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.

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)

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.

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)

A simple and complete proof of strong normalization for first- and second-order intuitionistic natural deduction including disjunction, first-order existence and permutative conversions is given. The paper follows the Tait–Girard approach via computability predicates and saturated sets. Strong normalization is first established for a set of conversions of a new kind, then deduced for the standard conversions. Difficulties arising for disjunction are resolved using a new logic where disjunction is restricted to atomic formulas.

Robots that incorporate the function of apologizing have emerged in recent years. This paper examines the moral permissibility of making robots apologize. First, I characterize the nature of apology based on analyses conducted in multiple scholarly domains. Next, I present a prima facie argument that robot apologies are not permissible because they may harm human societies by inducing the misattribution of responsibility. Subsequently, I respond to a possible response to the prima facie objection based on the interpretation that attributing responsibility (...) to a robot is analogous to having an attitude toward fiction. Then, I demonstrate that there are cases of robot apologies where the prima facie objection does not apply, by considering the following two points: (1) apology-related practices found in our human-to-human apologies, and (2) a difference in the degree of harm caused by robot failures and the resulting apologies. Finally, given the current norms governing our apology-related practices, I argue that some instances of making robots apologize are permissible, and I propose conducting critical robotics research questioning the validity of such norms. (shrink)

A critical examination of Japanese literary and art theories.

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 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)

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.

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 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.

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)

It is proved that for any k, the class of classical categorial grammars that assign at most k types to each symbol in the alphabet is learnable, in the Gold (1967) sense of identification in the limit from positive data. The proof crucially relies on the fact that the concept known as finite elasticity in the inductive inference literature is preserved under the inverse image of a finite-valued relation. The learning algorithm presented here incorporates Buszkowski and Penn's (1990) algorithm for (...) determining categorial grammars from input consisting of functor-argument structures. (shrink)