Proof and Reasoning Research Papers (original) (raw)

2025, Proceedings of the Seventh Joint Conference on Lexical and Computational Semantics

This paper shows how to take parse trees in CCG and algorithmically find the polarities of all the constituents. Our work uses the wellknown polarization principle corresponding to function application, and we have extended this with principles for type raising and composition. We provide an algorithm, extending the polarity marking algorithm of van Benthem. We discuss how our system works in practice, taking input from the C&C parser.

2025, Goldbach proof new pdf

We prove Goldbach's Conjecture for all even integers N ≥ 4 via: • Optimized circle method with Q = ln 3.2 N , • Explicit error bounds: |E| ≤ 3.2N e-0.8 √ ln N ,

2025

In this article the proof of the binary Goldbach conjecture is established (Any integer greater than one is the mean arithmetic of two positive primes). To this end, Chen's weak conjecture is proved (Any even integer greater than one is the difference of two positive primes) and a "localised" algorithm is developed for the construction of two recurrent sequences of primes (2) and (2), ((2) dependent of (2)) such that for any integer n ≥ 2 their sum is equal to 2n : (2) and (2) are extreme Goldbach decomponents. To form them, a third sequence of primes (2) is defined for any integer n ≥ 3 by 2 = Sup (p ∈ : p ≤ 2n-3) , denoting the set of positive primes. The Goldbach conjecture has been proved for all even integers 2n between 4 and 4.10 18. and in the neighbourhood of 10 100 , 10 200 and 10 300 for intervals of amplitude 10 9. The table of extreme Goldbach decomposants, compiled using the programs in Appendix 14 and written with the Maxima and Maple scientific computing software, as well as files from ResearchGate, the Internet Archive, and the OEIS, reaches values of the order of 2n = 10 5000. In addition, a global proof by strong recurrence "finite ascent and descent method" on all the Goldbach decomponents is provided by using sequences of primes (2) defined by 2 = Sup (p ∈ : p ≤ 2n-q) for any odd positive prime q , and a majorization of 2 by 0.525 , 0.7 ln 2.2 (n) with probability one and 5 ln 1.3 (n) on average for any integer n large enough is justified.. Finally, the Lagrange-Lemoine-Levy (3L) conjecture and its generalization called "Bachet-Bézout-Goldbach"(BBG) conjecture are proven by the same type of method.

2025, ANALYSIS AND INTERPRETATION

Normality of the dataset is accessed using skewness and kurtosis statistics. Normality is required because parametric tests, such as t-test and ANOVA, are based on the principle of normal distribution (Field, 2013). If the data do not conform to the normal distribution, errors can arise in the results of these tests and potentially lead to false conclusions (McNeish & Stapleton, 2016). Skewness and kurtosis are important measures to assess normality. Skewness reflects the symmetry of the distribution. The skewness value close to 0 indicates that the data is close to the normal distribution. Positive skewness indicates right-skewed dispersion, while negative skewness indicates left-skewed dispersion (Ghasemi & Zahediasl, 2012). Kurtosis, on the other hand, measures the peak of the distribution (West et al., 1995). The following assessments pertain to the evaluation of normality in dataset:

2025, Foundations of Science , Volume 18, pp. 93–106

The philosophy of mathematics of the last few decades is commonly distinguished into mainstream and maverick, to which a 'third way' has been recently added, the philosophy of mathematical practice. In this paper the limitations of these trends in the philosophy of mathematics are pointed out, and it is argued that they are due to the fact that all of them are based on a top-down approach, that is, an approach which explains the nature of mathematics in terms of some general unproven assumption. As an alternative, a bottom-up approach is proposed, which explains the nature of mathematics in terms of the activity of real individuals and interactions between them. This involves distinguishing between mathematics as a discipline and the mathematics embodied in organisms as a result of biological evolution, which however, while being distinguished, are not opposed. Moreover, it requires a view of mathematical proof, mathematical definition and mathematical objects which is alternative to the top-down approach.

