We prove that every countable non-standard model of WKL0 has a proper initial part isomorphic to itself. This theorem enables us to carry out non-standard arguments over WKL0.

We show that each of Δ13-CA0 + Σ13-IND and Π12-CA0 + Π13-TI proves Δ03-Det and that neither Σ31-IND nor Π13-TI can be dropped. We also show that neither Δ13-CA0 + Σ1∞-IND nor Π12-CA0 + Π1∞-TI proves Σ03-Det. Moreover, we prove that none of Δ21-CA0, Σ31-IND and Π21-TI is provable in Δ11-Det0 = ACA0 + Δ11-Det.

We show that each of $\Delta _{3}^{1}-{\rm CA}_{0}+\Sigma _{3}^{1}-{\rm IND}$ and $\Pi _{2}^{1}-{\rm CA}_{0}+\Pi _{3}^{1}-{\rm TI}$ proves $\Delta _{3}^{0}-{\rm Det}$ and that neither $\Sigma _{3}^{1}-{\rm IND}$ nor $\Pi _{3}^{1}-{\rm TI}$ can be dropped. We also show that neither $\Delta _{3}^{1}-{\rm CA}_{0}+\Sigma _{\infty}^{1}-{\rm IND}$ nor $\Pi _{2}^{1}-{\rm CA}_{0}+\Pi _{\infty}^{1}-{\rm TI}$ proves $\Sigma _{3}^{0}-{\rm Det}$. Moreover, we prove that none of $\Delta _{2}^{1}-{\rm CA}_{0}$, $\Sigma _{3}^{1}-{\rm IND}$ and $\Pi _{2}^{1}-{\rm TI}$ is provable in $\Delta _{1}^{1}-{\rm Det}_{0}={\rm ACA}_{0}+\Delta _{1}^{1}-{\rm Det}$.

Within a weak subsystem of second-order arithmetic , that is -conservative over , we reformulate Kreisel's proof of the Second Incompleteness Theorem and Boolos' proof of the First Incompleteness Theorem.

By , we denote the system of second-order arithmetic based on recursive comprehension axioms and Σ10 induction. is defined to be plus weak König's lemma: every infinite tree of sequences of 0's and 1's has an infinite path. In this paper, we first show that for any countable model M of , there exists a countable model M′ of whose first-order part is the same as that of M, and whose second-order part consists of the M-recursive sets and sets not (...) in the second-order part of M. By combining this fact with a certain forcing argument over universal trees, we obtain the following result : if proves X!Y with arithmetical, so does . We also discuss several improvements of this results. (shrink)

In [10], we have shown that the statement that all ∑ 1 1 partitions are Ramsey is deducible over ATR 0 from the axiom of ∑ 1 1 monotone inductive definition,but the reversal needs П 1 1 - CA 0 rather than ATR 0 . By contrast, we show in this paper that the statement that all ∑ 0 2 games are determinate is also deducible over ATR 0 from the axiom of ∑ 1 1 monotone inductive definition, but the (...) reversal is provable even in ACA 0 . These results illuminate the substantial differences among lightface theorems which can not be observed in boldface. (shrink)

Within a weak subsystem of second‐order arithmetic WKL0, we develop basic part of non‐standard analysis up to the Peano existence theorem.

By RCA 0 , we denote a subsystem of second order arithmetic based on Δ0 1 comprehension and Δ0 1 induction. We show within this system that the real number system R satisfies all the theorems (possibly with non-standard length) of the theory of real closed fields under an appropriate truth definition. This enables us to develop linear algebra and polynomial ring theory over real and complex numbers, so that we particularly obtain Hilbert’s Nullstellensatz in RCA 0.

In this paper, we show within RCA 0 that weak Konig's lemma is necessary and sufficient to prove that any (separable) compact group has a Haar measure. Within WKL 0 , a Haar measure is constructed by a non-standard method based on a fact that every countable non-standard model of WKL 0 has a proper initial part isomorphic to itself [10].

We give a simple game-theoretic proof of Silver's theorem that every analytic set is Ramsey. A set P of subsets of ω is called Ramsey if there exists an infinite set H such that either all infinite subsets of H are in P or all out of P. Our proof clarifies a strong connection between the Ramsey property of partitions and the determinacy of infinite games.

