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.

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)

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)

In this article, we examine philosophy of sport as a field of study in Japan, its history, characteristics, and future prospects, as part of a contribution to the international development of the discipline of sport philosophy. The Japan Society for the Philosophy of Sport and Physical Education has been holding an annual sport philosophy conference every year since its inception in 1978. Nevertheless, the trends of sport philosophy in Japan have not been conveyed abroad. The language barrier between Japanese and (...) English as an international communication tool makes it difficult to spread our work on the philosophy of sport throughout the world. The question arises as to whether the philosophy of sport in Japan has the same trends as those in the Western countries. Is it reasonable to assume that it has different aspects and interests than philosophy of sport in English-speaking countries? We will also try to address these questions for our audience. (shrink)

This is an attempt to view the most basic and fundamental part of modern logic from a perspective which shares no grounds with any established schools of philosophical logic, in that the truth and falsehood as judged by means of human interventions is denied and the notion of logical dimensions is introduced. It establishes the minimum irrefutable logical structure and proceeds to found the relations between logic and geometry. The description of symmetry creates and simultaneously constrains the logical structure, whereas (...) symmetry itself can only be postulated. (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)

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)

A Polish space is not always homeomorphic to a computably presented Polish space. In this article, we examine degrees of non-computability of presenting homeomorphic copies of compact Polish spaces. We show that there exists a $\mathbf {0}'$ -computable low $_3$ compact Polish space which is not homeomorphic to a computable one, and that, for any natural number $n\geq 2$, there exists a Polish space $X_n$ such that exactly the high $_{n}$ -degrees are required to present the homeomorphism type of $X_n$. (...) Along the way we investigate the computable aspects of Čech homology groups. We also show that no compact Polish space has a least presentation with respect to Turing reducibility. (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)

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。.

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。.

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)

To let humanoid robots behave socially adequate in a future society, we started to explore laughter as an important para-verbal signal known to influence relationships among humans rather easily. We investigated how the naturalness of various types of laughter in combination with different humanoid robots was judged, first, within a situational context that is suitable for laughter and, second, without describing the situational context. Given the variety of human laughter, do people prefer a certain style for a robot’s laughter? And (...) if yes, how does a robot’s outer appearance affect this preference, if at all? Is this preference independent of the observer’s cultural background? Those participants, who took part in two separate online surveys and were told that the robots would laugh in response to a joke, preferred one type of laughter regardless of the robot type. This result is contrasted by a detailed analysis of two more surveys, which took place during presentations at a Japanese and a German high school, respectively. From the results of these two surveys, interesting intercultural differences in the perceived naturalness of our laughing humanoids can be derived and challenging questions arise that are to be addressed in future research. (shrink)

Young children generally learn words from other people. Recent research has shown that children can learn new actions and skills from nonhuman agents. This study examines whether young children could learn words from a robot. Preschool children were shown a video in which either a woman or a mechanical robot labeled novel objects. Then the children were asked to select the objects according to the names used in the video. The results revealed that children in the human condition were more (...) likely to select the correct objects than those in the robot condition. Nevertheless, the five-year-old children in the robot condition performed significantly better than chance level, while the four-year olds did not. Thus there is a developmental difference in children’s potential to learn words from a robot. The results contribute to our understanding of how children interact with non-human agents. Keywords: developmental cybernetics; word learning; social cognition; cognitive development. (shrink)

We show that there is a computable procedure which, given an ∀∃-sentence ${\varphi}$ in the language of the partially ordered sets with a top element 1 and a bottom element 0, computes whether ${\varphi}$ is true in the Medvedev degrees of ${\Pi^0_1}$ classes in Cantor space, sometimes denoted by ${\mathcal{P}_s}$.

Targeted gene alteration (TGA) is a strategy for correcting single base mutations in the DNA of human cells that cause inherited disorders. TGA aims to reverse a phenotype by repairing the mutant base within the chromosome itself, avoiding the introduction of exogenous genes. The process of how to accurately repair a genetic mutation is elucidated through the use of single‐stranded DNA oligonucleotides (ODNs) that can enter the cell and migrate to the nucleus. These specifically designed ODNs hybridize to the target (...) sequence and act as a beacon for nucleotide exchange. The key to this reaction is the frequency with which the base is corrected; this will determine whether the approach becomes clinically relevant or not. Over the course of the last five years, workers have been uncovering the role played by the cells in regulating the gene repair process. In this essay, we discuss how the impact of the cell on TGA has evolved through the years and illustrate ways that inherent cellular pathways could be used to enhance TGA activity. We also describe the cost to cell metabolism and survival when certain processes are altered to achieve a higher frequency of repair. (shrink)

The need for a time-shift invariant formulation of quantum theory arises from fundamental symmetry principles as well as heuristic cosmological considerations. Such a description then leaves open the question of how to reconcile global invariance with the perception of change, locally. By introducing relative time observables, we are able to make rigorous the Page–Wootters conditional probability formalism to show how local Heisenberg evolution is compatible with global invariance.