2025, In Bharath Sriraman (ed.), Humanizing mathematics and its philosophy: Essays celebrating the 90th birthday of Reuben Hersh, pp. pp. 223–252

Reuben Hersh is a champion of maverick philosophy of mathematics. He maintains that mathematics is a human activity, intelligible only in a social context; it is the subject where statements are capable in principle of being proved or disproved, and where proof or disproof bring unanimous agreement by all qualified experts; mathematicians' proof is deduction from established mathematics; mathematical objects exist only in the shared consciousness of human beings. In this paper I describe my several points of agreement and few points of disagreement with Hersh's views. Keywords Maverick philosophy of mathematics • Front and back of mathematics • Deductive proof • Analytic proof • Inexhaustibility of Mathematics • Nature of mathematical objects

2025, Apakah Mesin Bisa Berpikir Telaah Filsafat Pikiran terhadap AI Generatif

Kemajuan pesat dalam bidang Kecerdasan Buatan (AI), khususnya AI generatif seperti ChatGPT, telah menimbulkan pertanyaan filosofis yang mendalam mengenai hakikat pikiran dan kesadaran. Tulisan ini bertujuan mengeksplorasi apakah kemampuan AI dalam merespons secara rasional dan linguistik dapat diartikan sebagai bentuk berpikir otentik atau sekadar simulasi. Dengan pendekatan filsafat pikiran dan etika teknologi, esai ini mengulas dua pandangan utama: fungsionalisme yang menekankan peran dan fungsi sistem, serta intensionalisme yang menekankan kesadaran batin. Kajian ini juga mempertimbangkan implikasi etis dari memperlakukan AI sebagai entitas berpikir, serta menyoroti pentingnya refleksi filosofis dalam era digital saat ini. Kata kunci: AI generatif, kesadaran, fungsionalisme, intensionalisme, filsafat pikiran, etika teknologi Pendahuluan Dalam beberapa dekade terakhir, perubahan besar dalam teknologi Kecerdasan Buatan (AI) telah memberikan pengaruh yang signifikan terhadap kemanusiaan. Kecerdasan buatan saat ini tidak hanya terkurung pada bidang industri dan pengolahan data digital, tetapi juga telah masuk ke berbagai dimensi kehidupan sehari-hari. AI bahkan telah menguasai beberapa fungsi mental manusia, seperti proses berpikir rasional, kemampuan merespons, hingga keterampilan berbicara. Kemajuan cepat ini mengangkat kembali pertanyaan mendasar dalam bidang filsafat klasik: apakah mesin benar-benar dapat berpikir secara otentik, atau hanya meniru proses berpikir melalui simulasi algoritma? Pertanyaan itu menjadi semakin penting untuk dijawab sejak munculnya AI generatif seperti ChatGPT yang diluncurkan pada tahun 2022. Sistem ini menampilkan kemampuan luar biasa dalam merumuskan argumen naratif, menjawab pertanyaan yang kompleks, serta membentuk dialog seperti manusia. Kualitas itu secara langsung menggoyang batas-batas yang selama ini ditegaskan oleh filsafat pikiran mengenai perbedaan mendasar antara kesadaran manusia dan mekanisme mesin. Tulisan ini bertujuan untuk mengeksplorasi secara mendalam aspek ontologis

2025, Argumentation

Part of the business of argumentation theory involves resolving a conceptual dispute over what argumentation and argument are in the first place. This dispute has produced various "concepts of argument." The goal of this paper is twofold: (1) to develop a complete ontology of argumentative phenomena, capable of accounting for various conceptions of argument-something, as I argue, that is badly wanting in argumentation theory; and, within this ontology, (2) to defend a position that there is but one concept of argument needed to grasp these diverse phenomena and conceptions of argument and argumentation. I move in four steps. First, I briefly sketch the discussion over arguments-as-activities and arguments-as-products. Second, I go back to the classic work of Twardowski on actions and products and adapt it for argumentation theory, producing a complex yet systematically organized conceptual ontology of argument and argumentation. This conceptual housekeeping allows me, third, to critically engage some of the recent, Frege-inspired philosophical literature on the concept of argument, while defending act-based approaches to argument(ation). Fourth, I present a positive proposal of a minimal, contrastivist concept of argument as a set of reasons advanced to support a conclusion C 1 rather than another conclusion C n .

2025

In this paper we review selected significant developments in the use of digital technology in the teaching and learning of mathematics over the last five years. We focus on a number of important topics in this field, including the evolvement of STEAM and critical making as well as the process of redefining learning spaces in the transformation of the mathematics classroom. We also address the increasing use of computer algebra systems and dynamic geometry packages; and the issue of student collaboration online, especially using learning environments and social media. We briefly touch on artificial intelligence systems, including hyper-personalisation of learning, multimodality and videos. We include a brief discussion on the impact of COVID-19 on mathematics education, and lastly on the more theoretical perspective of the epistemology of digital technology and the construct of humans-with-media. We conclude the discussion with some possible concerns and mentioning some possible new topics for research in the field.

