There are close similarities between the Weihrauch lattice and the zoo of axiom systems in reverse mathematics. Following these similarities has often allowed researchers to translate results from one setting to the other. However, amongst the big five axiom systems from reverse mathematics, so far $\mathrm {ATR}_0$ has no identified counterpart in the Weihrauch degrees. We explore and evaluate several candidates, and conclude that the situation is complicated.

The apologetic method of the Nyāya is inductive. The subject is distilled from the scripture and the Nyāya investigates it through logical argument. Through this procedure of partial verification, the reliability of the composer is established, and consequently the authority of the entire scripture is justified. The domains of thescripture and rational investigation overlap in significant issues such as the reality of the Self, and therefore, they can cooperate to establish the common truth. In Mīmāṃsā apologetics, the domain of the (...) scripture and that of rational argument are mutually exclusive. Their apologetic program is basically accomplished as a process of purely rational investigation without referring to the content of the scripture. But at the same time, the authority of the Veda is regarded as innate and has no external basis. Working autonomously, the rational investigation imposes its own limitation from within and thereby secures the scriptural domain that is free from the intervention of any other kind of knowledge. The overlap between the domains of the scripture and the ordinary experience including rational investigation constitutes a necessary condition for the Nyāya apologetics, whereas in Mīmāṃsā apologetics, it is the absence of the overlapping domain that assures the unique authority of the Veda. This difference is supposed to be rooted in their disagreement on whether a man is able, or qualified, to examine the content of the scripture or not. (shrink)

本書の3つの工夫:(1)企業不祥事や長時間労働など、現実のさまざまな問題を取り上げて解説しています。(2)倫理学や経済学を学んだことがなくても読み進められるように、用語の説明を丁寧に行っています。(3 )興味や関心に合わせて読むことができるように、各章のタイトルを問いかけの形式にしています。.

コーシーとワイエルシュトラスによって構築されたε‐σ論法を論理学の基礎から解説。.

AI systems, which receive vast amounts of information including privacy information, are emerging. Protecting the privacy of the general public is an important issue for democracies. In this study, “Public space watched by AI- connected cameras” is taken as an example of an AI-system that is expected to be used for public purposes and has a relatively high privacy violation risk. It is defined as a wide public area where every point is monitored by multiple AI-connected street cameras. The following (...) four socially acceptable applications of “Public space watched by AI- connected cameras” are discussed: (1) Human/vehicle tracking, (2) Watching over children, (3) Detection of abnormal situations, (4) Criminal and terrorist behavior pattern analysis. As for privacy protection measures for AI systems, in addition to reliable protection itself, reliable recording and auditing to deter misuse and abuse is considered a prerequisite to ensure that the general public can feel secure. In this paper, the concept of “Verifiable record of AI output”, which is a verifiable and tamper-proof record and disclosure of AI output is proposed. “Verifiable record of AI output” is based on the idea that it may be more realistic to apply a simple exit control only for AI output to confirm rule conformance, rather than anonymizing huge AI inputs such as Big Data or controlling internal AI processes that are black-boxed. A concrete example of implementing “Verifiable record of AI output” in “Public space watched by AI-connected cameras” is proposed. In the “Verifiable record of AI output”, the AI system is enclosed in an outbound firewall, and only AI outputs that are confirmed to be in line with “the purpose of use approved in advance through social discussion” are allowed to be transmitted. The process from application to permission of transmission is anonymized and disclosed in a verifiable and tamper-proof manner. This public record can be verified by the general public or an auditing organization to ensure that any misuse or abuse of the AI system will be exposed. The “Verifiable record of AI output” proposed in this paper is characterized by reliable measurement and recording of AI output, and its disclosure for auditing purposes. The possibility of using this as a template to apply to other AI systems that receive Big Data input, including the privacy of the general public, is considered. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and (...) made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This paper considers the efficiency of the political market in the California State legislature. I analyzed the property tax limitation voter initiative, Proposition 13. I found that districts which supported Proposition 13 more strongly were more likely to oppose the incumbents regardless of whether the incumbents had the different preferences for property taxes from their districts. I also studied how legislators voted on the bills adopted after the passage of Proposition 13 to finance local governments. I found that legislators tended (...) to follow the constituents tax-cutting message expressed by the passage of Proposition 13. (shrink)

