We argue that the language of Zermelo Fraenkel set theory with definitions and partial functions provides the most promising bedrock semantics for communicating and sharing mathematical knowledge. We then describe a syntactic sugaring of that language that provides a way of writing remarkably readable assertions without straying far from the set-theoretic semantics. We illustrate with some examples of formalized textbook definitions from elementary set theory and point-set topology. We also present statistics concerning the complexity of these definitions, under (...) various complexity measures. (shrink)

We argue that the language of Zermelo Fraenkel set theory with definitions and partial functions provides the most promising bedrock semantics for communicating and sharing mathematical knowledge. We then describe a syntactic sugaring of that language that provides a way of writing remarkably readable assertions without straying far from the set-theoretic semantics. We illustrate with some examples of formalized textbook definitions from elementary set theory and point-set topology. We also present statistics concerning the complexity of these definitions, under (...) various complexity measures. (shrink)

Much work in MKM depends on the application of formal logic to mathematics. However, much mathematical knowledge is informal. Luckily, formal logic only represents one tradition in logic, specifically the modeling of inference in terms of logical form. Many inferences cannot be captured in this manner. The study of such inferences is still within the domain of logic, and is sometimes called informal logic. This paper explores some of the benefits informal logic may have for the management (...) of informal mathematical knowledge. (shrink)

We propose an infrastructure for collaborative content management and version control for structured mathematical knowledge. This will enable multiple users to work jointly on mathematical theories with minimal interference. We describe the API and the functionality needed to realize a cvs-like version control and distribution model. This architecture extends the cvs architecture in two ways, motivated by the specific needs of distributed management of structured mathematical knowledge on the Internet. On the one hand (...) the one-level client/server model of cvs is generalized to a multi-level graph of client/server relations, and on the other hand the underlying change-detection tools take the math-specific structure of the data into account. (shrink)

Accessing knowledge of a single knowledge source with different client applications often requires the help of mediator systems as middleware components. In the domain of theorem proving large efforts have been made to formalize knowledge for mathematics and verification issues, and to structure it in databases. But these databases are either specialized for a single client, or if the knowledge is stored in a general database, the services this database can provide are usually limited and hard (...) to adjust for a particular theorem prover. Only recently there have been initiatives to flexibly connect existing theorem proving systems into networked environments that contain large knowledge bases. An intermediate layer containing both, search and proving functionality can be used to mediate between the two. In this paper we motivate the need and discuss the requirements for mediators between mathematical knowledge bases and theorem proving systems. We also present an attempt at a concurrent mediator between a knowledge base and a proof planning system. (shrink)

‘Semantic technologies’ are touted as the next big wave in Educational Technology and as the solution to many problems in this arena. Interdisciplinary work between the fields of Knowledge Management (KM) and Educational Technology (ET) is booming. But the crop of actual systems and semantically enhanced learning objects is still meager, maybe KM and EL they are lacking a consensus on the underlying notions e.g. of ‘semantics’, yielding specific problems in their interplay. In this paper we take a (...) look at semantic educational technologies and draw conclusions for their approach in KM. In particular, we (re)-evaluate the notions of ‘semantics’, ‘knowledge’, ‘learning’, their role for learning materials in ET, and how they interact with the contexts involved in the learning/teaching process. Based on this, we distill a list of conditions the underlying knowledge representation format must fulfil to support these. As these conditions are still rather abstract, we show how they can be realized in a concrete language design, taking in our OMDoc (Open Mathematical Documents) format as a point of departure. (shrink)

In this paper we present a paradigmatic example of the use in knowledge management of techniques from other fields, namely mathematical analysis. We also highlight that the Jacobi method presented here takes precedence over the better known Hungarian method. Finally, we signify that the Jacobi method represents the first known or recognized case of serendipity in both knowledge management and operational research. This paper thus demonstrates the intersection between knowledge management, mathematical analysis (...) and operational research and how taking historical perspectives are important for recognising future applications of knowledge management. This results in a better understanding of knowledge management and how it can be applied in the future. It has been shown how knowledge management relates to historical mathematical principles. (shrink)

The significance of and the role played by Knowledge Management (KM) is ever increasing in today's business and organizational decision-making environment. This paper attempts to underline the importance of organizing knowledge not for its own sake, but for its efficient use in organizational decision making. The tremendous explosion of knowledge resources, both electronic and conventional, within the last few decades calls for an understanding of how knowledge is organized for management of data and information. (...) This is so for the reason that they can be proficiently employed to create value and utility. This also calls for a search for 'relevance' in KM with regard to its situated nature in different contexts within which knowledge is situated, and that which nevertheless indirectly refers to its ontological scaffolding. We have devised two simple mathematical models of reference with regard to the design of the systems mostly intended for organizing knowledge in knowledge organizations for its most efficient utilization. The model specifies several unique scenarios aided by discovery of arguments related to its ontological framework within which knowledge is situated. Several contexts were drawn to draw inferences from the research study. The results bear relevance to knowledge managers who make important decisions for realization of organizational goals and objectives. (shrink)

This book introduces readers to the concept of the neutrosophic set which can deal with dynamic and complex decision-making problems. With the complexity of the socio-economic environment, today's decision-making is one of the most notable ventures, whose mission is to decide the best alternative under numerous known or unknown criteria. This book provides a large amount of theoretical and practical information about the latest research in the field, allowing readers to gain an extensive understanding of both the fundamentals and applications (...) of neutrosophic sets to solve different kinds of decision-making problems and mathematical programming such as medical diagnosis, pattern recognition, construction problems, technology selection etc. (shrink)