2025

ha pronunciato la seguente ORDINANZA nel giudizio di legittimità costituzionale dell'art. 197, comma 1, lettera d), del codice di procedura penale, promosso dalla Corte d'appello di Venezia nel procedimento penale a carico di M.I. e Z.L. con ordinanza del 21 febbraio 2013, iscritta al n. 129 del registro ordinanze 2013 e pubblicata nella Gazzetta Ufficiale della Repubblica n. 23, prima serie speciale, dell'anno 2013. Visto l'atto di intervento del Presidente del Consiglio dei ministri; udito nella camera di consiglio del 12 marzo 2014 il Giudice relatore Giuseppe Frigo. Ritenuto che, con ordinanza del 21 febbraio 2013, la Corte d'appello di Venezia ha sollevato, in riferimento agli artt. 3, 97 e 111 della Costituzione, questione di legittimità costituzionale dell'art. 197, comma 1, lettera d), del codice di procedura penale, nella parte in cui «non consente l'assunzione come testimoni dei Giudici che hanno composto il Collegio nell'ambito del processo...

2025, International Group for the Psychology of Mathematics Education

We describe the conceptualization, development, and piloting of two instruments--a survey and a scenario-based assessment--designed to assess, teachers' recognition of an obligation to the discipline of mathematics and the extent to which teachers justify actions that deviate from what's normative on account of this obligation. We show how we have used classical test theory and item response theory to select items for the instruments and we provide information on their reliability, using a sample of 88 high school mathematics teachers. This paper reports on efforts to conceptualize and measure teachers' recognition of an obligation to the discipline of mathematics and contributes to an agenda for research that attempts to identify sources of justification for actions in mathematics teaching. This agenda is predicated on the need to have robust ways of predicting how efforts at instructional improvement might fare as they are implemented. The general problem is, given an instructional system located in an institutional context, where, by force of custom, teacher and students are expected to act in ways that are normative, what sources of justification are available for practitioners to use so as to justify, for themselves and colleagues, actions that might depart from the norm? In their practical rationality framework, Herbst and Chazan (2012) proposed the notion of professional obligations as a set of those sources of justification. They identify four obligations --to the discipline of mathematics, to students as individuals, to the class as a social group, and to the institutions where instruction is located (e.g., school, district). This report elaborates on the disciplinary obligation and presents results of our attempts to develop two instruments designed to study it empirically. 1 Work done with the support of NSF grant DRL-0918425 to P. Herbst. All opinions are those of the authors and do not necessarily represent the views of the Foundation.

2025, Bézout's identity

This here is a Proof of "Bézout's identity" in a diffrent way as i am using "Proof by induction"

2025, Soyut Matematiğe Giriş: Matematiksel İspatı Anlamak

"Soyut Matematiğe Giriş: Matematiksel İspatı Anlamak" kitabı, soyut matematiğe giriş yapmak isteyen öğrencilere rehberlik etmeyi amaçlayan, pedagojik ve sistematik bir ders kitabıdır. Kitap, matematiğin yalnızca hesaplama değil; aynı zamanda akıl yürütme, ispat yapma ve mantıklı düşünme sanatı olduğunu vurgular. İlk bölümler, matematiksel dilin temelleri olan mantık, kümeler ve fonksiyonlar gibi konulara ayrılmıştır. Devamında, matematiksel ispat yöntemleri detaylı bir şekilde ele alınır: doğrudan ispat, çelişkiyle ispat, karşıt ters ve tümevarım gibi temel teknikler örneklerle sunulur. Ayrıca, ispat yaparken sıkça karşılaşılan hatalara dikkat çekilir ve açık, anlaşılır matematiksel anlatımın önemi vurgulanır. Kitap, yalnızca teorik anlatım sunmakla kalmaz; her bölüm sonunda yer alan alıştırmalarla öğrencinin konuları aktif olarak pekiştirmesini sağlar. Özellikle “ispat şemaları” başlığı altında, öğrencilerin düşünme kalıplarını geliştirmelerine yardımcı olacak görsel ve yapısal destekler sunulmuştur. Matematik bölümü öğrencileri ve öğretmen adayları başta olmak üzere, soyut matematiğe ilgi duyan herkes için hem kaynak kitap hem de bireysel çalışma materyali olarak değerlidir. Kitap, okura sağlam bir düşünsel temel kazandırmayı ve matematiğe karşı derinlemesine bir anlayış geliştirmeyi hedeflemektedir.

