In this paper, we propose an extension of the Minimal Generation Gap (MGG) to reduce the number of fitness evaluation for the real-coded GAs (RCGA). When MGG is applied to actual engineering problems, for example applied to optimization of design parameters, the fitness calculating time is usually huge because MGG generates many children from one pair of parents and the fitness is calculated by repetitive simulation or analysis. The proposed method called Saving MGG reduces the number of fitness evaluation by (...) estimating the promising degrees of children using individual distribution and fitness information of population, and selecting children based on the promising degree before evaluating the fitness. Experimental results show that RCGA with Saving MGG can provide large reducing effects on 20 or 30 dimensional Sphere functions, Rosenbrock functions, ill-scaled Rosenbrock functions, and Rastrigin function. (shrink)

Web-based learning resources provide learners with hyperspace where they can navigate in a self-directed way to learn the contents included in the Web pages. The navigation involves making a sequence of the pages visited, which is called navigation path. However, learners often fail in making the navigation path due to a cognitive overload, which is caused by diverse cognitive efforts at comprehending the contents in Web pages, and monitoring the navigation process such as planning and reflection of navigation path. In (...) the self-directed learning, in particular, it is difficult for learners to maintain the navigation monitoring. Focusing on navigation planning, this paper addresses the issue of how to facilitate learners' navigation monitoring to promote their learning in hyperspace provided by Web-based learning resources. Our approach to this issue is to provide learners with a space, in which they can see through the learning resources to plan a navigation path, apart from hyperspace. In this paper, we also demonstrate an assistant system for the navigation planning, which is composed of hyperspace map, page previewer, and path previewer. These facilities give learners an overview of Web pages and navigation path to help them make a navigation path plan without visiting Web pages in hyperspace. This paper also describes a case study with the assistant system. The results indicate that the system facilitates navigation particularly in a more complicated hyperspace. (shrink)

コンピュータの歴史、アルゴリズムの理論の解説を経て、未解決であるミレニアム問題のひとつ、「P≠NP問題」に迫ります!

Kripke completeness of some infinitary predicate modal logics is presented. More precisely, we prove that if a normal modal logic above is -persistent and universal, the infinitary and predicate extension of with BF and BF is Kripke complete, where BF and BF denote the formulas pi pi and x x, respectively. The results include the completeness of extensions of standard modal logics such as , and its extensions by the schemata T, B, 4, 5, D, and their combinations. The proof (...) is obtained by extending the correspondence between the representation of modal algebras and the completeness of propositional modal logic to infinite. (shrink)

メタ倫理学、規範倫理学、応用倫理学を体系的に概説した入門書。大学における倫理学教育のミニマム・エッセンスを体系的に学べるユニークなテキスト。.

November 4th-5th, 2012 at Kyoto University. Organizers: Hisashi Nakao & Pierre-Alain Braillard.

RésuméDans la partie duŠifāʾqui porte “sur les plantes”, Avicenne aboutit à cette conclusion inattendue que celles-ci ne seraient pas vivantes. Cette thèse surprend étant donné l'opinion d'Aristote voulant que tout ce qui a une âme est vivant. Cet article montre qu'Avicenne a évolué quant à la question de la vie des plantes. Il commence par adopter la conception aristotélicienne selon laquelle les plantes sont vivantes dans la mesure où elles sont dotées d'une âme, comme il ressort de son œuvre précoce (...) qu'est leCompendium sur l'âme.Ensuite cependant, une fois qu'Avicenne a analysé les facultés de l'âme comme il le fait principalement dans sonCanon de Médecine, il est conduit à conclure que les plantes ne pouvaient pas être dites vivantes. Cet article illustre ainsi l'intérêt qu'il y a, lorsqu'on étudie le développement de la pensée d'Avicenne, à prendre en compte l'impact de ses découvertes médicales sur ses réflexions philosophiques. (shrink)

Set theory is an autonomous and sophisticated field of mathematics, enormously successful not only at its continuing development of its historical heritage but also at analyzing mathematical propositions cast in set-theoretic terms and gauging their consistency strength. But set theory is also distinguished by having begun intertwined with pronounced metaphysical attitudes, and these have even been regarded as crucial by some of its great developers. This has encouraged the exaggeration of crises in foundations and of metaphysical doctrines in general. However, (...) set theory has proceeded in the opposite direction, from a web of intensions to a theory of extensionpar excellence, and like other fields of mathematics its vitality and progress have depended on a steadily growing core of mathematical structures and methods, problems and results. There is also the stronger contention that from the beginning set theory actually developed through a progression ofmathematicalmoves, whatever and sometimes in spite of what has been claimed on its behalf.What follows is an account of the development of set theory from its beginnings through the creation of forcing based on these contentions, with an avowedly Whiggish emphasis on the heritage that has been retained and developed by current set theory. The whole transfinite landscape can be viewed as the result of Cantor's attempt to articulate and solve the Continuum Problem. (shrink)

