We propose a new game to strategically justify the constrained equal awards rule in claims problems. Our game is “procedurally fair” and “multilateral”. In addition, even if claimants cannot reach an agreement in any period, they can renegotiate in the next period. We show that, for each claims problem, the awards vector chosen by the constrained equal awards rule achieved at period 1 is the unique subgame perfect equilibrium outcome of the game.

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.

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)

Akama et al. [1] systematically studied an arithmetical hierarchy of the law of excluded middle and related principles in the context of first-order arithmetic. In that paper, they first provide a prenex normal form theorem as a justification of their semi-classical principles restricted to prenex formulas. However, there are some errors in their proof. In this paper, we provide a simple counterexample of their prenex normal form theorem [1, Theorem 2.7], then modify it in an appropriate way which still serves (...) to largely justify the arithmetical hierarchy. In addition, we characterize a variety of prenex normal form theorems by logical principles in the arithmetical hierarchy. The characterization results reveal that our prenex normal form theorems are optimal. For the characterization results, we establish a new conservation theorem on semi-classical arithmetic. The theorem generalizes a well-known fact that classical arithmetic is $\Pi _2$ -conservative over intuitionistic arithmetic. (shrink)

Estrogen receptor α (ERα) is a ligand‐dependent transcription factor that regulates the expression of estrogen‐responsive genes. Approximately 70% of patients with breast cancer are ERα positive. Estrogen stimulates cancer cell proliferation and contributes to tumor progression. Endocrine therapies, which suppress the ERα signaling pathway, significantly improve the prognosis of patients with breast cancer. However, the development of de novo or acquired endocrine therapy resistance remains a barrier to breast cancer treatment. Therefore, understanding the regulatory mechanisms of ERα is essential to (...) overcome the resistance to treatment. This review focuses on the regulation of ERα expression, including copy number variation, epigenetic regulation, transcriptional regulation, and stability, as well as functions from the point of view post‐translational modifications. (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)

In this paper, I show that the availability of what some authors have called the weak reading and the strong reading of donkey sentences with relative clauses is systematically related to monotonicity properties of the determiner. The correlation is different from what has been observed in the literature in that it concerns not only right monotonicity, but also left monotonicity (persistence/antipersistence). I claim that the reading selected by a donkey sentence with a double monotone determiner is in fact the one (...) that validates inference based on the left monotonicity of the determiner. This accounts for the lack of strong reading in donkey sentences with MON determiners, which have been neglected in the literature. I consider the relevance of other natural forms of inference as well, but also suggest how monotonicity inference might play a central role in the actual process of interpretation. The formal theory is couched in dynamic predicate logic with generalized quantifiers. (shrink)

On sait que Platon fait grand cas des êtres intelligibles en instaurant la théorie des Idées. Mais il n’est pas approprié de le considérer comme penseur qui néglige le rôle de l’apparence sensible. Ce philosophe demeure très sensible à la modalité par laquelle les phénomènes apparaissent dans le champ de notreperception. En distinguant deux types d’apparence : image et simulacre, il donne à l’image le rôle d’intermédiaire actif entre le sensible et l’intelligible. L’examen des modalités des actions humaines qui reçoivent (...) et créent des images, nous aide à voir comment Platon intègre la fonction des images dans la structure de sa philosophie. La réception et la création des images sont étroitement reliées et synthétisées pour former le système original de Platon, système dans lequel le fondement de la théorie des Idées relève d’un certain dynamisme de l’action humaine. Dans la recherche relative à la modalité de réception et de création des images, je porte mon attention sur l’usage platonicien du terme tupos qui exprime le principe de la conformité de l’image et de son modèle.Notamment dans la théorie de la formation des futurs gardiens de la cité idéale, le tupos fonctionne, comme un principe qui réglemente et oriente à plusieurs niveaux les activités de la mimèsis et de la poièsis qui portent sur les images. La réflexion sur cette fonction conductrice. (shrink)

We provide a fine‐grained analysis on the relation between König's lemma, weak König's lemma, and the decidable fan theorem in the context of constructive reverse mathematics. In particular, we show that double negated variants of König's lemma and weak König's lemma are equivalent to double negated variants of the general decidable fan theorem and the binary decidable fan theorem, respectively, over a nearly intuitionistic system containing a weak countable choice only. This implies that the general decidable fan theorem is not (...) equivalent to the binary decidable fan theorem in the absence of a strong countable choice. In addition, we introduce a principle which fills the gap between König's lemma and weak König's lemma, and show that König's lemma is equivalent to weak König's lemma plus this principle. We also solve several problems arising from the investigation. (shrink)

We systematically study several principles and give a principle which is weaker than disjunctive Markov’s principle. We also show that the principle is underivable and strictly weaker than MP∨ in certain extensions of the system EL of elementary analysis.