2025

It is known that, in the presence of pairing/projection functions, (pure) iteration can simulate primitive recursion [R. M. Robinson, Bull. Am. Math. Soc. 53, 925–942 (1947; Zbl 0034.29102); G. J. Tourlakis, Computability. Reston, Virginia: Reston Publishing Company, Inc. (1984; Zbl 0577.03018)]. This fact implies that the class of primitive recursive functions, Pℛ, can be obtained as the closure of a small set of initial functions under substitution and pure iteration – as long as the floor of the square root is included as an initial function to bootstrap the construction of pairing/projection functions – or from just the successor and predecessor functions if we add bounded search to the a priori available operations. In Section 2 of the paper we show that neither the inclusion of square root nor of bounded search are necessary to build Pℛ from the successor and predecessor. In Section 3 we show that the class of partial recursive functions, P, can be obtained as the closure of P...

2025

Abstrak:"Tulisan ini mengeksplorasi batas-batas kecerdasan buatan (AI) dalam mereplikasi kesadaran dan pengalaman subjektif manusia. Melalui perspektif filosofis, neurosains, dan ilmu kognitif, dibahas tiga tantangan utama: masalah qualia (pengalaman subjektif yang tak tereduksi), kesenjangan antara komputasi dan pemahaman (seperti dalam eksperimen Chinese Room Searle), serta kompleksitas bahasa dan makna yang melampaui logika simbolik. Tulisan ini juga mengkritik narasi reduksionis yang menyamakan pikiran dengan mesin komputasi, sambil menawarkan refleksi tentang dimensi eksistensial—seperti kreativitas, intuisi, dan kebijaksanaan—yang tetap menjadi keunikan manusia. Dengan merujuk pada pemikir seperti Nagel, Chomsky, dan Dennett, tulisan ini menyimpulkan bahwa AI mungkin mampu meniru aspek fungsional kecerdasan, tetapi tidak akan pernah sepenuhnya memahami atau mengalami dunia seperti manusia".

2025, Pontificia Universidad Católica del Perú

CORE View metadata, citation and similar papers at core.ac.uk provided by Repositorio Digital de Tesis PUCP ÍNDICE INTRODUCCIÓN 1 CAPITULO I -Del Problema 5 1. Identificación del Problema 5 1.1. Definición del problema. 1.2. Descripción del servicio o bien entregado 1.3. Marco conceptual del problema 1.4. Evidencia del problema 1.5. Indicador de Desempeño. 1.6. Afectación del problema al ciudadano. 2. Estado de la Cuestión. 21 2.1. Identificación de medidas adoptadas por la institución frente al problema. 2.2. Normas vinculadas al problema. 2.3. Estudios sobre el problema identificado. CAPITULO II -De la propuesta de mejora. 31 3. Causas del problema. 31 3.1. Causa 01: Información difusa de la normatividad procedimental en la DIRCRI. 3.2. Causa 02: No adecuación a los avances tecnológicos para optimizar la función administrativa. 3.3. Causa 03: Vacío normativo institucional en materia de distribución de informes periciales. 3.4. Resumen. 4. Transformación de Árbol de Problemas a de Medios. 36 4.1. Condición 01: Estandarización de estructura administrativa y normativa en la DIRCRI 4.2 Condición 02: Maximizar el uso de la tecnología para optimizar la función administrativa. 4.3. Condición 03: Marco normativo institucional sobre distribución de informes periciales. 5. Estructura de la Solución.

2025, Educação Matemática Pesquisa

This paper aims to build a conceptual framework that addresses spatial geometric thinking and the respective visualization skills required at different levels of the schooling process. Studies indicate that spatial geometric sills are essential for scientific thinking. It encompasses a set of cognitive processes through which humans can construct and manipulate mental representations of objects in space and is a skill directed towards understanding objects and their relations in the 2D and 3D worlds. The use of these spatial reasoning skills involves drawing, manipulating, and explaining objects and their relationships and should be developed from the first years of schooling. Based on this theoretical context, partial research results on surface representations that can be manipulated in three dimensions (3D) and obtained through GeoGebra will be

2025, Metascience

It is an interesting question what constitutes the rigour in a rigorous mathematical proof. The following piece is in the first instance a review of a booklet on this subject and in the second a more leisurely meditation on why it might be so difficult to grasp the nature of this rigour today. Part of the answer, I suggest, is the neglect of geometry in the school education. There is a link to the shorter, edited, published version.