For the modern set theorist the empty set Ø, the singleton {a}, and the ordered pair 〈x, y〉 are at the beginning of the systematic, axiomatic development of set theory, both as a field of mathematics and as a unifying framework for ongoing mathematics. These notions are the simplest building locks in the abstract, generative conception of sets advanced by the initial axiomatization of Ernst Zermelo [1908a] and are quickly assimilated long before the complexities of Power Set, Replacement, and Choice (...) are broached in the formal elaboration of the ‘set of’f {} operation. So it is surprising that, while these notions are unproblematic today, they were once sources of considerable concern and confusion among leading pioneers of mathematical logic like Frege, Russell, Dedekind, and Peano. In the development of modern mathematical logic out of the turbulence of 19th century logic, the emergence of the empty set, the singleton, and the ordered pair as clear and elementary set-theoretic concepts serves as amotif that reflects and illuminates larger and more significant developments in mathematical logic: the shift from the intensional to the extensional viewpoint, the development of type distinctions, the logical vs. the iterative conception of set, and the emergence of various concepts and principles as distinctively set-theoretic rather than purely logical. Here there is a loose analogy with Tarski's recursive definition of truth for formal languages: The mathematical interest lies mainly in the procedure of recursion and the attendant formal semantics in model theory, whereas the philosophical interest lies mainly in the basis of the recursion, truth and meaning at the level of basic predication. Circling back to the beginning, we shall see how central the empty set, the singleton, and the ordered pair were, after all. (shrink)

Ernst Friedrich Ferdinand Zermelo transformed the set theory of Cantor and Dedekind in the first decade of the 20th century by incorporating the Axiom of Choice and providing a simple and workable axiomatization setting out generative set-existence principles. Zermelo thereby tempered the ontological thrust of early set theory, initiated the delineation of what is to be regarded as set-theoretic, drawing out the combinatorial aspects from the logical, and established the basic conceptual framework for the development of modern set theory. Two (...) decades later Zermelo promoted a distinctive cumulative hierarchy view of models of set theory and championed the use of infinitary logic, anticipating broad modern developments. In this paper Zermelo's published mathematical work in set theory is described and analyzed in its historical context, with the hindsight afforded by the awareness of what has endured in the subsequent development of set theory. Elaborating formulations and results are provided, and special emphasis is placed on the to and fro surrounding the Schröder-Bernstein Theorem and the correspondence and comparative approaches of Zermelo and Gödel. Much can be and has been written about philosophical and biographical issues and about the reception of the Axiom of Choice, and we will refer and defer to others, staying the course through the decidedly mathematical themes and details. (shrink)

Paul Erdős was a mathematicianpar excellencewhose results and initiatives have had a large impact and made a strong imprint on the doing of and thinking about mathematics. A mathematician of alacrity, detail, and collaboration, Erdős in his six decades of work moved and thought quickly, entertained increasingly many parameters, and wrote over 1500 articles, the majority with others. Hismodus operandiwas to drive mathematics through cycles of problem, proof, and conjecture, ceaselessly progressing and ever reaching, and hismodus vivendiwas to be itinerant (...) in the world, stimulating and interacting about mathematics at every port and capital. (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)

Set theory, it has been contended, developed from its beginnings through a progression ofmathematicalmoves, despite being intertwined with pronounced metaphysical attitudes and exaggerated foundational claims that have been held on its behalf. In this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs. membership (...) distinction, a distinction only clarified at the turn of this century, remarkable though this may seem. Russell runs with this distinction, but is quickly caught on the horns of his well-known paradox, an early expression of our motif. The motif becomes fully manifest through the study of functionsof the power set of a set into the set in the fundamental work of Zermelo on set theory. His first proof in 1904 of his Well-Ordering Theoremis a central articulation containing much of what would become familiar in the subsequent development of set theory. Afterwards, the motif is cast by Kuratowski as a fixed point theorem, one subsequently abstracted to partial orders by Bourbaki in connection with Zorn's Lemma. Migrating beyond set theory, that generalization becomes cited as the strongest of fixed point theorems useful in computer science.Section 1 describes the emergence of our guiding motif as a line of development from Cantor's diagonal proof to Russell's Paradox, fueled by the clarification of the inclusion vs. membership distinction. Section 2 engages the motif as fully participating in Zermelo's work on the Well-Ordering Theorem and as newly informing on Cantor's basic result that there is no bijection. Then Section 3 describes in connection with Zorn's Lemma the transformation of the motif into an abstract fixed point theorem, one accorded significance in computer science. (shrink)

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...) this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)