In this study, we investigated how students manage their lack of/insufficient understanding of the content of a mathematical task with the aim of reaching shared understanding and epistemic balance in peer interaction. The data consist of recordings collected during a mathematics project in a Finnish lower secondary school. The findings, drawing on conversation analysis, showed two markedly different sequence trajectories: how interaction between a K+ and a K− student proceeded relatively smoothly when these positions were accepted by both participants, (...) and consequently the K+ led epistemic work by designing turns that resembled teachers’ practices; and how the K+/k− interaction became extended when a K− challenged the K+’s knowledge claims, and furthermore, how a K− steered the epistemic work using polar and wh-interrogatives. The findings contribute to a better understanding of the ways the management of epistemic imbalance can progress during peer group work. (shrink)

The book addresses for the first time the dynamics associated with the modernization of mathematics in China from the nineteenth to the mid-twentieth century from a transcultural global historical perspective. Rather than depict the transformations of mathematical knowledge in terms of a process of westernization, the book analyzes the complex interactions between different scientific communities and the ways in which the past, modernity, language, and mathematics were negotiated in a global context. In each chapter, Andrea Bréard provides vivid (...) portraits of a series of go-betweens based on a vast array of translated primary sources hitherto unavailable to a non-Chinese readership. They not only illustrate how Chinese scholars mediated between new mathematical objects and discursive modes, but also how they instrumentalized their autochthonous scientific roots in specific political and intellectual contexts. While sometimes technical in style, the book addresses all readers who are interested in the global and cultural history of science and the complexities involved in the making of universal mathematics. “While the pursuit of modernity is in the title, entanglement is of as much interest. Using the famous ‘Nine Chapters’ as a framework, Bréard considers a wide range of that entanglement from divination to data management. Bréard’s analysis and thought-provoking insights show once again how much we can learn when two cultures intersect. A fascinating read!”. (shrink)

Just started a new book. The aim is to establish a science of knowledge in the same way that we have a science of physics or a science of materials. This might appear as an overly ambitious, possibly arrogant, objective, but bear with me. On the day I am beginning to write it–June 7th, 2020–, I think I am in possession of a few things that will help me to achieve this objective. Again, bear with me. My aim is (...) well reflected in the title I chose (just now) for this book: Knowledge & Logic: Towards a science of knowledge. Its most important feature is that I shall take logic to be to knowledge science as calculus is to physics or to materials science. I do not intend to reclaim knowledge from the bosom of philosophy, in which, known as epistemology its erudite discussion has hardly progressed since Plato first defined it as true belief with logos. With only a few adjustments, it will actually provide me with the right, science-bound start. More recently, knowledge has been reclaimed by the field of BA, a reclaim that has opened the box of Pandora: Among the evils, and perhaps at the head of the list, is an overly lay, essentially naive, notion of knowledge. But the very idea that one can have something like “knowledge (management) software” puts us on the right track. (shrink)

Who gets to contribute to knowledge production of an epistemic community? Scholarship has focussed on unjustified forms of exclusion. Here I study justified forms of exclusion by investigating the phenomenon of so-called ‘cranks’ in mathematics. I argue that workload-management concerns justify the exclusion of these outsiders from mathematical knowledge-making practices. My discussion reveals three insights. There are reasons other than incorrect mathematical argument that justify exclusions from mathematical practices. There are instances in which mathematicians (...) are justified in rejecting even correct mathematical arguments. Finally, the way mathematicians spot mathematical crankery does not support the pejorative connotations of the ‘crank’ terminology. (shrink)

Mathematics and music in practice and performance, and in learning and teaching, share many characteristics, such as beauty and harmony, memory and intuition and mind or intellect. These raise the principles of processing information in mathematics and music and, by implication, the role of an acquaintance with the essentials of perception, abstraction and affective connaturality in teacher education. This paper compares mathematics and music and considers the acquisition of knowledge and skills through the external and internal senses and emotions, (...) utilizing the role of knowledge through multiple intelligences. In doing so it does not canvas the utilities of mathematics and music as fields of human endeavour so much as their role in the cultivation of serenity and knowledge in the cultured mind. This is a theoretical paper but it is based on nearly a century of teaching from the combined work of the two authors in the teaching of music and mathematics. The paper highlights the importance of inspiration in teaching, inspiration built on a thorough basis of the foundations of anthropology to include the emotions as well as the intellect. While teacher education programs rightly concern themselves with knowledge of the field of study, knowledge of pedagogy, they do not always consider the ability to inspire which is at the heart of managing and mentoring people. (shrink)

A central challenge for research on how we should prepare students to manage crossing boundaries between different knowledge settings in life long learning processes is to identify those forms of knowledge that are particularly relevant here. In this paper, we develop by philosophical means the concept of a dialectical system as a general framework to describe the de-velopment of knowledge networks that mark the starting point for learning processes, and we use semiotics to discuss the epistemological thesis (...) that any cognitive access to our world of objects is mediated by signs and diagrammatic reasoning and abduction as those forms of practical knowledge that are crucial for the development of knowledge networks. The rich-ness of this theoretical approach becomes evident by applying it to an example of learning in a biological research context. At the same time, we take a new look at the role of mathematical knowledge in this process. (shrink)

The merits of set theory as a foundational tool in mathematics stimulate its use in various areas of artificial intelligence, in particular intelligent information systems. In this paper, a study of various nonstandard treatments of set theory from this perspective is offered. Applications of these alternative set theories to information or knowledge management are surveyed.

