We prove in the framework of Bishop's constructive mathematics that the sequential completion equation image of the space [MATHEMATICAL SCRIPT CAPITAL D] is filter-complete. Then it follows as a corollary that the filter-completeness of [MATHEMATICAL SCRIPT CAPITAL D] is equivalent to the principle BD-ℕ, which can be proved in classical mathematics, Brouwer's intuitionistic mathematics and constructive recursive mathematics of Markov's school, but does not in Bishop's constructive mathematics. We also show that equation image is identical with the filter-completion which was (...) provided by Bishop. (shrink)

We show, within the framework of Bishop's constructive mathematics, that (sequential) completeness of the locally convex space $\mathcal{D} (\mathbb{R})$ of test functions is equivalent to the principle BD-N which holds in classical mathemtatics, Brouwer's intuitionism and Markov's constructive recursive mathematics, but does not hold in Bishop's constructivism.

We show, within the framework of Bishop's constructive mathematics, that (sequential) completeness of the locally convex space $\mathcal{D} (\mathbb{R})$ of test functions is equivalent to the principle BD-N which holds in classical mathemtatics, Brouwer's intuitionism and Markov's constructive recursive mathematics, but does not hold in Bishop's constructivism.

This article offers a characterization of what I call multiple-models juxtaposition, a strategy for managing trade-offs among modeling desiderata. MMJ displays models of distinct phenomena to...

As I have pointed out in a series of papers, which appeared about fifteen years ago in the Revue de l'histoire des religions, there are numerous resemblances between the ancient myths of the Indo-Europeans, on the one hand, and those of Japan, on the other. These resemblances, relating both to the fundamental structures of the two mythological systems and to a number of curious details, constitute an assemblage which seems too conspicuous to be regarded as either accidental or the result (...) of a similitude of human mentalities, manifesting itself, so it seems, through the creation of a great many similar myths and legends throughout the length and breadth of the surface of our planet. (shrink)

本書は、人間的営みとしての学びの広さ・深さ・自由さを確認していく。人間の成長、人間形成という視点から、学びの実践を通して「学び」の人間学的原理、学ぶ主体にとっての意味を考察。個人の具体的な経験を通して 、多様な学びのあり方を提示。日本人の学び方、教え方の伝統や特徴とその問題について考察。.

日本の固有の宗教神道より説き起こし、日本の仏教、歌人・念仏者・茶人・武人・医者・妙好人・禅僧・真宗僧侶・作家・俳人と多種な人間像を通して、日本人の生き生きとした生命の躍動感を解き明かす。.

S-Modulin is a frog homolog of recoverin. The function and the underlying mechanism of the action of these proteins are now understood in general. However, there remain some unsolved issues including; two distinct effects of S-modulin; Ca2+-dependent binding of S-modulin to membranes and a possible target protein; S-modulin-like proteins in other neurons. These issues are considered in this commentary.

In dieser Abhandlung versuchen wir die Theorie des Erhabenen bei Kant als eine Logik der reflektierenden Urteilskraft darzustellen, die den Ubergang des Sinnlichen ins Ubersinnliche ermoglicht. Die Urteilskraft bezieht die Spannung der Einbildungskraft vor dem Nicht-Darstellbaren auf das Ubersinnliche, und in dieser Beziehung sieht Kant "eine a priori im Subjekte liegende Zweckmassigkeit". Durch die Vorstellung der gewaltigen Natur kann unsere innere Idee erweckt werden, wenn wir berucksichtigen, "dass auf jene moralischen Anlagen bei jeder schicklichen Veranlassung Rucksicht genommen werden sollte". Durch (...) das Urteil uber das Erhabene erhalten wir eine Veranlassung fur diejenige Reflexion, die innerhalb der Natur auch die ubersinnliche Idee (oder ein gottliches Wesen) denkt. (edited). (shrink)

Despite the tendency to be otherwise, some non-classical logics are known to validate formulas that are invalid in classical logic. A subclass of such systems even possesses pairs of a formula and its negation as theorems, without becoming trivial. How should these provable contradictions be understood? The present paper aims to shed light on aspects of this phenomenon by taking as samples the constructive connexive logic C, which is obtained by a simple modification of a system of constructible falsity, namely (...) N4, as well as its non-constructive extension C3. For these systems, various observations concerning provable contradictions are made, using mainly a proof-theoretic approach. The topics covered in this paper include: how new contradictions are found from parts of provable contradictions; how to characterise provable contradictions in C3 that are constructive; how contradictions can be seen from the relative viewpoint of strong implication; and as an appendix an attempt at generating provable contradictions in C3. (shrink)

We show that length initial submodels of S12 can be extended to a model of weak second order arithmetic. As a corollary we show that the theory of length induction for polynomially bounded second order existential formulae cannot define the function division.

