正しいから証明できるのか、証明できるから正しいのか。数学にとって証明とは何か、正しさとは何なのかは数学基礎論の根本的な問題である。様相論理を軸とした、証明と真理に関わる数学基礎論の古典的な結果から最先 端の議論までを解説した。.

Genome maintenance requires various nucleoid-associated factors in prokaryotes. Among them, the SMC protein has been thought to play a static role in the organization and segregation of the chromosome during cell division. However, recent studies have shown that the bacterial SMC is required to align left and right arms of the emerging chromosome and that the protein dynamically travels from origin to Ter region. A rod form of the SMC complex mediates DNA bridging and has been recognized as a machinery (...) responsible for DNA loop extrusion, like eukaryotic condensin or cohesin complexes, which act as chromosome organizers. Attention is now turning to how the prototype of the complex is loaded on the entry site and translocated on chromosomal DNA, explaining its overall conformational changes at atomic levels. Here, we review and highlight recent findings concerning the prokaryotic SMC complex and discuss possible mechanisms from the viewpoint of protein architecture. Recent studies show dynamic movements of the prokaryotic SMC protein complex: initial loading, translocation on DNA for bacterial chromosome organization. The recent structural models of the protein also provide a new vision for the structure-function relationship. (shrink)

One of the problems we face in many-valued logic is the difficulty of capturing the intuitive meaning of the connectives introduced through truth tables. At the same time, however, some logics have nice ways to capture the intended meaning of connectives easily, such as four-valued logic studied by Belnap and Dunn. Inspired by Dunn’s discovery, we first describe a mechanical procedure, in expansions of Belnap-Dunn logic, to obtain truth conditions in terms of the behavior of the Truth and the False, (...) which gives us intuitive readings of connectives, out of truth tables. Then, we revisit the notion of functional completeness, which is one of the key notions in many-valued logic, in view of Dunn’s idea. More concretely, we introduce a generalized notion of functional completeness which naturally arises in the spirit of Dunn’s idea, and prove some fundamental results corresponding to the classical results proved by Post and Słupecki. (shrink)

The purpose of this paper is to argue that the hybrid formalism fits naturally in the context of David Lewis’s counterfactual logic and that its introduction into this framework is desirable. This hybridization enables us to regard the inference “The pig is Mary; Mary is pregnant; therefore the pig is pregnant” as a process of updating local information (which depends on the given situation) by using global information (independent of the situation). Our hybridization also has the following technical advantages: (i) (...) it preserves the completeness and decidability of Lewis’s logic; (ii) it allows us to characterize the Limit Assumption as a proof-rule with some side-conditions; and (iii) it enables us to establish a general Kripke completeness result by using the proof-rule corresponding to the Limit Assumption. Keywords Counterfactual logic - David Lewis - Contextually definite description - Hybrid logic - Arthur Prior - The limit assumption - Strong completeness - Decidability - Bisimulation - Pure completeness. (shrink)

This paper deals with two main topics: One is a semantical investigation for a bimodal language with a modal operator \blacksquare associated with the intersection of the accessibility relation R and the inequality ≠. The other is a generalization of some of the former results to general extended languages with modal operators. First, for our language L\sb{\square\blacksquare}, we prove that Segerberg's theorem (equivalence between finite frame property and finite model property) fails and establish both van Benthem-style and Goldblatt-Thomason-style characterizations. We (...) extract the notion of \blacksquare-realizer (a generalization of bulldozing) as an essence from the proofs of our results. Second, we generalize the notion of \blacksquare-realizer and prove quite general versions of these semantical characterization results. The known and previously unknown characterization results for almost all of the languages extended with modal operators already proposed will be immediate corollaries. (shrink)

We develop intuitionistic public announcement logic over intuitionistic \({\textbf{K}}\), \({{\textbf{K}}}{{\textbf{T}}}\), \({{\textbf{K}}}{{\textbf{4}}}\), and \({{\textbf{S}}}{{\textbf{4}}}\) with distributed knowledge. We reveal that a recursion axiom for the distributed knowledge is _not_ valid for a frame class discussed in [ 12 ] but valid for the restricted frame class introduced in [ 20, 26 ]. The semantic completeness of the static logics for this restricted frame class is established via the concept of pseudo-model.