Ever since the early decades of this century, there have emerged a number of competing schools of ecology that have attempted to weave the concepts underlying natural resource management and natural-historical traditions into a formal theoretical framework. It was widely believed that the discovery of the fundamental mechanisms underlying ecological phenomena would allow ecologists to articulate mathematically rigorous statements whose validity was not predicated on contingent factors. The formulation of such statements would elevate ecology to the standing of a (...) rigorous scientific discipline on a par with physics. However, there was no agreement as to the fundamental units of ecology. Systems ecologists sought to identify the fundamental organization that tied the physical and biological components of ecosystems into an irreducible unit: the ecosystem was their fundamental unit. Population ecologists sought, instead, to identify the biological mechanisms regulating the abundance and distribution of plant and animal species: to these ecologists, the individual organism was the fundamental unit of ecology, and the physical environment was nothing more than a stage upon which the play of individuals in perennial competition took place. As Joel Hagen has pointed out, the two schools were thus dividied by fundamentally different and irreconcilable assumptions about the nature of ecosystems.Notwithstanding these divisive efforts to elevate the image of ecology, the discipline remained in the shadows of American academia until the mid-1960s, when systems ecologists succeeded in projecting ecology onto the national scene. They did so by seeking closer involvement with practical problems: they argued before Congress that their approach to the theoretical problems of ecology was uniquely suited to the solution of the impending “environmental crisis.” With the establishment of the International Biological Program, they succeeded in attracting unprecedented levels of funding for systems ecology research. Theoretical population ecologists, on the other hand, found themselves consigned to the outer regions of this new institutional landscape. The systems ecologists' successful capture of the limelight and the purse brought the divisions between them and population ecologists into sharper relief — hence the hardening of the division of ecology observed by Hagen.45I have argued that the population biologist Richard Levins, prompted by these institutional developments, sought to challenge the social position of systems ecology, and to assert the intellectual priority of theoretical population ecology. He attempted to do so by articulating a nontrivial and rather carefully thought out classification of ecological models that led to the disqualification of systems analysis as a legitimate approach to the study of ecological phenomena. I have suggested that — ultimately —Levins's case against systems analysis in ecology rested on the view that an aspiration to realism and prediction was incompatible with an interest in theoretical issues, a concern that he equated with the search for generality. He sought to reinforce this argument by exploiting the fact that systems ecologists had staked their future on the provision of technical solutions to the problems of the “environmental crisis”: he associated systems ecologists' aspiration to realism and precision with a concern for practical issues, trading on the widely accepted view that practical imperatives are incompatible with the aims of scientific inquiry.46 These are plausible, but nonetheless questionable, claims which have now become an integral part of ecological knowledge. And finally, I hope to have shown how even the most abstract levels of scientific argument are shaped by political considerations, and how discussions of the conceptual development of modern ecology might benefit from a greater consideration of its historical and social dimensions.47. (shrink)

This book provides a multidisciplinary approach to Corporate Social Responsibility. While for decades a purely mathematical-technical orientation dominated the business curriculum, this book presents CSR and sustainability as a business concept embedded in its cultural and spiritual context. It initially approaches practical wisdom from different cultural and religious traditions as a source of spiritual capital for sustainable business practices. Subsequently, it links current CSR concepts and the latest thinking in CSR with long-standing cultural and spiritual knowledge, promoting a (...) more comprehensive view on sustainability management and its implementation at business enterprises. The book collects and unites viewpoints from various cultural and religious contexts, offering a comprehensive guide for international and globally active companies. (shrink)

Context: Constructivist teachers who find themselves working within an educational system that adopts a realist epistemology, may find themselves at odds with their own beliefs when they catch themselves paying closer attention to the knowledge authorities intend them to teach rather than the knowledge being constructed by their learners. Method: In the preliminary analysis of the mathematical learning of six low-performing Year 7 boys in a Maltese secondary school, whom one of us taught during the scholastic year (...) 2014-15, we constructed a conceptual framework which would help us analyze the extent to which he managed to be sensitive to constructivism in a typical classroom setting. We describe the development of the framework M-N-L as a viable analytical tool to search for significant moments in the lessons in which the teacher appeared to engage in what we define as “constructivist teaching” during mathematics lessons. The development of M-N-L is part of a research program investigating the way low-performing students make mathematical sense of new notation with the help of the software Grid Algebra. Results: M-N-L was found to be an effective instrument which helped to determine the extent to which the teacher was sensitive to his own constructivist beliefs while trying to negotiate a balance between the mathematical concepts he was expected to teach and the conceptual constructions of his students. Implications: One major implication is that it is indeed possible for mathematics teachers to be sensitive to the individual constructions of their learners without losing sight of the concepts that society, represented by curriculum planners, deems necessary for students to learn. The other is that researchers in the field of education may find M-N-L a helpful tool to analyze CT during typical didactical situations established in classroom settings. (shrink)

We present a collection of TEX macro packages that allow to markup TEX/L ATEX documents semantically without leaving the document format, essentially turning TEX/L ATEX into a document format for mathematical knowledge management (MKM).