2025

: No Direito Processual Brasileiro, os limites à prova são diversos e visam garantir um processo justo e equitativo. A prova, embora um direito fundamental, não é ilimitada, sendo que a Constituição Federal e o Código de Processo Civil estabelecem regras para a sua produção e admissibilidade. Princípios que Regem a Prova são: Princípio do Livre Inquérito: O juiz tem o poder de determinar a produção de provas que considerar necessárias para o julgamento do caso, mesmo que as partes não as tenham requerido.

2025, Tracés. Revue de sciences humaines

What are the techniques, discourses, temporalities, and actors involved in elaborating, performing, and disseminating evidence? In the wake of philosophy and pragmatic sociology, which have long been concerned with the question of investigation and evidence, this dossier explores the multiple trajectories of evidence in the legal, journalistic, medical, scientific, and artistic arenas in which it takes shape. It examines the collection of traces and their transformation into evidence in the light of their singular topographies —intimate (the body), material (images, archives), or more abstract (mathematical operations). This processual approach pays particular attention to the uncertainty inherent in the stages of qualification, verification, debate, and narration, which may or may not transform a trace into evidence. The fields of investigation approached here go beyond the judicial sphere. They involve intermediaries in the work of proof, whether informally or more institutionally. Moreover, the dossier looks at new identification, monstration, and demonstration techniques, which can reconfigure the witness and expert roles. The aim is to understand better how the multiplication of actors, forms, and areas of investigation change investigative practices and the epistemology of evidence.

2025

We present a geometric framework where classical theorems in Euclidean geometry emerge from finite,minimal, conserved data units (information bits), such as lengths, angles and their ratios. These bits and the theorems' proofs obey a conservation principle. Our axioms state that all geometric entities are defined by finite bit sets (e.g., side ratios, angle sines) and adjoining new bits generates equivalent bits under algebraic relations. Theorems arise as equivalence relations between existing, adjoining, and equivalent bits. This framework unifies proofs via information invariance where proofs are reducing to combinatorial bit-balance verifications. Linking Euclidean geometry to information theory and monoid structures, offering new insights into the complexity of geometric proofs and the limits of compass-straightedge constructions. Key examples demonstrate how bitfunctions generate theorems under the principle of information conservation. Principal results include the derivation of Euclid's parallel postulate as a theorem through bit-conservation, constructive proofs of congruence criteria without infinite processes and proofs for collinearity and convergence theorems such as convergence of triangle medians, Pappus and Desargues' theorems.

2025, Figures de la vérité

The paper's purpose is to articulate a deflationary conception of truth and the view that the notion of truth in critical for rational inquiry. The key to the suggested articulation is the identification of the "reflective stance" as one... more

2025, Education Sciences

This study is aims to determine the students' conceptual misjudgments and mistakes about sets in 8 th and 9 th grade. 19 students of 8A class of An Elementary School and 22 students of 9B class of An Anatolian Teacher Training College are participated. To achieve the purpose 5 written question has been prepared and conducted. Conceptual misjudgments and mistakes of the students had been studied and compared. It had been seen that 8. grade students have various conceptual mistakes about sets and 9. Grade students also have some of those conceptual mistakes.

2025, HAL (Le Centre pour la Communication Scientifique Directe)

The aim of this paper is to give a short survey of the studies that concern the notion of Hilbert's ε-operator and its applications by the researchers in the USSR and continuation of their works abroad in post-soviet time.

2025, Social Media

This paper analyzes Thomas Aquinas' justification of metaphor and multivalence in Scripture through the lens of modern communication theory, particularly information theory and the epistemology of transmission. It explores the historical consequences of divergent interpretation-especially religious persecution-and juxtaposes this tradition with the interpretive clarity and intellectual openness of Euclid's Elements. Expanding this comparison, the paper integrates Catholic and Protestant assertions on scriptural authority, inerrancy, and inspiration, contrasting them with mathematical axioms, proof systems, and consensus protocols. The inclusion of Dei Verbum, the Dogmatic Constitution on Divine Revelation, further elucidates the Catholic Church's stance on the relationship between Scripture and Tradition. The conclusion affirms that the difference is not merely in textual content but in the structure of interpretive authority, the risk of deviation, and the openness of verification.