We define a theory of two-sort bounded arithmetic whose provably total functions are exactly those in ${\mathcal{F}_{LOGCFL}}$ by way of a generalized quantifier that expresses computations of SAC 1 circuits. The proof depends on Kolokolova’s conditions for the connection between the provable capture in two-sort theories and descriptive complexity.

We define a fragment of Primitive Recursive Arithmetic by replacing the defining axioms for primitive recursive functions by those for functions in some specific complexity class. In this note we consider such theory for AC0. We present a model-theoretical property of this theory, by means of which we are able to characterize its provably total functions. Next we consider the problem of how strong the induction scheme can be in this theory.

We will give a two-sort system which axiomatizes winning strategies for the combinatorial game Node Kayles. It is shown that our system captures alternating polynomial time reasonings in the sense that the provably total functions of the theory corresponds to those computable in APTIME. We will also show that our system is equivalently axiomatized by Sprague–Grundy theorem which states that any Node Kayles position is provably equivalent to some NIM heap.

Strong negation is a well-known alternative to the standard negation in intuitionistic logic. It is defined virtually by giving falsity conditions to each of the connectives. Among these, the falsity condition for implication appears to unnecessarily deviate from the standard negation. In this paper, we introduce a slight modification to strong negation, and observe its comparative advantages over the original notion. In addition, we consider the paraconsistent variants of our modification, and study their relationship with non-constructive principles and connexivity.

We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as co-negation, corresponds to different logics under different semantics. We then establish the relationship between logics related to these negations under unified syntax and semantics based on R. Sylvan's CCω.

We investigate a subsystem of minimal logic related to D. Vakarelov’s logic \, using the framework of subminimal logics by A. Colacito, D. de Jongh and A. L. Vargas. In the course of it, the relationship between the two semantics in the respective frameworks is clarified. In addition, we introduce a sequent calculus for the investigated subsystem, and some proof-theoretic properties are established. Lastly, we formulate a new infinite class of subsystems of minimal logics.

Eukaryotic genome DNA is wrapped around core histones and forms a nucleosome structure. Together with associated proteins and RNAs, these nucleosomes are organized three‐dimensionally in the cell as chromatin. Emerging evidence demonstrates that chromatin consists of rather irregular and variable nucleosome arrangements without the regular fiber structure and that its dynamic behavior plays a critical role in regulating various genome functions. Single‐nucleosome imaging is a promising method to investigate chromatin behavior in living cells. It reveals local chromatin motion, which reflects (...) chromatin organization not observed in chemically fixed cells. The motion data is like a gold mine. Data analyses from many aspects bring us more and more information that contributes to better understanding of genome functions. In this review article, we describe imaging of single‐nucleosomes and their tracked behavior through oblique illumination microscopy. We also discuss applications of this technique, especially in elucidating nucleolar organization in living cells. (shrink)

The literature on human and animal learning suggests that individuals attend to and act on cues differently based on the order in which they were learned. Recent studies have proposed that one specific type of learning outcome, the highlighting effect, can serve as a framework for understanding a number of early cognitive milestones. However, little is known how this learning effect itself emerges among children, whose memory and attention are much more limited compared to adults. Two experiments were conducted using (...) different versions of the general highlighting paradigm: Experiment 1 tested 3 to 6 year olds with a newly developed image-based version of the paradigm, which was designed specifically to test young children. Experiment 2 tested the validity of an image-based implementation of the highlighting paradigm with adult participants. The results from Experiment 1 provide evidence for the highlighting effect among children 3–6 years old, and they suggest age-related differences in dividing attention among multiple cues during learning. Experiment 2 replicated results from previous studies by showing robust biases for both image-based and text-based versions of the highlighting task. This study suggests that sensitivity to learning order emerges early through the process of cued attention, and the role of the highlighting effect in early language learning is discussed. (shrink)