Hegel, in his work _Philosophy of Right_, defines ownership through three elements: acquisition by occupation, use, and transfer. To own something involves mere acquisition and encompasses its appropriate use and potential transfer to others. Subsequently, the final aspect mentioned was the concept of infinite judgement. The acts of owning and transferring to others are diametrically opposed, and Hegel’s unique logic forcibly connects these opposing concepts. This form of infinite judgement was advocated by the young Hegel during the era of _Phenomenology (...) of Spirit_. There, he stated, “Spirit is a bone”. However, when he later wrote _Science of Logic_ or _Encyclopedia_, the formulation of infinite judgement changed to “Spirit is not something that is bone”. This shift was influenced by Kant. In _Logic_, the discourse advances into syllogism, inferential theory, leading to “Spirit is a bone for such-and-such reasons”. In essence, Hegel binarily connected spirit and bone in his youth and introduced a mediating term in this connection later in his life, establishing inferential links. However, the notion of forcibly connecting opposing concepts remains. Therefore, the statement “Ownership is transfer” represents an infinite judgement while simultaneously signifying syllogism that “I truly own this object if I can transfer it to others”. This contributes to the reasoning that “I and objects can be connected through the intermediary of others”, progressing to the inference that “I and others can be connected through objects”, thereby laying the foundation for society. (shrink)

Chaotic dynamics can be related to analog computation. A possibility of electronically implementing the chaos -driven contracting system in the target article is explored with an analog electronic circuit with inevitable noise from the viewpoint of analog computation with chaotic neurons.

Reinforcement learning has recently received much attention as a learning method for complicated systems, e.g., robot systems. It does not need prior knowledge and has higher capability of reactive and adaptive behaviors. However increase in dimensionality of the action-state space makes it diffcult to accomplish learning. The applicability of the existing reinforcement learning algorithms are effective for simple tasks with relatively small action-state space. In this paper, we propose a new reinforcement learning algorithm: “Q-learning with Dynamic Structuring of Exploration Space (...) Based on Genetic Algorithm ”. The algorithm is applicable to systems with high dimensional action and interior state spaces, for example a robot with many redundant degrees of freedom. To demonstrate the effectiveness of the proposed algorithm simulations of obstacle avoidance by a 50 links manipulator have been carried out. It is shown that effective behavior can be learned by using the proposed algorithm. (shrink)

Reinforcement learning is very effective for robot learning. Because it does not need priori knowledge and has higher capability of reactive and adaptive behaviors. In our previous works, we proposed new reinforcement learning algorithm: “Q-learning with Dynamic Structuring of Exploration Space Based on Genetic Algorithm (QDSEGA)”. It is designed for complicated systems with large action-state space like a robot with many redundant degrees of freedom. And we applied it to 50 link manipulator and effective behavior is acquired. However optimality and (...) fault tolerance of the proposed algorithm were not considered and to demonstrate effectiveness of the proposed algorithm other applications are necessary. Acquiring of locomotion patterns by a multi-legged robot is a very interesting problem. As it has many redundant degrees of freedom, application of usual reinforcement learning is difficult and an optimal locomotion has not been acquired using previous reinforcement learning algorithm. And the redundancy of the robot is effective to the fault tolerance and various locomotion patterns can be acquired for adapting the faults of the legs. In this paper, we applied QDSEGA to acquiring of locomotion pattern by the multi-legged robot and considered the optimality and fault tolerance. Effective behavior has been obtained by using our proposed algorithm. (shrink)

あはれ・わび・いきなどの美意識や芸術の本質について、和辻哲郎、九鬼周造などの知の巨人から学ぶ。.

In this paper, using Mark Schroeder’s (2008a) expressivist semantic framework for normative language as a case study, I will identify difficulties that even an expressivist semantic theory capable of addressing the Frege-Geach problem will encounter in handling the logical possibility of moral dilemmas. To this end, I will draw on a classical puzzle formulated by McConnell (1978) that the logical possibility of moral dilemmas conflicts with some of the prima facie plausible axioms of the standard deontic logic, which include obligation (...) implies permission. On the tentative assumption that proponents of ethical expressivism should be generally committed to securing the logical possibility of moral dilemmas in their semantic theories, I will explore whether and how expressivists can successfully invalidate obligation implies permission within the framework developed by Schroeder. The case study eventually reveals that this can indeed be a hard task for expressivists. Generalizing from the case study, I will suggest that the source of the difficulty ultimately lies in the mentalist assumption of the expressivist semantic project that the logico-semantic relations exhibited by normative sentences should be modeled in terms of the psychological attitudes that speakers express by uttering them. My final goal will be to show that the difficulty expressivists face in dealing with the logical possibility of moral dilemmas is a reflection of the more general problem that their commitment to the mentalist assumption prevents them from flexibly adopting or dropping axioms in their semantic theories to get the right technical results. (shrink)