We refine the arithmetical hierarchy of various classical principles by finely investigating the derivability relations between these principles over Heyting arithmetic. We mainly investigate some restricted versions of the law of excluded middle, De Morgan's law, the double negation elimination, the collection principle and the constant domain axiom.

We systematically study conservation theorems on theories of semi-classical arithmetic, which lie in-between classical arithmetic $\mathsf {PA}$ and intuitionistic arithmetic $\mathsf {HA}$. Using a generalized negative translation, we first provide a structured proof of the fact that $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over $\mathsf {HA} + {\Sigma _k}\text {-}\mathrm {LEM}$ where ${\Sigma _k}\text {-}\mathrm {LEM}$ is the axiom scheme of the law-of-excluded-middle restricted to formulas in $\Sigma _k$. In addition, we show that this conservation theorem is optimal in the (...) sense that for any semi-classical arithmetic T, if $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over T, then ${T}$ proves ${\Sigma _k}\text {-}\mathrm {LEM}$. In the same manner, we also characterize conservation theorems for other well-studied classes of formulas by fragments of classical axioms or rules. This reveals the entire structure of conservation theorems with respect to the arithmetical hierarchy of classical principles. (shrink)

The issue of justice after catastrophe is an enormous challenge to contemporary theories of distributive justice. In the past three decades, the controversy over distributive justice has centered on the ideal of equality. One of intensely debated issues concerns what is often called the “equality of what,” on which there are three primary views: welfarism, resourcism, and the capabilities approach. Another major point of dispute can be termed the “equality or another,” about which three positions debate: egalitarianism, prioritarianism, and sufficientarianism. (...) On these topics of distributive justice, authors are concerned with the current difference between the better-off and the worse-off or the present situation of the badly-off. By contrast, it is essential to take account of the past distribution of well-being as well as the present situation in order to explore questions of post-catastrophe justice. Without looking at the pre-disaster distribution of income, preference satisfaction, or basic capabilities among affected people, no present assessment of the damage caused by the disaster could be correct and no proposed remedy adequate. It is true that luck egalitarians assess the current distribution among people by referring to the decision that each individual made. Yet they pay scant attention to the situation in which each one stayed in the past. Therefore, we can legitimately say that most theorists of distributive justice, including luck egalitarians, have failed to give consideration to the past state of each person. -/- To fill this gap in the literature, the present article explores philosophical questions that arise when we take account of each person’s past and present situations in discussing distributive justice regarding public compensation and assistance to survivors and families of victims of natural and industrial disasters. In addressing these novel questions, I develop and refine various concepts, ideas, and arguments that have been presented in the study of distributive justice in normal settings. I tackle two tasks, the first of which is to explore the foundation and scope of luck egalitarianism. Despite the moral appeal it has in many cases, luck egalitarianism has attracted the so-called harshness objection. Some luck egalitarians attempt to avoid this objection in a pragmatic way by combining the luck egalitarian doctrine with the principle of basic needs satisfaction. However, they do not provide any systematic rationale for this combination. In contrast with such pragmatic responses, I seek to offer a principled argument for holding individuals responsible for their choices only when their basic needs are met, by invoking the ideas of respect for human voluntariness and rescue of human vulnerability. Based on this argument, I propose a form of responsibility-sensitive theory, which considers the pre-disaster distribution of well-being as a default position. The second task I take on is to refine sufficientarianism in the context of post-catastrophe justice. Luck egalitarianism with boundaries set by the basic needs principle seems to indicate the potential for sufficientarianism. But major proponents of this view conceive the welfarist assumption, a considerably high standard of well-being, and the controversial treatment of persons staying below the threshold, all of which seem problematic in the post-disaster situation. I try to construct a new version of sufficientarianism by replacing these current features with more robust ones. (shrink)

The uniform continuity theorem states that every pointwise continuous real‐valued function on the unit interval is uniformly continuous. In constructive mathematics, is strictly stronger than the decidable fan theorem, but Loeb [17] has shown that the two principles become equivalent by encoding continuous real‐valued functions as type‐one functions. However, the precise relation between such type‐one functions and continuous real‐valued functions (usually described as type‐two objects) has been unknown. In this paper, we introduce an appropriate notion of continuity for a modulus (...) of a continuous real‐valued function on [0, 1], and show that real‐valued functions with continuous moduli are exactly those functions induced by Loeb's codes. Our characterisation relies on two assumptions: (1) real numbers are represented by regular sequences (equivalently Cauchy sequences with explicitly given moduli); (2) the continuity of a modulus is defined with respect to the product metric on the regular sequences inherited from the Baire space. Our result implies that is equivalent to the statement that every pointwise continuous real‐valued function on [0, 1] with a continuous modulus is uniformly continuous. We also show that is equivalent to a similar principle for real‐valued functions on the Cantor space. These results extend Berger's [2] characterisation of for integer‐valued functions on and unify some characterisations of in terms of functions having continuous moduli. (shrink)