequential learning. In this study, we investigated whether the consistent reversal of triads of learned components would support the implicit transfer of their temporal structure in visuomotor sequence learning. A triad comprised three sequential button presses ([1][2][3]) and seven consecutive triads comprised a sequence. Participants learned sequences by trial and error, until they could complete it 20 times without error. Then, they learned another sequence, in which each triad was reversed ([3][2][1]), (...) partially reversed ([2][1][3]), or switched so as not to overlap with the other conditions ([2][3][1] or [3][1][2]). Even when the participants did not notice the alternation rule, the consistent reversal of the temporal structure of each triad led to better implicit transfer; this was confirmed in a subsequent experiment. These results suggest that the implicit transfer of the temporal structure of a learned sequence can be influenced by both the structure and consistency of the change. (shrink)

This study adopted an empirical method to investigate lay people’s attitudes toward the bioethical issues of human-animal chimeric brains. The results of online surveys showed that (1) people did not entirely reject chimeric brain research, but showed slightly more negative responses than ordinary animal testing; and that (2) their ethical concerns arose in connection with the perception that chimerism in the brain would humanize the animal. This means that people’s psychology was consistent with the ethical argument that crossing the human-animal (...) boundary would bring moral confusion to our society. Meanwhile, it was not in line with another argument that moral status depended on having high capacities, and that chimerism would cause a problem if it enhanced animals’ capacities. Furthermore, this study analyzed additional psychological factors related to people’s moral judgment and the relationship among those factors. Several psychological factors, such as the perception that chimeric brain research is unnatural, were identified as mediating the relationship between perception of animal humanization and ethical concerns about creating and using chimeric brains. Introducing an empirical approach to the ethics of human-animal chimeric brains brought two findings: (1) this study informed us of socially shared intuition regarding this novel technology; and (2) it unveiled the psychological processes behind people’s ethical concerns in more detail than they spontaneously mentioned. These findings will help to build normative arguments and future policies that are understandable and acceptable to society. (shrink)