My life as a quantum physicist / M. Nakahara -- A review on operator quantum error correction - Dedicated to Professor Mikio Nakahara on the occasion of his 60th birthday / C.-K. Li, Y.-T. Poon and N.-S. Sze -- Implementing measurement operators in linear optical and solid-state qubits / Y. Ota, S. Ashhab and F. Nori -- Fast and accurate simulation of quantum computing by multi-precision MPS: Recent development / A. Saitoh -- Entanglement properties of a quantum lattice-gas model on (...) square and triangular ladders / S. Tanaka, R. Tamura and H. Katsura -- On signal amplification from weak-value amplification / Y. Shikano -- Topological protection of quantum information / K. Fujii -- Quantum annealing with antiferromagnetic fluctuations for mean-field models / Y. Seki and H. Nishimori -- A method to change phase transition nature - Toward annealing methods / R. Tamura and S. Tanaka -- Computational analysis of the first stage of the photosynthetic system, the light-dependent reaction, by quantum chemical simulation method / M. Tada-Umezaki -- Two-qubit gate operation on selected nearest neighboring qubits in a neutral atom quantum computer / E. Hosseini Lapasar... [et al.] -- A simple operator quantum error correction scheme avoiding fully correlated errors / C. Bagnasco, Y. Kondo and M. Nakahara -- Black hole predictability, classical and quantum / A. Ishibashi -- Classical field simulation of finite-temperature Bose gases / T. Sato -- Atomic quantum simulations of lattice gauge theory: Effect of gauge symmetry breaking / K. Kasamatsu, I. Ichinose and T. Matsui -- Recursive construction of noiseless subsystem for qudits / U. Gungordu... [et al.] -- Composite quantum gates for precise quantum control / M. Bando... [et al.] -- New formulation of statistical mechanics using thermal pure quantum states / S. Sugiura and A. Shimizu -- Thermodynamics in unitary time evolution / T. N. Ikeda -- Second law of thermodynamics with QC-mutual information / T. Sagawa. (shrink)

U ovom radu, koristeći Mark Schroederov (2008a) semantički okvir za ekspresivistički normativni jezik kao studiju slučaja, identificirat ću poteškoće s kojima će se čak i ekspresivistička semantička teorija sposobna za rješavanje Frege-Geach problema susresti pri objašnjenju logičke mogućnosti moralnih dilema. U tu svrhu, oslonit ću se na klasičnu zagonetku koju je formulirao McConnell (1978)a pokazuje da se logička mogućnost moralnih dilema sukobljava s nekim od naizgled opravdanih aksioma standardne deontičke logike, među kojima je i aksiom da obaveza implicira dopuštenost. Na (...) temelju tentativne pretpostavke da zastupnici etičkog ekspresivizma trebaju općenito biti posvećeni osiguravanju logičke mogućnosti moralnih dilema u svojim semantičkim teorijama, istražit ću da li i kako ekspresivisti mogu uspješno opovrgnuti aksiom da obaveza implicira dopuštenje unutar okvira koji je razvio Schroeder. Studija slučaja konačno otkriva da to može biti zaista težak zadatak za ekspresiviste. Generalizirajući iz studije slučaja, sugerirat ću da izvor poteškoće leži u mentalističkoj pretpostavci ekspresivističkog semantičkog projekta da bi logičko-semantički odnosi prikazani normativnim rečenicama trebali biti modelirani pomoću psiholoških stavova koje govornici izražavaju izgovarajući ih. Moj konačni cilj će biti pokazati da je poteškoća s kojom se ekspresivisti susreću u suočavanju s logičkom mogućnosti moralnih dilema odraz općeg problema da njihova predanost mentalističkoj pretpostavci sprječava fleksibilno usvajanje ili odbacivanje aksioma u njihovim semantičkim teorijama kako bi dobili ispravne tehničke rezultate. (shrink)