While it is generally accepted that texts concerning navigation written by the Portuguese mathematician and cosmographer Pedro Nunes (1502–1578) were influential in erudite circles of Europe, less is known about the real impact and diffusion of his work among the less educated, such as professionals associated with sea voyages. Did Nunes' theoretical contributions reach the relevant artisans and practitioners? If so, how did this come about?This paper uses the case of Pedro Nunes to investigate how complex theoretical ideas were transmitted (...) to artisans in early modern Europe. It begins by examining the ways in which Nunes managed to interface with practitioners while working as a cosmographer. Second, it focuses on how his ideas, techniques, and results were used and transmitted by other agents, such as fellow cosmographers, navigation teachers, or mathematical practitioners. This paper concentrates on the transmission of such knowledge through vernacular texts – mainly navigation manuals and class notes – produced in the Iberian Peninsula and England in the 16th and 17th centuries. It shows how these agents facilitated the convergence between two distinct intellectual worlds – those of scholars and those of artisans – by rendering highly mathematical subjects more accessible to practitioners. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Abraham, Planter of Mathematics":Histories of Mathematics and Astrology in Early Modern EuropeNicholas PopperFrancis Bacon's 1605 Advancement of Learning proposed to dedicatee James I a massive reorganization of the institutions, goals, and methods of generating and transmitting knowledge. The numerous defects crippling the contemporary educational regime, Bacon claimed, should be addressed by strengthening emphasis on philosophy and natural knowledge. To that end, university positions were to be created (...) devoted to "Artes and Sciences at large," rather than to the professions. High salaries would render lecturers "able and sufficient," undistracted from their task. Most famously, he argued that teaching of the "operatiue studie of many Scyences" should involve sophisticated technical education. The study of natural philosophy demanded not only books, but globes, astrolabes, and other "instrumentals." Most significantly, yielding reliable and meaningful knowledge from experiential gleanings required a rigorous system of deductive reasoning.The legacy of this colossal proposal has earned Bacon honored status as devisor of the scientific method.1 But Bacon's educational reform extended [End Page 87] beyond the methods of producing and transmitting knowledge. To facilitate more efficient "vse and administration" of the knowledge produced by his system, he also demanded a searching examination of the history of learning. This history would provide a mirror enabling his contemporaries to deploy the fruits of his method, by considering how learning in the past had been used successfully or ill-advisedly. Producing this history was the ambition of the Advancement, for he explained: "no man hath propounded to himselfe the generall state of learning to bee described and represented from age to age, as many have done the works of Nature, & the State civile and Ecclesiastical." He continued:And yet I am not ignorant that in divers particular sciences, as of the Iurisconsults, the Mathematicians, the Rhetoricians, the Philosophers, there are set down some smal memorials of the Schooles, Authors, and Bookes: and so likewise some barren relations touching the Invention of Arts, or usages. But a iust story of learning, containing the Antiquities and Originalls of Knowledges, & their Sects; their Inventions, their Traditions; their diverse Administrations and Managings; their Flourishings, their Oppositions, Decayes, Depressions, Oblivions, Removes, with the causes, and occasions of them, and all other events concerning learning, throughout the ages of the world; I may truly affirme to be wanting.2Bacon thus positioned himself not only as a Father of Modern Science, but also a Father of the History of Science.Following Bacon's suggestion, I will examine the "small memorials" of the history of mathematics—and particularly the mathematical art of astrology—in the sixteenth and seventeenth centuries. My conclusion, however, will not bear out Bacon's claims. Despite his frustration, Bacon was only one of many early modern scholars appraising the role of mathematics within history. And he devoted less energy than others to mapping its origins and tracing its transmissions between communities. In fact, Bacon's 1605 proposal for a history of mathematics was already out-of-date. Discussions [End Page 88] of the history of mathematics had been rife on the continent and in England throughout the previous century.3The evidence that Renaissance scholars inherited was sprawling and inconclusive. Several genealogies for mathematics could be found within classical Greek, Latin, and patristic references. One lineage claimed mathematics began in ancient Assyria, where the priestly caste, the Chaldeans, practiced a form of mathematics that seemed a corrupt admixture of philosophy, medicine, and religion, and relied heavily on observation of the heavens. Other scholars traced the origins to Egypt, claiming that the field developed to survey lands frequently flooded by the Nile. The real problem for ancient, late antique, and medieval scholars had not been the origins of mathematics, but what exactly mathematics were. For some, the term strictly referred to the quadrivium: geometry, arithmetic, astronomy, and music. But for others, mathematics' origins amongst the Egyptians or Chaldeans inextricably linked it to forms of astrological divination, augury, and necromancy that were unsavory to both Latin and Christian traditions. Mathematici were included alongside ghastly lists of Magi, Brahmins, Aruspices, Genethliaci, and other diabolic practitioners of idolatrous magic. These might or might not be distinguished from mathematici such as Pythagoras... (shrink)

One of the fundamental and seemingly simple aims of mathematical knowledge management (MKM) is to develop and standardize formats that allow to “represent the meaning of the objects of mathematics”. The open formats OpenMath and MathML address this, but differ subtly in syntax, rigor, and structural viewpoints (notably over calculus). To avoid fragmentation and smooth out interoperability obstacles, effort is under way to align them into a joint format OpenMath/MathML 3. We illustrate the issues that come up (...) in such an alignment by looking at three main areas: bound variables and conditions, calculus (which relates to the previous) and “lifted” n-ary operators. (shrink)

Employing Searle’s views, I begin by arguing that students of Mathematics behave similarly to machines that manage symbols using a set of rules. I then consider two types of Mathematics, which I call Cognitive Mathematics and Technical Mathematics respectively. The former type relates to concepts and meanings, logic and sense, whilst the latter relates to algorithms, heuristics, rules and application of various techniques. I claim that an upgrade in the school teaching of Cognitive Mathematics is necessary. The aim is to (...) change the current mentality of the stakeholders so as to compensate for the undue value presently attached to Technical Mathematics, due to advances in technology and its applications, and thus render the two sides of Mathematics equal. Furthermore, I suggest a reorganization/systematization of School Mathematics into a cognitive network to facilitate students’ understanding of the subject. The final goal is the transition from mechanical execution of rules to better understanding and in-depth knowledge of Mathematics. (shrink)

All logic instruments and tools in possession of, and used by researchers are generally considered as the results of bivalent logic. A common error to people interested in science is that, usually, they don’t known with certainty which things are true and which are false. But they are sure that things are true or false. No ways in the middle. The fuzzy principle asserts that this is completely a question of measure. Fuzziness is the opposite concept to bivalency, while fuzzy (...) quality means polyvalency. Fuzzy logic is able to manage uncertain knowledge and, more precisely, to manage those rules difficult to formalize. In many cases, such rules haven’t got, or cannot have, the necessary precision, required for a whole formalization. (shrink)