An assessment of mood or emotion is important in developing mental health measures, and facial expressions are strongly related to mood or emotion. This study thus aimed to examine the relationship between levels of negative mood and characteristics of mouth parts when moods are drawn as facial expressions on a common platform. A cross-sectional study of Japanese college freshmen was conducted, and 1,068 valid responses were analyzed. The questionnaire survey consisted of participants’ characteristics, the Profile of Mood States, and a (...) sheet of facial expression drawing, and the sheet was digitized and analyzed using an image-analysis software. Based on the total POMS score as an index of negative mood, the participants were divided into four groups: low, normal, high, and very high. Lengths of drawn lines and between both mouth corners were significantly longer, and circularity and roundness were significantly higher in the L group. With increasing levels of negative mood, significant decreasing trends were observed in these lengths. Convex downward and enclosed figures were significantly predominant in the L group, while convex upward figures were significantly predominant and a tendency toward predominance of no drawn mouths or line figures was found in the H and VH groups. Our results suggest that mood states can be significantly related to the size and figure characteristics of drawn mouths of FACED on a non-verbal common platform. That is, these findings mean that subjects with low negative mood may draw a greater and rounder mouth and figures that may be enclosed and downward convex, while subjects with a high negative mood may not draw the line, or if any, may draw the line shorter and upward convex. (shrink)

It is known that for any subdirectly irreducible finite Heyting algebra A and any Heyting algebra, B, A is embeddable into a quotient algebra of B, if and only if Jankov's formula ${\rm{\chi A}}$ A for A is refuted in B. In this paper, we present an infinitary extension of the above theorem given by Jankov. More precisely, for any cardinal number ${\rm{\kappa }}$, we present Jankov's theorem for homomorphisms preserving infinite meets and joins, a class of subdirectly irreducible complete (...) ${\rm{\kappa }}$ - Heyting algebras and ${\rm{\kappa }}$ - infinitary logic, where a ${\rm{\kappa }}$ -Heyting algebra is a Heyting algebra A with ${\rm{\# A}} \le {\rm{\kappa }}$ and ${\rm{\kappa }}$ - infinitary logic is the infinitary logic such that for any set ${\rm{\Theta }}$ of formulas with ${\rm{\# \Theta }} \le {\rm{\kappa }}$ ⌈ Θ and ‷ Θ are well defined formulas. (shrink)

We discuss the work of Paul Cohen in set theory and its influence, especially the background, discovery, development of forcing.

Narrative views of the self argue that we constitute our self in self-narratives. Embodied views hold that our self is shaped through embodied experiences. In that case, what is the relation between embodiment and narrativity in the process of self-constitution? The question demands a clear definition of embodiment, but existing studies remains unclear on this point (section 2). We offer a correction to this situation by drawing on Merleau-Ponty’s analysis of the body that highlights its habituality. On this account, the (...) body has an inherent tendency to cultivate an organization of habits through its history of engagement with the world (section 3). Next, we explore its role in narrative self-constitution by distinguishing between two aspects of the narrative self, the narrated I and the narrating I (section 4). We argue on phenomenological grounds that self-narratives are informed by bodily perspectives in both respects. Furthermore, a focus on the habituality of the body allows for a better explanation of self-constitution than those based on implicit self-narratives (section 5). For these phenomenological and theoretical reasons, we conclude that narrative self-constitution is an embodied and embedded practice (section 6). (shrink)

Dharmakīrti argues that there is no pramāṇa (valid means of cognition or source of knowledge) for a thesis that is a self-contradiction (svavacanavirodha). That is, self-contradictions such as ‘everything said is false’ and ‘my mother is barren’ cannot be known to be true or false. The contemporary scholar Tillemans challenges Dharmakīrti by arguing that we can know that self-contradictions are false by means of a formal logical inference. The aims of the paper are to answer Tillemans’ challenge from what we (...) take to be Dharmakīrti’s or Dharmakīrtian (someone who is like Dharmakīrti) perspective and to demonstrate the unique features of Dharmakīrti’s view of inference. By so doing, we show that the epistemology in relation to the formal conception of logic that underlies Tillemans’ challenge is problematic from Dharmakīrti’s or Dharmakīrtian perspective. The paper, thus, presents Dharmakīrti’s view of inference and logical reasoning as well as a Dharmakīrtian challenge to the formal conception of logic that is the dominant contemporary conception. (shrink)

The author reflects on his long career as an educational psychologist and on the role of literature in his vision of psychological science. The author followed with great interest the major developments in psychology around the world, but he felt himself progressively alienated from the revealing power of art and literature. At one moment, he realized that a simple narrative constitutes the most profound and also the most effective means of transmitting genuine insights about teaching from one generation to another. (...) This narrative reveals a career guided by high ideals and compromised by the harsh realities of the discipline of psychology. (shrink)