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.

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)

The author proposes the development of systems learning guidebooks to accompany famous children's classic books. Children's classic books can make excellent bases for children's learning guidebooks on systems thinking and global ecology, because they are fun to read and well known worldwide. If such learning guidebooks are properly designed with humor and entertaining aspects, they could stimulate children to learn more about systems thinking. Lewis Carroll's Alice's Adventures in Wonderland is chosen as a pilot case for developing such a children's (...) guidebook. The systems learning guidebook that accompanies Alice's Wonderland shall be entitled Alice in Systems Wonderland and will help its readers look at the Alice's Wonderland story with a systems perspective. (shrink)

As its name implies, Vasubandhu’s _Vyākhyāyukti_ (VyY) explains the logic or methodology (_yukti_) of exegesis or sūtra interpretation (_vyākhyā_) and only survives in a Tibetan translation. In recent years, research on this treatise has been gradually accumulating. However, due to the difficulty of the Tibetan translation, some of the arguments therein have been misunderstood. In this article, after reviewing the general framework of Vasubandhu’s method of interpreting the sūtras, I will present a newly discovered parallel regarding his discussion of the (...) “purpose, _prayojana_” of the sūtras and reread it through a close philological examination of various sources in Sanskrit and Tibetan. Thus, this article will first elucidate the details of Vasubandhu’s explanation of the purpose of the Buddha’s preaching using synonyms and will clarify an aspect of his views on the Buddha’s word. In addition, concerning this “purpose,” I will elucidate the characteristics of the final chapter of this text, which provides stories about hearing the Buddha’s words with respect. By doing so, I would like to reveal the characteristics of the VyY as a manual for vivid preaching. (shrink)

It is one of the peculiar features of the movement of translation of Western scientific treatises from Dutch into Japanese, known as Dutch learning , that if first originated in Nagasaki with a group of Japanese interpreters. This group differed from the scholarly community of the capital, Edo, by both training and social status. This article shows how this difference contributes to explaining some of the particularities of rangaku in its initial phase. A case in point is Shizuki Tadao's introduction (...) of Newtonian physics and astronomy. Yet, Sugita Genpaku, a major representative of the Edo scholarly community, gave an account of the beginning of Dutch learning that attempted to minimise, or even to erase, the contribution of the Nagasaki interpreters, who were dismissed as unscholarly. This attempt, too, is best understood in the light of the difference between the two communities. (shrink)

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)

Iron Eyes: The Life and Teachings of Obaku Zen Master Tetsugen Doko, Helen J. Baroni, pp. ix+259, ISBN 0-7914-6892-5.

Media, politicians, and the courts portray college campuses as divided over diversity and affirmative action. But what do students and faculty really think? This book uses a novel technique to elicit honest opinions from students and faculty and measure preferences for diversity in undergraduate admissions and faculty recruitment at seven major universities, breaking out attitudes by participants' race, ethnicity, gender, socio-economic status, and political partisanship. Scholarly excellence is a top priority everywhere, but the authors show that when students consider individual (...) candidates, they favor members of all traditionally underrepresented groups - by race, ethnicity, gender, and socio-economic background. Moreover, there is little evidence of polarization in the attitudes of different student groups. The book reveals that campus communities are less deeply divided than they are often portrayed to be; although affirmative action remains controversial in the abstract, there is broad support for prioritizing diversity in practice. (shrink)

Mediator is a coregulatory complex that plays essential roles in multiple processes of transcription regulation. One of the human Mediator subunits, MED26, has a role in recruitment of the super elongation complex (SEC) to polyadenylated genes and little elongation complex (LEC) to non‐polyadenylated genes, including small nuclear RNAs (snRNAs) and replication‐dependent histone (RDH) genes. MED26‐containing Mediator plays a role in 3′ Pol II pausing at the proximal region of transcript end sites in RDH genes through recruitment of Cajal bodies (CBs) (...) to histone locus bodies (HLBs). This finding suggests that Mediator is involved in the association of CBs with HLBs to facilitate 3′ Pol II pausing and subsequent 3′‐end processing by supplying 3′‐end processing factors from CBs. Thus, we argue the possibility that Mediator is involved in the organization of nuclear bodies to orchestrate multiple processes of gene transcription. (shrink)