This paper studies a combined system of intuitionistic and classical propositional logic from proof-theoretic viewpoints. Based on the semantic treatment of Humberstone (J Philos Log 8:171–196, 1979) and del Cerro and Herzig (Frontiers of combining systems: FroCoS, Springer, 1996), a sequent calculus $$\textsf{G}(\textbf{C}+\textbf{J})$$ is proposed. An approximate idea of obtaining $$\textsf{G}(\textbf{C}+\textbf{J})$$ is adding rules for classical implication on top of the intuitionistic multi-succedent sequent calculus by Maehara (Nagoya Math J 7:45–64, 1954). However, in the semantic treatment, some formulas do not (...) satisfy heredity, which leads to the necessity of a restriction on the right rule for intuitionistic implication to keep the soundness of the calculus. The calculus $$\textsf{G}(\textbf{C}+\textbf{J})$$ enjoys cut elimination and Craig interpolation, whose detailed proofs are described in this paper. Cut elimination enables us to show the decidability of this combination both directly and syntactically. This paper also employs a canonical model argument to establish the strong completeness of Hilbert system $$\mathbf {C+J}$$ proposed by del Cerro and Herzig (Frontiers of combining systems: FroCoS, Springer, 1996). (shrink)

The inositol phosphate metabolism network has been found to be much more complex than previously thought, as more and more inositol phosphates and their metabolizing enzymes have been discovered. Some of the inositol phosphates have been shown to have biological activities, but little is known about their signal transduction mechanisms except for that of inositol 1,4,5‐trisphosphate. The recent discovery, however, of a number of binding proteins for inositol high polyphosphate [inositol 1,3,4,5‐tetrakisphosphate (IP4), inositol 1,3,4,5,6‐pentakisphosphate, or inositol hexakisphosphate] enables us to (...) speculate on the physiological function of these compounds. In this article we focus on two major issues: (1) the roles of inositol high polyphosphates in vesicular trafficking, especially exocytosis, and (2) pleckstrin homology domaincontaining IP4 binding proteins involved in the Ras signaling pathway. (shrink)

The present contribution shows that a Hilbert-style axiomatization for dynamic logic of relation changers is complete for the standard Kripke semantics not by a well-known rewriting technique but by the idea of an auxiliary semantics studied by van Benthem and Wang et al. A key insight of our auxiliary semantics for dynamic logic of relation changers can be described as: “relation changers are bounded morphisms.” Moreover, we demonstrate that this semantic insight can be used to provide a modular cut-free labelled (...) sequent calculus for the logic in the sense that our calculus can be regarded as a natural expansion of a labelled sequent calculus of iteration-free propositional dynamic logic. (shrink)

This paper shows Hilbert system (C+J)-, given by del Cerro and Herzig (1996) is semantically incomplete. This system is proposed as a proof theory for Kripke semantics for a combination of intuitionistic and classical propositional logic, which is obtained by adding the natural semantic clause of classical implication into intuitionistic Kripke semantics. Although Hilbert system (C+J)- contains intuitionistic modus ponens as a rule, it does not contain classical modus ponens. This paper gives an argument ensuring that the system (C+J)- is (...) semantically incomplete because of the absence of classical modus ponens. Our method is based on the logic of paradox, which is a paraconsistent logic proposed by Priest (1979). (shrink)

Intuitionistic epistemic logic by Artemov and Protopopescu (Rev Symb Log 9:266–298, 2016) accepts the axiom “if A, then A is known” (written $$A \supset K A$$ ) in terms of the Brouwer–Heyting–Kolmogorov interpretation. There are two variants of intuitionistic epistemic logic: one with the axiom “ $$KA \supset \lnot \lnot A$$ ” and one without it. The former is called $$\textbf{IEL}$$, and the latter is called $$\textbf{IEL}^{-}$$. The aim of this paper is to study first-order expansions (with equality and function (...) symbols) of these two intuitionistic epistemic logics. We define Hilbert systems with additional axioms called geometric axioms and sequent calculi with the corresponding rules to geometric axioms and prove that they are sound and complete for the intended semantics. We also prove the cut-elimination theorems for both sequent calculi. As a consequence, the disjunction property and existence property are established for the sequent calculi without geometric implications. Finally, we establish that our sequent calculi can also be formulated with admissible structural rules (i.e., in terms of a G3-style sequent calculus). (shrink)