N. Kamide introduced a pair of classical and constructive logics, each with a peculiar type of negation: its double negation behaves as classical and intuitionistic negation, respectively. A consequence of this is that the systems prove contradictions but are non-trivial. The present paper aims at giving insights into this phenomenon by investigating subsystems of Kamide’s logics, with a focus on a system in which the double negation behaves as the negation of minimal logic. We establish the negation inconsistency of the (...) system and embeddability of contradictions from other systems. In addition, we attempt at an informational interpretation of the negation using the dimathematical framework of H. Wansing. (shrink)

Intuitionistic logic formalises the foundational ideas of L.E.J. Brouwer’s mathematical programme of intuitionism. It is one of the earliest non-classical logics, and the difference between classical and intuitionistic logic may be interpreted to lie in the law of the excluded middle, which asserts that either a proposition is true or its negation is true. This principle is deemed unacceptable from the constructive point of view, in whose understanding the law means that there is an effective procedure to determine the truth (...) of all propositions. This understanding of the distinction between the two logics supports the view that negation plays a vital role in the formulation of intuitionistic logic.Nonetheless, the formalisation of negation in intuitionistic logic has not been universally accepted, and many alternative accounts of negation have been proposed. Some seek to weaken or strengthen the negation, and others actively supporting negative inferences that are impossible with it.This thesis follows this tradition and investigates various aspects of negation in intuitionistic logic. Firstly, we look at a problem proposed by H. Ishihara, which asks how effectively one can conserve the deducibility of classical theorems into intuitionistic logic, by assuming atomic classes of non-constructive principles. The classes given in this section improve a previous class given by K. Ishii in two respects: (a) instead of a single class for the law of the excluded middle, two classes are given in terms of weaker principles, allowing a finer analysis and (b) the conservation now extends to a subsystem of intuitionistic logic called Glivenko’s logic. This section also discusses the extension of Ishihara’s problem to minimal logic.Secondly, we study the relationship between two frameworks for weak constructive negation, the approach of D. Vakarelov on one hand and the framework of subminimal negation by A. Colacito, D. de Jongh, and A. L. Vargas on the other hand. We capture a version of Vakarelov’s logic with the semantics of the latter framework, and clarify the relationship between the two semantics. This also provides proof-theoretic insights, which results in the formulation of a cut-free sequent calculus for the aforementioned system.Thirdly, we investigate the ways to unify the formalisations of some logics with contra-intuitionistic inferences. The enquiry concerns paraconsistent logics by R. Sylvan and A. B. Gordienko, as well as the logic of co-negation by G. Priest and of empirical negation by M. De and H. Omori. We take Sylvan’s system as basic, and formulate the frame conditions of the defining axioms of the other systems. The conditions are then used to obtain cut-free labelled sequent calculi for the systems.Finally, we consider L. Humberstone’s actuality operator for intuitionistic logic, which can be seen as the dualisation of a contra-intuitionistic negation. A compete axiomatisation of intuitionistic logic with actuality operator is given, and comparisons are made for some related operators.Abstract prepared by Satoru Niki.E-mail:Satoru[email protected]. (shrink)

Ishihara's problem of decidable variables asks which class of decidable propositional variables is sufficient to warrant classical theorems in intuitionistic logic. We present several refinements to the class proposed by Ishii for this problem, which also allows the class to cover Glivenko's logic. We also treat the extension of the problem to minimal logic, suggesting a couple of new classes.

We continue the investigation of the first paper where we studied logics with various negations including empirical negation and co-negation. We established how such logics can be treated uniformly with R. Sylvan's CCω as the basis. In this paper we use this result to obtain cut-free labelled sequent calculi for the logics.

Aversive memories have the potential to impair one’s psychological well-being. It is desirable to reduce the anguish over such memories, as well as the chance that they will be retrieved. In two experiments, we investigated whether retrieval stopping reduces the distress elicited by negative memories retrieved from cues and how the effects of retrieval stopping are modulated by mental disorders, such as depression and anxiety. Participants engaged in retrieval stopping of aversive scene memories without any diversionary thoughts (direct suppression, Experiment (...) 1) or with diversionary positive thoughts (thought substitution, Experiment 2). Direct suppression reduced arousal elicited by the retrieval of aversive memories, while thought substitution did not only reduce arousal but also increased positive valence. Self-reported anxious/depressive symptoms negatively modulated the effects of direct suppression. For no or mild anxious/depressed individuals, direct suppression alleviated negative valence and high arousal when retrieving aversive memories. The negative relationship was not observed between the severity of the symptoms and the effect of thought substitution. These findings suggest that both retrieval stopping strategies can reduce distress from aversive memories. (shrink)