Product acceptance determination using similarity measure index by neutrosophic statistics / Muhammad Aslam and Rehan Ahmed Khan Sherwani -- New concepts of strongly edge irregular interval-valued neutrosophic graphs / A.A.Talebi, Hossein Rashmanlou and Masoomeh Ghasemi -- The link between neutrosophy and learning : through the related concepts of representation and compression / Philippe Schweizer -- Neutrosophic soft cubic M-subalgebras of B-algebras / Mohsin Khalid, Neha Andaleeb Khalid and Hasan Khalid -- Alpha, beta and gamma product of neutrosophic graphs / Nasir (...) Shah, Said Broumi, Abdul Raheem and Tahir Imran -- Neutrosophic cubic normal ideal and neutrosophic cubic closed normal ideal of PS-algebra / Mohsin Khalid, Hasan khalid and Neha Andaleeb Khalid -- Neutrosophic multisets : an overview / Vakkas Uluçay -- Neutrosophy as a model for knowledge : the influence of representative models on thinking / Philippe Schweizer -- When neutrosophic theory meets three-way decisions / Rui Ren, Chao Zhang and Deyu Li -- Neutrosophic economic order quantity model with more than one price breaks / R. Surya, M. Mullai and G. Madhan Kumar -- General non-square systems of linear equations in single-valued triangular neutrosophic number environment / S.A. Edalatpanah -- Hesitant neutrosophic soft set relations / Abhijit Saha -- Computer application of neutrosophic set operations / S. Saranya, M. Vigneshwaran, Said Broumi -- Triangular bipolar neutrosophic based transportation problem / Avishek Chakraborty -- Studying neutrosophic variables / Rafif Alhabib and Ahmad Salama -- Decision making for logistics center location selection in trapezoidal neutrosophic environment / Kalyan Mondal and Surapati Pramanik -- Weighted similarity measure and decision making model for clinical application of single valued neutrosophic set / R.Binu and P. Isaac -- Rough neutrosophic set : an overview / Surapati Pramanik -- Some new concepts on normalized SVTN-number and multiple criteria decision making / İrfan Deli and Emel Kırmızı Öztürk. (shrink)

Education and the collective construction of knowledge. An overview -- Teaching modality : a corpus analysis of the use of must by university Spanish learners of English -- Motivation and anxiety towards mathematical learning in primary education -- Criteria for the sequencing of contemporary music in education -- Sustainability training evaluation of Spanish university students -- Art as a means of fostering peace, communication and freedom of expression from childhood -- Culturemes vs. humoremes as translation problems in practice (...) exemplified in the German Cabaret of Marc-Uwe Kling and his Kangaroo stories -- Is there homogeneity among business students regarding the level of concern towards the sustainable development goals? A cluster analysis -- Use trends and methodological pertinence of Delphi within educational research in IberoAmerica : a systematic review in Scopus -- Gamification in the improvement of speaking competences in the English as a foreign language classroom : a case study -- Quality management in the Spanish university : an analysis of the success and performance rates in communication degree programs -- Teacher stories from the future : technology for the language and literature classroom. (shrink)

This paper is an attempt to understand how social knowledge affects human economic decision making. The paper discusses the nature of social knowledge in today’s context with special reference to how social knowledge influences consumers’ sentiments and their economic decisions. Social networks are being continuously flooded with various kinds of information and disinformation. Some of the information becomes knowledge for social network users who browse various kinds of content that are either entertaining or related to products (...) and marketing. Although reliability remains a critical issue regarding online information from social networks, it, however, provides some knowledge about diverse things, goods, and products being in use in different societies around the world. Some products advertised on social networks like Facebook may affect consumer decisions or provide information about new products. This paper presents a formal discussion on what social knowledge is and how it is originated, and what use it might have for such consumers. The paper designs a simplistic mathematical model for a theoretical understanding of the assumption that has practical implications regarding its utility in society. It is found that social networks generate enough social information that can influence user choice and preferences. The study has implications for both the users and the developers of social networking sites. (shrink)

The interest of the field of Mathematical Knowledge Management is predicated on the assumption that by investing into markup or formalization of mathematical knowledge, we can reap benefits in managing (creating, classifying, reusing, verifying, and finding) mathematical theories, statements, and objects. This global value proposition has been used to motivate the pursuit of technologies that can add machine support to these knowledge management tasks. But this (rather naive) technology-centered motivation takes a view (...) merely from the global (macro) perspective, and almost totally disregards the user’s point of view and motivations for using it, the local (micro) perspective. In this paper we go a first step into a more principled analysis of the MKM value proposition by focusing on motivations for mathematical search engines from the micro perspective. We will use a table-based method called the “Added-Value Analysis” (AVA) developed by one of the authors. Even though we apply the AVA only to mathematical search engines, the method quickly leads to value considerations that are relevant for the whole field of MKM. (shrink)

"An in-depth examination of the foundations of mathematics reveals how its treatment is centered around the topic of “unique foundation vs. no need for a foundation” in a traditional setting. In this paper, I show that by applying Shelah’s stability procedures to mathematics, we confine ourselves to a certain section that manages to escape the Gödel phenomenon and can be classified. We concentrate our attention on this mainly because of its tame nature. This result makes way for a new approach (...) in foundations through model-theoretic methods. We then cover Penelope Maddy’s “foundational virtues” and what it means for a theory to be foundational. Having explored what a tame foundation can amount to, we argue that it can fulfil some of Maddy’s foundational qualities. In the last part, we will examine the consequences of this new paradigm – some philosophical in nature – on topics like philosophy of mathematical practice, the incompleteness theorems and others. Keywords: foundations of mathematics, tame mathematics, clarity-based knowledge, philosophy of mathematical practice, incompleteness theorems ". (shrink)