This paper explores preferences and attitudes related to fiscal federalism held by the ASEAN people in the context of environmental issues. Fiscal federalism would predict that local environmental problems will be handled more efficiently by local governments, while national environmental problems will be solved more efficiently by the national government. But it is not obvious whether citizens consider in the same way as economics theory predicts. To unveil this point, I address questions of whether those who have higher consciousness toward (...) environmental issues at the neighbor or local level prefer local governments to decide environment policies, whether those who have more consciousness about environmental issues at the national level prefer the national government to decide the policies, and whether those who have higher consciousness toward environmental problems at global level prefer higher levels government such as the United Nations to decide the policies. By fitting multi-level probit regressions to cross-national survey data collected in ASEAN countries, I found the results supporting the hypotheses. The country analyses show the results which support the hypotheses in Brunei, Indonesia, and the Philippines. (shrink)

In this article, we propose a new classification of $\Sigma ^0_2$ formulas under the realizability interpretation of many-one reducibility (i.e., Levin reducibility). For example, $\mathsf {Fin}$, the decision of being eventually zero for sequences, is many-one/Levin complete among $\Sigma ^0_2$ formulas of the form $\exists n\forall m\geq n.\varphi (m,x)$, where $\varphi $ is decidable. The decision of boundedness for sequences $\mathsf {BddSeq}$ and for width of posets $\mathsf {FinWidth}$ are many-one/Levin complete among $\Sigma ^0_2$ formulas of the form $\exists n\forall (...) m\geq n\forall k.\varphi (m,k,x)$, where $\varphi $ is decidable. However, unlike the classical many-one reducibility, none of the above is $\Sigma ^0_2$ -complete. The decision of non-density of linear orders $\mathsf {NonDense}$ is truly $\Sigma ^0_2$ -complete. (shrink)

This paper generalizes the simple regret model by Bell in Operations Research 30(5), 961-981 and Loomes and Sugden in The Economic Journal 92(368), 805-824 to cope with the situation in which decision outcomes are multi-attributed. We propose a model that combines the simple regret model for ex ante preferences and the additive difference representation for ex post preferences. We first present a necessary and sufficient axiomatization of our model in Savage’s framework. The proposed model is composed of three types of (...) functions. One is a value function for each attribute. The others are attribute-dependent and holistic regret-rejoicing functions that capture trade-offs among value-differences of chosen and forgone outcomes for each attribute and among all attributes, respectively. We then provide constructive procedures for those functions and methods for consistency checks of the procedures. We, finally, conduct an experiment to estimate those functions in the two attributes case by means of the constructive procedure and give an application of the model and our findings. (shrink)

This paper considers a monthly pattern in government spending. I have found that public spending increases at the end of the fiscal year for both the Japanese central government and the US federal government and that the effects are stronger in recent years than in the past. I then propose two hypotheses that would explain why public spending increases at the end of the fiscal year.

Quantum measurement is a physical process. A system and an apparatus interact for a certain time period, and during this interaction, information about an observable is transferred from the system to the apparatus. In this study, we quantify the energy fluctuation of the quantum apparatus required for this physical process to occur autonomously. We first examine the so-called standard model of measurement, which is free from any non-trivial energy–time uncertainty relation, to find that it needs an external system that switches (...) on the interaction between the system and the apparatus. In such a sense this model is not closed. Therefore to treat a measurement process in a fully quantum manner we need to consider a “larger” quantum apparatus which works also as a timing device switching on the interaction. In this setting we prove that a trade-off relation, \, holds between the energy fluctuation \ of the quantum apparatus and the measurement time \. We use this trade-off relation to discuss the spacetime uncertainty relation concerning the operational meaning of the microscopic structure of spacetime. In addition, we derive another trade-off inequality between the measurement time and the strength of interaction between the system and the apparatus. (shrink)