This study realizes belief/reliability change of a judge in a legal judgment by dynamic epistemic logic. A key feature of DEL is that possibilities in an agent’s belief can be represented by a Kripke model. This study addresses two difficulties in applying DEL to a legal case. First, since there are several methods for constructing a Kripke model, our question is how we can construct the model from a legal case. Second, since this study employs several dynamic operators, our question (...) is how we can decide which operators are to be applied for belief/reliability change of a judge. In order to solve these difficulties, we have implemented a computer system which provides two functions. First, the system can generate a Kripke model from a legal case. Second, the system provides an inconsistency solving algorithm which can automatically perform several operations in order to reduce the effort needed to decide which operators are to be applied. By our implementation, the above questions can be adequately solved. With our analysis method, six legal cases are analyzed to demonstrate our implementation. (shrink)

Is the societal-level of analysis sufficient today to understand the values of those in the global workforce? Or are individual-level analyses more appropriate for assessing the influence of values on ethical behaviors across country workforces? Using multi-level analyses for a 48-society sample, we test the utility of both the societal-level and individual-level dimensions of collectivism and individualism values for predicting ethical behaviors of business professionals. Our values-based behavioral analysis indicates that values at the individual-level make a more significant contribution to (...) explaining variance in ethical behaviors than do values at the societal-level. Implicitly, our findings question the soundness of using societal-level values measures. Implications for international business research are discussed. (shrink)

Is the societal-level of analysis sufficient today to understand the values of those in the global workforce? Or are individual-level analyses more appropriate for assessing the influence of values on ethical behaviors across country workforces? Using multi-level analyses for a 48-society sample, we test the utility of both the societal-level and individual-level dimensions of collectivism and individualism values for predicting ethical behaviors of business professionals. Our values-based behavioral analysis indicates that values at the individual-level make a more significant contribution to (...) explaining variance in ethical behaviors than do values at the societal-level. Implicitly, our findings question the soundness of using societal-level values measures. Implications for international business research are discussed. (shrink)

The industrial society in Japan is now entering into a new era of an advanced information society or a network society. AI as a knowledge information processing technology is becoming an integral part of the society. This emerging era is being supported by the information industry.

Artemov and Protopopescu introduced a Brouwer-Heyting-Kolmogorov interpretation of knowledge operator to define the intuitionistic epistemic logic IEL, where the axiom A⊃KA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A\supset KA$$\end{document} is accepted but the axiom KA⊃A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$KA\supset A$$\end{document} is refused. This paper studies the notion of distributed knowledge on an expansion of the multi agent variant of IEL. We provide a BHK interpretation of distributed knowledge operator to define the intuitionistic epistemic (...) logic with distributed knowledge DIEL. We construct Hilbert system and cut-free sequent calculus for DIEL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {DIEL}$$\end{document} and show that they are sound and complete for the intended Kripke semantics. (shrink)

Daily rhythms are a ubiquitous feature of living systems. Generally, these rhythms are not just passive consequences of cyclic fluctuations in the environment, but instead originate within the organism. In mammals, including humans, the master pacemaker controlling 24‐hour rhythms is localized in the suprachiasmatic nuclei of the hypothalamus. This circadian clock is responsible for the temporal organization of a wide variety of functions, ranging from sleep and food intake, to physiological measures such as body temperature, heart rate and hormone release. (...) The retinal circadian clock was the first extra‐SCN circadian oscillator to be discovered in mammals and several studies have now demonstrated that many of the physiological, cellular and molecular rhythms that are present within the retina are under the control of a retinal circadian clock, or more likely a network of hierarchically organized circadian clocks that are present within this tissue. BioEssays 30:624–633, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

This paper explicates the counting ten coins metaphor as it appears in Fazang’s Treatise on the Five Teachings of Huayan. The goal is to transform Fazang’s inexact and obscure mentions of the metaphor into something that is clearer and more precise. The method for achieving this goal is threefold: first, presenting Fazang’s version of the metaphor as improving upon prior efforts by Zhiyan and Ŭisang to interpret a brief stanza in the Avataṁsaka sutra; second, providing textual evidence to support this (...) interpretation; third, contrasting this interpretation with alternatives from Francis Cook as well as Yasuo Deguchi and Katsuhiko Sano. (shrink)