A comprehensive, self-contained survey of the theory and applications of differential games, one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is required, a basic knowledge of linear algebra, ordinary differential equations, mathematical programming and probability theory is necessary. Part One presents the theory of differential games, starting with the basic concepts of game (...) theory and going on to cover control theoretic models, Markovian equilibria with simultaneous play, differential games with hierarchical play, trigger strategy equilibria, differential games with special structures, and stochastic differential games. Part Two offers applications to capital accumulation games, industrial organization and oligopoly games, marketing, resources and environmental economics. (shrink)

Fuzzy cognitive maps is a system modeling methodology which applies mostly in complex dynamic systems by describing causal relationships that exist between its parameters called concepts. Fuzzy cognitive map theories have been used in many applications but they present several drawbacks and deficiencies. These limitations are addressed and analyzed fuzzy cognitive map theories are readdressed. A new novel approach in modelling fuzzy cognitive maps is proposed to increase the knowledge of the system and overcome some of its limitations. The (...) state space approach is used for the new model to disaggregate the concepts into different categories. The disaggregation of the concepts into state concepts, input concepts and output concepts is mathematically formulated. The proposed method and the new model is used for the calculation of a building’s energy consumption and the management of its load. Simulations are performed as a case study testing the new proposed method. The problem of the high energy consumption of the building sector is studied using the new fuzzy cognitive map model. Discussions of the obtained results along with future research directions are provided. (shrink)

What were the reasons of the Copernican Revolution ? How did modern science (created by a bunch of ambitious intellectuals) manage to force out the old one created by Aristotle and Ptolemy, rooted in millennial traditions and strongly supported by the Church? What deep internal causes and strong social movements took part in the genesis, development and victory of modern science? The author comes to a new picture of Copernican Revolution on the basis of the elaborated model of scientific revolutions (...) that takes into account some recent advances in philosophy, sociology and history of science. The model was initially invented to describe Einstein’s Revolution of the XX century beginning. The model considers the growth of knowledge as interaction, interpenetration and unification of the research programmes, springing out of different cultural traditions. Thus, Copernican Revolution appears as a result of revealation and (partial) resolution of the dualism , of the gap between Ptolemy’s mathematical astronomy and Aristotelian qualitative physics. The works of Copernicus, Galileo, Kepler and Newton were all the stages of mathematics descendance from skies to earth and reciprocal extrapolation of earth physics on skies. The model elaborated enables to reassess the role of some social factors crucial for the scientific revolution. It is argued that initially modern science was a result of the development of Christian Weltanschaugung . Later the main support came from the absolute monarchies. In the long run the creators of modern science appeared to be the “apparatchics” of the “regime of truth” built-in state machine. Natural science became a part of ideological state apparatus providing not only scientific education but the internalization of values crucial for the functioning of state. -/- . (shrink)

We relax the assumption that priors are common knowledge, in the standard model of games of incomplete information. We make the realistic assumption that the players are boundedly rational: they base their actions on finite-order belief hierarchies. When the different layers of beliefs are independent of each other, we can retain Harsányi's type-space, and we can define straightforward generalizations of Bayesian Nash Equilibrium and Rationalizability in our context. Since neither of these concepts is quite satisfactory, we propose a hybrid (...) concept, Mirage Equilibrium, providing us with a practical tool to work with inconsistent belief hierarchies. When the different layers of beliefs are correlated, we must enlarge the type-space to include the parametric beliefs. This presents us with the difficulty of the inherent openness of finite belief subspaces. Appealing to bounded rationality once more, we posit that the players believe that their opponent holds a belief hierarchy one layer shorter than they do and we provide alternative generalizations of BNE and Rationalizability. Finally, we show that, when beliefs are degenerate point beliefs, the definition of Mirage Equilibrium coincides with that of the generalized BNE. (shrink)

The study aimed to identify the knowledge management processes and their role in achieving competitive advantage at Al-Quds Open University. The study was based on the descriptive analytical method, and the study population consists of academic and administrative staff in each of the branches of Al-Quds Open University in (Tulkarm, Nablus and Jenin). The researchers selected a sample of the study population by the intentional non-probability method, the size of (70) employees. A questionnaire was prepared and supervised by (...) a number of specialists in order to obtain the results of the study. The study concluded that there is a positive direct relationship, that is, the higher the degree of application of knowledge management processes, the greater the degree of competitive advantage. Knowledge Technology came first with a score of 80.02% on all items. Competitive advantage came second with 81.74%. In the third place came "knowledge generation" where the total score on all paragraphs in this area (78.24%). In the fourth place, "knowledge transfer" (77.21%). "Developing and storing knowledge" came in fifth place (77.13%). "Acquisition of knowledge" came in sixth place (76.45%). Knowledge Organization ranked seventh (74.26%). The study recommended that the university should enable the employees to benefit from the experiences and expertise available to help generate knowledge. The University encourages the creation of knowledge through the system of incentives and open the way for creators to apply their creations and spread and invest in excellence and creativity. The university should design work performance levels based on the integration of knowledge and organize it according to policies that support freedom of research. The need for Palestinian universities to adopt a knowledge management approach. The need to adopt a system of incentives that rewards cognitive efforts, and give workers enough freedom to enable them to apply their knowledge. (shrink)

On knowledge and practices: a manifesto -- The web of practices -- Agents and frameworks -- Complementarity in mathematics -- Ancient Greek mathematics: a role for diagrams -- Advanced math: the hypothetical conception -- Arithmetic certainty -- Mathematics developed: the case of the reals -- Objectivity in mathematical knowledge -- The problem of conceptual understanding.