Possible worlds have revolutionised philosophy and some related fields. But, in recent years, tools based on possible worlds have been found to be limited in many respects. Impossible worlds have been introduced to overcome these limitations. This Element aims to raise and answer the neglected question of what is characteristically impossible about impossible worlds. The Element sheds new light on the nature of impossible worlds. It also aims to analyse the main features and utility of impossible worlds and examine how (...) impossible worlds can capture distinctions which are unavailable if we limit ourselves to possible world-based tools. (shrink)

Background: Dementia is one the major problems of aging societies, and, novel and effective non-drug therapies are required as interventions in the oldest-old to prevent cognitive decline.Objective: This study aims to examine the efficacy and safety of reminiscence using immersive virtual reality focusing on anxiety that often appears with cognitive decline. The secondary objective is to reveal the preference for VR image types for reminiscence: live-action or computer graphics.Methods: This was a pilot, open-label, and randomized crossover study which was conducted (...) on January 2020 at a single nursing home. The subjects were randomly divided into two groups in equal numbers, and they alternately viewed two types of VR images themed on the mid- to late Showa era in Japan. In group A, the CG images were viewed first, and then the LA images were viewed. In group B, the images were viewed in the opposite order. Before VR viewing, subjects responded to Mini-Mental State Examination Japanese version and State-Trait Anxiety Inventory Japanese version. After viewing the first and second VR, subjects responded to STAI and the numerical rating scale for satisfaction and side effects.Results: Ten subjects participated in this study. The values of analyses are presented in the mean. The age was 87.1 years, and the MMSE was 28.5. The total STAI score before VR viewing was 36.1, but it significantly decreased to 26.8 after the first VR viewing, and further decreased to 23.4 after the second VR viewing. The NRS score for satisfaction tended to be higher after viewing LA in group A vs. 8.6, P = 0.0993), while in group B, the score after CG was slightly lower than that after LA. There were no serious side effects.Conclusions: This study suggests that iVR reminiscence can reduce anxiety in the oldest-old without causing serious side effects. Furthermore, the impacts might be better with LA images. (shrink)

Although numerous disciplines recognize multiple ways of conceptualizing time, Stefan Tanaka argues that scholars still overwhelmingly operate on chronological and linear Newtonian or classical time that emerged during the Enlightenment. This short, approachable book implores the humanities and humanistic social sciences to actively embrace the richness of different times that are evident in non-modern societies and have become common in several scientific fields throughout the twentieth century. Tanaka first offers a history of chronology by showing how the social (...) structures built on clocks and calendars gained material expression. Tanaka then proposes that we can move away from this chronology by considering how contemporary scientific understandings of time might be adapted to reconceive the present and pasts. This opens up a conversation that allows for the possibility of other ways to know about and re-present pasts. A multiplicity of times will help us broaden the historical horizon by embracing the heterogeneity of our lives and world via rethinking the complex interaction between stability, repetition, and change. This history without chronology also allows for incorporating the affordances of digital media. (shrink)

世界に溢れ続けるイメージは喫緊の思想的・文化的テーマである。像=イメージを行為主体と捉えるブレーデカンプによる像行為論の可能性を検討しつつ、独自の「像即是空、空即是像」たる「かげ」としての論理へと至る 最新論集。.

三島由紀夫、江藤淳、西部邁...戦後日本の保守論客たちの自死は何を意味するのか?「近代」思想が破壊しようとする、伝統文化と秩序。その背景にあるユダヤ思想の正体、そしてマルクス主義との関連を明らかにする 。日本人の劣化・自滅は防げるか?

This book enables readers to understand contemporary Japanese society and culture. Since it is written by experts, it allows readers to start with any chapters they are interested in. It also provides a unique way to introduce Japanese society and culture to those who have never visited or studied Japanese society by reading articles from various authors on topics such as gender, family, economy, natural disasters and politics and laws. It provides scholars, academics, graduate students and the general educated audience (...) all the information required to understand contemporary Japanese society and culture fully and see the diverse perspectives available. (shrink)

In this paper, we argue that a distinction ought to be drawn between two ways in which a given world might be logically impossible. First, a world w might be impossible because the laws that hold at w are different from those that hold at some other world (say the actual world). Second, a world w might be impossible because the laws of logic that hold in some world (say the actual world) are violated at w. We develop a novel (...) way of modelling logical possibility that makes room for both kinds of logical impossibility. Doing so has interesting implications for the relationship between logical possibility and other kinds of possibility (for example, metaphysical possibility) and implications for the necessity or contingency of the laws of logic. (shrink)