Consider a randomness notion C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}. A uniform test in the sense of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} is a total computable procedure that each oracle X produces a test relative to X in the sense of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}. We say that a binary sequence Y is C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-random uniformly relative to (...) X if Y passes all uniform C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} tests relative to X. Suppose now we have a pair of randomness notions C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} and D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{D}}$$\end{document} where C⊆D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C} \subseteq \mathcal{D}}$$\end{document}, for instance Martin-Löf randomness and Schnorr randomness. Several authors have characterized classes of the form Low which consist of the oracles X that are so feeble that C⊆DX\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C} \subseteq \mathcal{D}^X}$$\end{document}. Our goal is to do the same when the randomness notion D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{D}}$$\end{document} is relativized uniformly: denote by Low \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\star}$$\end{document} the class of oracles X such that every C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-random is uniformly D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{D}}$$\end{document}-random relative to X. We show that X∈Low⋆\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\in Low ^\star}$$\end{document} if and only if X is c.e. tt-traceable if and only if X is anticomplex if and only if X is Martin-Löf packing measure zero with respect to all computable dimension functions. We also show that X∈Low⋆\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\in Low^\star}$$\end{document} if and only if X is computably i.o. tt-traceable if and only if X is not totally complex if and only if X is Schnorr Hausdorff measure zero with respect to all computable dimension functions. (shrink)

江戸時代中期に開学した漢学塾懐徳堂。中井竹山・履軒兄弟が展開した懐徳堂儒学と朱子学との関係、思想史的意義を明らかにする。.

Louveau showed that if a Borel set in a Polish space happens to be in a Borel Wadge class $$\Gamma $$, then its $$\Gamma $$ -code can be obtained from its Borel code in a hyperarithmetical manner. We extend Louveau’s theorem to Borel functions: If a Borel function on a Polish space happens to be a $$ \underset{\widetilde{}}{\varvec{\Sigma }}\hbox {}_t$$ -function, then one can find its $$ \underset{\widetilde{}}{\varvec{\Sigma }}\hbox {}_t$$ -code hyperarithmetically relative to its Borel code. More generally, we prove (...) extension-type, domination-type, and decomposition-type variants of Louveau’s theorem for Borel functions. (shrink)

In this article, we study an analogue of tt-reducibility for points in computable metric spaces. We characterize the notion of the metric tt-degree in the context of first-level Borel isomorphism. Then, we study this concept from the perspectives of effective topological dimension theory and of effective fractal dimension theory.

We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox “absolute” quantities are good representatives of observable relative quantities if the reference state is suitably localised. We use this relational formalism to critique the literature on the relationship between reference frames and superselection rules, settling a (...) long-standing debate on the subject. (shrink)

This paper reports our research efforts on social robots that recognize interpersonal relationships. These investigations are carried out by observing group behaviors while the robot interacts with people. Our humanoid robot interacts with children by speaking and making various gestures. It identifies individual children by using a wireless tag system, which helps to promote interaction such as the robot calling a child by name. Accordingly, the robot is capable of interacting with many children, causing spontaneous group behavior from the children (...) around it. Here, group behavior is associated with social relationships among the children themselves. For example, a child may be accompanied by his or her friends and then play together with them. We propose the hypothesis that our interactive robot prompts a child’s friends to accompany him or her; thus, we can estimate their friendship by simply observing their accompanying behaviors. We conducted a field experiment for two weeks in a Japanese elementary school to verify this hypothesis. In the experiment, two “Robovie” robots were placed where children could freely interact with them during recesses. As a result, we found that they mostly prompted friend-accompanying behavior. Moreover, we could estimate some of their friendly relationships, in particular among the children who often appeared around the robot. For example, we could estimate 5% of all friendships with 80% accuracy, and 15% of them with nearly 50% accuracy. Thus, this result basically supports our hypothesis on friendship estimation from an interactive humanoid robot. We believe that this ability to estimate human relationships is essential for robots to behave socially. (shrink)

Negative attitudes toward robots are considered as one of the psychological factors preventing humans from interacting with robots in the daily life. To verify their influence on humans‘ behaviors toward robots, we designed and executed experiments where subjects interacted with Robovie, which is being developed as a platform for research on the possibility of communication robots. This paper reports and discusses the results of these experiments on correlation between subjects’ negative attitudes and their behaviors toward robots. Moreover, it discusses influences (...) of gender and experience of real robots on their negative attitudes and behaviors toward robots. (shrink)