Publication date: 29 September 2016 Source: Author: Samy S. Abu Naser, Mazen J. Al Shobaki, Youssef M. Abu Amuna This paper aims to measure knowledge management maturity in higher education institutions to determine the impact of knowledge management on high performance. Also the study aims to compare knowledge management maturity between universities and intermediate colleges. This study was applied on five higher education institutions in Gaza strip, Palestine. Asian productivity organization model was applied to (...) measure Knowledge Management Maturity. Second dimension which assess high performance was developed by the authors. The controlled sample was. Several statistical tools were used for data analysis and hypotheses testing, including reliability correlation using Cronbach’s alpha, “ANOVA”, Simple Linear Regression and Step Wise Regression. The overall findings of the current study shows that maturity level is in the second level. Findings also support the main hypothesis and it is sub- hypotheses. The most important factors effecting high performance are: Processes, knowledge management leadership, People, knowledge management Outcomes. Furthermore the current study is unique by the virtue of its nature, scope and way of implied investigation, as it is the first comparative study between universities and intermediate colleges in Gaza Strip that explores the status of knowledge management maturity using the Asian productivity Model. (shrink)

This paper aims to assess knowledge management maturity at HEI to determine the most effecting variables on knowledge management that enhance the total performance of the organization. This study was applied on Al-Azhar University in Gaza strip, Palestine. This paper depends on Asian productivity organization model that used to assess KM maturity. Second dimension assess high performance was developed by the authors. The controlled sample was (364). Several statistical tools were used for data analysis and hypotheses (...) testing, including reliability Correlation using Cronbach’s alpha, “ANOVA”, Simple Linear Regression and Step Wise Regression. The overall findings of the current study suggest that KMM is suitable for measuring and lead to enhance high performance. KMM assessment shows that the university maturity level is in level three. Findings also support the main hypothesis and it is subhypotheses. The most important factors effecting high performance are: Processes, KM leadership, People, KM Outcomes, Knowledge Process. Furthermore the current study is unique by the virtue of its nature, scope and way of implied investigation, as it is the first study at HEI in Palestine explores the status of KMM using the Asian productivity model. (shrink)

In the last two decades, the World Wide Web has become the universal, and — for many users — main information source. Search engines can efficiently serve daily life information needs due to the enormous redundancy of relevant resources on the web. For educational — and even more so for scientific information needs, the web functions much less efficiently: Scientific publishing is built on a culture of unique reference publications, and moreover abounds with specialized structures, such as technical nomenclature, notational (...) conventions, references, tables, or graphs. Moreover, many of these structures are peculiar to specialized communities determined by nationality, research group membership, or adherence to a special school of thought. To keep the much-lamented “digital divide” from becoming a “cultural divide”, we have to make online material more accessible and adaptable to individual users. In this paper we attack this goal for the field of mathematics where knowledge is abstract, highly structured, and extraordinarily interlinked. Modern, content-based representation formats like OpenMath or content MathML allow us to capture, model, relate, and represent mathematical knowledge objects and thus make them context-aware and machine-adaptable to the respective user contexts. Building on previous work which can make mathematical notations adaptable we employ user modeling techniques to make them adaptive to relieve the reader of configuration tasks. We present a comprehensive framework for adaptive notation management and evaluate it on an implementation integrated in the e-learning platform panta rhei. (shrink)

The paper assesses Knowledge Management Maturity(KMM) in the universities to determine the impact of knowledge management on performance excellence. This study was applied on Al-Azhar University and Al-Quds Open University in Gaza strip, Palestine. This paper depends on Asian productivity organization model that used to assess KMM. Second dimension which assess performance excellence was developed by the authors. The controlled sample was (610). Several statistical tools were used for data analysis and hypotheses testing, including reliability Correlation (...) using Cronbach’s alpha, “ANOVA”, Simple Linear Regression and Step Wise Regression. The overall findings of the current study suggest that KMM is suitable for measuring performance excellence. KMM assessment shows that both universities maturity level is in level three. Findings also support the main hypothesis and it is sub- hypotheses. The most important factors effecting performance excellence are: Processes, KM leadership, People, KM Outcomes. Furthermore the current study is unique by the virtue of its nature, scope and way of implied investigation, as it is the first comparative study in the universities of Palestine explores the status of KMM using the Asian productivity Model. (shrink)

How can we identify and estimate workers’ tacit knowledge? How can we design a personnel mix aimed at improving and speeding up its transfer and development? How is it possible to implement tacit knowledge sustainable projects in remote areas? In order to answer these questions, it is necessary to distinguish between types of tacit knowledge, to establish what they allow for and to consider their sources. It is also essential to find a way of managing the tacit (...) knowledge ‘stock’ and distribution within the workforce. In short, a conceptual framework is needed to manage tacit knowledge. Based on previous works and 2 years of action research, this paper introduces such a framework and describes its partial application to support the pre-operational training and hiring in a large industrial plant in Brazil. Two contributions emerge from the research. First, the concept of ‘levels of similarity’ is introduced as a means to qualify the experience of workers and estimate the associated tacit knowledge. Second, the capability of carrying out three types of judgement properly and speedily is put forward as being a core ability of those who possess what has been called ‘collective tacit knowledge’ (Collins in Organ Stud 28(2):257–262, 2007). In practical terms, the results indicate the opportunity for companies to capitalize on the experience and tacit knowledge of their workers in a systematic way and with due recognition. Ultimately, positive impacts are expected in their absorptive capacity as well as in their management and human resources systems, accident prevention, productivity and the development of sustainable projects in remote areas. (shrink)