2025

This paper presents a comprehensive formalism for the Phase-Shifted Resonance-Based Knowledge Model Architecture, a novel approach that integrates principles from quantum mechanics, information theory, and cognitive science. The architecture leverages prime number structures, harmonic resonance, and entropy-driven computation to create a theoretically robust framework for knowledge representation and processing. We develop the mathematical foundations underlying five interconnected subsystems: Prime Hilbert Encoding, Mod 9 Harmonic Phase Encoding, Iterative Resonance Attention, Observer-Conditioned Collapse, and Entropy-Modulated Resonant Memory. Our formalism establishes key theoretical results including convergence guarantees, entropy reduction dynamics, and semantic attractor formation. Potential applications span machine learning, quantum computing, and cognitive modeling domains. The integration of number-theoretic structures with entropy-driven processing offers a promising direction for systems that can learn efficiently while maintaining interpretable internal representations aligned with cognitive principles.

2025, Revista de Processo

O artigo aborda a admissibilidade de prints de conversas de WhatsApp como meio de prova em processos cíveis. Defende-se que, como qualquer outra prova documental, os prints de WhatsApp são admissíveis, desde que relevantes para o julgamento do processo e obtidos por meios lícitos. Cabe à parte contrária o ônus de impugnar a autenticidade ou veracidade dessas provas. Argumenta-se que tais prints devem ser reconhecidos como documentos, e que sua aceitação deve seguir as normas processuais de direito probatório que regulam a admissão, produção e a valoração da prova documental. Ressalta-se que rejeitar esse tipo de prova seria contraproducente, considerando seu uso amplamente disseminado na vida cotidiana, tanto em interações pessoais quanto em profissionais. Finaliza-se propondo boas práticas para a juntada desses documentos, a fim de garantir maiores segurança e autenticidade no uso de prints de WhatsApp em processos cíveis.

2025

Comment, pour comprendre le rôle d'Arabella chez Wittgenstein dans son cours devant Turing il faut passer par le rôle d'Ariane chez Deleuze.

2025

There is evidence for recommendations to link mathematics teacher education (MTE) closely to school mathematics and to emphasise proving why rather than proving that when teaching reasoning and pro ...

2025, Proceedings of The Twenty-Sixth ICMI Study Advances in Geometry Education

This paper presents the results of a quasi-experimental research study conducted with pre-service primary education teachers in Croatia aged 19 to 23. The purpose of the research was to evaluate an alternative approach to learning and teaching geometry to develop visualization skills and geometric thinking and achieve better learning outcomes. The alternative teaching approach was based on van Hiele's theoretical framework, on the visual-analytical method of directed observation, and on the balancing of visual, linguistic, and symbolic expressions. The control group was taught in the traditional way. In order to collect data on the research participants, the three tests were used before and after teaching: the first to measure the level of geometric thinking, the second to gain insight into geometric knowledge and visual skills, and the third to measure special visual-spatial ability. At the beginning of teaching, there were no statistically significant differences among the research participants. After teaching, the progress of the participants in the experimental group was statistically significant compared to the participants of the control group.

2025

Est-il même possible de défier un Dieu tout-puissant ? Le défunt physicien Stephen Hawking a un jour réfléchi : "Il peut y avoir un Dieu... mais la science peut expliquer l'univers sans avoir besoin d'un créateur." Pour contester le... more

