In this paper we give an axiom system of a logic which we call an approximation logic (AL), whose Lindenbaum-Tarski algebra is a strong Bunge algebra (or simply s-Bunge algebra), and show thatFor every s-Bunge algebra , a quotient algebra by a maximal filter is isomorphic to the simplest nontrivial s-Bunge algebra ;The Lindenbaum algebra of AL is an s-Bunge algebra;AL is complete;AL is decidable.

本書は、生活者のハピネス(豊かさや幸せ)の視点から科学技術や社会の変革を考える『因果関係から相関へ、個別技術からシステムへ』と題した『武田シンポジウム2018』の内容をまとめたものです。昨今最も注目を 浴びている科学技術である「AI」、「免疫システム研究」、「民間宇宙ロケット開発」の3つと異なる切り口から、ビッグデータと言われる時代の科学の方法論、個の集積以上の意味をもつシステムとしてのアプローチに ついて立体的に考察します。.

Fuzzy logic has become an important tool for a number of different applications ranging from the control of engineering systems to artificial intelligence. In this concise introduction, the author presents a succinct guide to the basic ideas of fuzzy logic, fuzzy sets, fuzzy relations, and fuzzy reasoning, and shows how they may be applied. The book culminates in a chapter which describes fuzzy logic control: the design of intelligent control systems using fuzzy if-then rules which make use of human knowledge (...) and experience to behave in a manner similar to a human controller. Throughout, the level of mathematical knowledge required is kept basic and the concepts are illustrated with numerous diagrams to aid in comprehension. As a result, all those curious to know more about fuzzy concepts and their real-world application will find this a good place to start. (shrink)

Court judgments contain valuable information on how statutory laws and past court precedents are interpreted and how the interdependence structure among them evolves in the courtroom. Data-mining the evolving structure of such customs and norms that reflect myriad social values from a large-scale court judgment corpus is an essential task from both the academic and industrial perspectives. In this paper, using data from approximately 110,000 court judgments from Japan spanning the period 1998–2018 from the district to the supreme court level, (...) we propose two tasks that grasp such a structure from court judgments and highlight the strengths and weaknesses of major machine learning models. One is a prediction task based on masked language modeling that connects textual information to legal codes and past court precedents. Another is a dynamic link prediction task where we predict the hidden interdependence structure in the law. We make quantitative and qualitative comparisons among major machine learning models to obtain insights for future developments. (shrink)

The Christian philosopher Muto Kazuo contributed substantially to the predominantly Buddhist “Kyoto School of Philosophy.” Through critical exchange with its representatives, he opened up new perceptions of Christian faith, enabled mutual understanding between Buddhism and Christianity, and challenged the Western dialectical method.

Since the discovery that the characteristics of dreaming sleep are far stronger in Stage 1 rapid eye movement sleep than in any other biological state, investigators have attempted to determine the relative responsibility of the tonic versus the phasic properties of REM sleep for the different characteristics of dreaming–features such as the amount of information in the dream report, the brightness and clarity of the visual images, shifts in thematic continuity, and incongruities of image and meaning. The present experiment is (...) designed to identify dream characteristics that are specifically associated with tonic changes in level of cortical activation within sleep. It samples reports of imagery and thought during spontaneous variations within one phase of the 24-h diurnal rhythm and across the REM-NREM sleep cycle in order to identify the independent and joint contributions of the two cycles to imagery and thought. The rising phase of the diurnal cycle in the late night and morning was estimated from clock time during the late night and early morning and was varied by delaying the sleep onset and waking time of the subjects. Considered together with other studies, the results suggest that the major determinant of vivid visual imagery and enhanced cognitive activity during sleep is a pattern of subcortical and cortical activation that is common to both the REM phase of the REM-NREM cycle and the activated phase of the 24-h diurnal wake-sleep cycle. (shrink)

京都を知る，アルゴリズムを知る。アルゴリズムとはそもそも，何か物事を行うときの“具体的手順”のことである。私たちは日々，意識するかしないかに関わらず，次々とアルゴリズムの設計をしながら生活をしている。 本書は，岩間一雄教授が京都の町を題材にアルゴリズムの思考を伝える，読み物的手法をとった数学書である。読者はその奥深い世界へと誘われてゆくだろう。 巻末には本書で取り上げた京都関連の名所・行事などの索引があり，逆引きで読んでいくことができる。 【目次】 1．斜め横断 2．アイドルタイム 3．人事部長の悩み 4．チームワーク 5．神様との勝負 6．アルゴリズムからメカニズムへ 7．一番でなくとも 8．千年に1回も起こらない 9．自分のページランクを上げたい 10．対話のアルゴリズム 11．ビットコインの素晴らしさ 12．P対NP問題：ノーベル賞以上？ 13．アルゴリズムから見た進化論.

日本古来の神々の色、陰陽五行説の色、武将たちに愛された色、雅な平安の色、粋な大江戸の色彩から、昭和の流行色まで、ビジュアルで辿る日本の色を探る旅。.

In this paper we shall first show that for every weak DeMorgan algebra $L$ of order $n$ , there is a quotient weak DeMorgan algebra $L{\sim}$ which is embeddable in the finite WDM-$n$ algebra $\Omega $. We then demonstrate that the finite WDM-$n$ algebra $\Omega $ is functionally free for the class $CL$ of WDM-$n$ algebras. That is, we show that any formulas $f$ and $g$ are identically equal in each algebra in $CL$ if and only if they are identically (...) equal in $\Omega $. Finally we establish that there is no weak DeMorgan algebra whose quotient algebra by a maximal filter has exactly seven elements. (shrink)