This paper is concerned with the genesis of mathematical knowledge. While some philosophers might argue that mathematics has no real subject matter and thus is not a body of knowledge, I will not try to dissuade them directly. I shall not attempt such a refutation because it seems clear to me that mathematicians do know such things as the Mean Value Theorem, The Fundamental Theorem of Arithmetic, Godel's Theorems, etc. Moreover, this is much more evident to me (...) than any philosophical view of mathematics I know of — including my own. So I am going to take mathematics as my starting point. (shrink)

We argue that mathematical knowledge is context dependent. Our main argument is that on pain of distorting mathematical practice, one must analyse the notion of having available a proof, which supplies justification in mathematics, in a context dependent way.

Although the paradigm of problems and their solutions are vastly diverse in business organizations, yet this paper focuses on two specific but important issues relating employee empowerment to their efficiency that are tied to higher attrition rates in some companies that are of much concern to senior managements. The causes are modelled and explained. The causes often relate to faulty and inadequate employee empowerment and motivation systems in place. This paper attempts to address two unique problems associated with workforce learning (...) and organizational empowerment that could be solved using knowledge management approaches. These are: i. What causes high attrition and reduced performance? ii. What changes in organizational learning structures should be implemented to address these problems? A mathematical model has been designed based on which axiomatic inferences have been derived to explain the problems and seek strategic solutions for the same. Our findings suggest that organizations must do more to support and promote employee empowerment by looking categorically into the problem issues that affect overall organizational efficiency. We hope our model successfully helps to elucidate the problem explained insofar in this research by addressing the core issues that define such problem statements. Organizations should strive to develop strategic tools to handle problems of employee attrition that are often the result of lack of oversight, and implementation of poorly executed strategies. (shrink)

This paper explores the issue of knowledge management in modern Democracies, along with the demands posed by the truth problem. While a singular concept of truth can neither be epistemically safe, thus becoming flexible for partial or subjective demonstrations of its authentic or ideal value, nor applicable for every society, it can still take the form of a critical consensus, based on two new principles that are introduced here. The continuity of such a consensus that lies beyond the (...) manipulation of an un-ethical rhetoric or demagogy can safeguard the existence of the Polis, without having to cease espousing typical logic syllogisms as well as the moral qualities that are essential for a meaningful way of social and political life. If not conducive to the collective good, the search for truth remains futile in the practical level of making people’s lives better and of enhancing their common bonds. (shrink)

This chapter tries to answer the following question: How should we conceive of the method of mathematics, if we take a naturalist stance? The problem arises since mathematical knowledge is regarded as the paradigm of certain knowledge, because mathematics is based on the axiomatic method. Moreover, natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some authors (...) tried to naturalize mathematics by relying on evolutionism. But several difficulties arise when we try to do this. This chapter suggests that, in order to naturalize mathematics, it is better to take the method of mathematics to be the analytic method, rather than the axiomatic method, and thus conceive of mathematical knowledge as plausible knowledge. (shrink)

The ARXMLIV corpus is a remarkable collection of text containing scientific mathematical discourse. With more than half a million documents, it is an ambitious target for large scale linguistic and semantic analysis, requiring a generalized and distributed approach. In this paper we implement an architecture which solves and automates the issues of knowledge representation and knowledge management, providing an abstraction layer for distributed development of semantic analysis tools. Furthermore, we enable document interaction and visualization and present (...) current implementations of semantic tools and follow-up applications using this architecture. We identify five different stages, or purposes, which such architecture needs to address, encapsulating each in an independent module. These stages are determined by the different properties of the document formats used, as well as the state of processing and linguistic enrichment introduced so far. We discuss the need of migration between XML representations and the challenges it would pose on our system, revealing the benefits and trade-off of each format we employ. In the heart of the architecture lies the Semantic Blackboard module. The Semantic Blackboard comprises a system based on a centralized RDF database which can facilitate distributed corpus analysis of arbitrary applications, or analysis modules. This is achieved by providing a document abstraction layer and a mechanism for storing, reusing and communicating results via RDF stand-off annotations deposited in the central database. Achieving a properly encapsulated and automated pipeline from the input corpus document to a semantically enriched output in a state-of-the-art representation is the task of the Preprocessing, Semantic Result and Output Generation modules. Each of them addresses the task of format migration and enhances the document for further semantic enrichment or aggregation. The fifth module, targeting Visualization and Feedback, enables user interaction and display of different stages of processing.. (shrink)

What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions.

Knowledge management hinges upon the presumption that workers within an organization possess knowledge that can be converted into concrete business improvements if the information is harvested and disseminated to others to whom it could be of use. True knowledge management must involve capturing the internal knowledge generated by a firm—its best thinking on products, customers, competitors and processes—and sharing it. Insofar as organizations are concerned, postmodernists argue that one view that has been in appropriately (...) privileged is that of the organization rather than the process of organizing. They draw our attention to the link between individual and collective identity. If there is a link between individual identity and how that individual behaves, there may also a link between collective identity and organizational action, for which a study on discourse ethics is essential. After considering the implications of knowledge management and the actual situation and work culture where the knowledge workers are in action, this paper raises and explores the questions wherein lies our individual identity and what its functional relation ship with the collective identity is. It has been envisaged in this article that through principles-driven cross-functional teams and innovative organizational mechanisms, sharing and conviction building need to be facilitated in modern organizations phasing out bureaucratic approaches and hierarchical power domination. Flexibility with a focused attitude is a must for organizations to adapt in a changing environment. (shrink)