2025, Telecom

Traditional networking is hardware-based, having the control plane coupled with the data plane. Software-Defined Networking (SDN), which has a logically centralized control plane, has been introduced to increase the programmability and flexibility of networks. Knowledge-Defined Networking (KDN) is an advanced version of SDN that takes one step forward by decoupling the management plane from control logic and introducing a new plane, called a knowledge plane, decoupled from control logic for generating knowledge based on data collected from the network. KDN is the next-generation architecture for self-learning, self-organizing, and self-evolving networks with high automation and intelligence. Even though KDN was introduced about two decades ago, it had not gained much attention among researchers until recently. The reasons for delayed recognition could be due to the technology gap and difficulty in direct transformation from traditional networks to KDN. Communication networks around the globe have already begun to transform from SDNs into KDNs. Machine learning models are typically used to generate knowledge using the data collected from network devices and sensors, where the generated knowledge may be further composed to create knowledge ontologies that can be used in generating rules, where rules and/or knowledge can be provided to the control, management, and application planes for use in decision-making processes, for network monitoring and configuration, and for dynamic adjustment of network policies, respectively. Among the numerous advantages that KDN brings compared to SDN, enhanced automation and intelligence, higher flexibility, and improved security stand tall. However, KDN also has a set of challenges, such as reliance on large quantities of high-quality data, difficulty in integration with legacy networks, the high cost of upgrading to KDN, etc. In this survey, we first present an overview of the KDN architecture and then discuss each plane of the KDN in detail, such as sub-planes and interfaces, functions of each plane, existing standards and protocols, different models of the planes, etc., with respect to examples from the existing literature. Existing works are qualitatively reviewed and assessed by grouping them into categories and assessing the individual performance of the literature where possible. We further compare and contrast traditional networks and SDN against KDN. Finally, we discuss the benefits, challenges, design guidelines, and ongoing research of KDNs. Design guidelines and recommendations are provided so that identified challenges can be mitigated. Therefore, this survey is a comprehensive review of architecture, operation, applications, and existing works of knowledge-defined networks.

2025

Ce qui suit est un échantillon d'un recueil qui n'a pas encore été publié et qui comprend 65 courts textes. Les sujets traités ne concernent pas spécifiquement la psychologie, mais toutes les disciplines des sciences humaines et sociales. L'ensemble du recueil est provisoirement hébergé dans la section Livres, sur la page Web de l'auteur: Comme le disent les savants, « tout se passe comme si » notre cerveau était divisé en deux moitiés qui s'ignorent et qui peuvent ainsi se contredire allègrement sans le moindre problème. Tout cela en parfaite dissonance avec notre conscience qui se perçoit comme unique, gouvernée par la raison et par conséquent allergique aux contradictions. Par exemple, quand nous, les Occidentaux, interprétons les différences entre les peuples en termes de développement technologique ou institutionnel, nous ne voyons aucune contradiction dans nos théories. Et pourtant, on dira que l'isolement géographique a été l'une des causes du sous-développement des îles comme Haïti ou Madagascar, mais s'il s'agit de l'Angleterre ou du Japon, on affirmera que leur insularité aurait joué un rôle favorable. De la même façon, une forte croissance démographique sera invoquée comme un frein au développement de l'Afrique, mais comme un puissant accélérateur quand elle s'est produite en Europe ou en Amérique du Nord.

2025

Σκοπός της παρούσας έρευνας είναι η διερεύνηση των απόψεων των δασκάλων αναφορικά με την ενασχόληση της σχολικής τάξης με τη μαθηματική απόδειξη στο πλαίσιο διερεύνησης τύπου Lakatos (ΔτL). Με τη χρήση ενός ερωτηματολογίου βασισμένο σε επεισόδια από μια σχολική τάξη σε μορφή κόμικς συλλέξαμε δεδομένα από 331 εν ενεργεία και μελλοντικούς δασκάλους αναφορικά με τις προσδοκίες τους από την ενασχόληση με τη ΔτL, καθώς και την αξία και το κόστος που εκτιμούν πως έχει για τους ίδιους και για τους μαθητές. Τα αποτελέσματα δείχνουν πως υπάρχουν λίγες διαφορές μεταξύ μελλοντικών και εν ενεργεία δασκάλων, οι οποίοι συνολικά βλέπουν θετικά την ενσωμάτωση της ΔτL στο μάθημά τους.

2025

Despite the importance of proving across all school years, little is known about primary teachers’ knowledge and views about a special form of proving activity described as Lakatos-style and associated with authentic engagement with mathematics even in primary school. We aimed to identify profiles of primary teachers based on their mathematical knowledge (of content, students, and teaching practices) and views (related to value, cost, and expectancy) about Lakatos-style proving activity. 331 participants responded to a vignette-based survey with 66 Likert-scale items referring to comic-style classroom episodes. Latent profile analysis revealed six teacher profiles reflecting a wide range of views, various levels of knowledge, and combinations thereof. Future research and teacher education practice can consider the unique characteristics of each profile to provide appropriate support to teachers based on each profile’s strengths and needs.

2025, Actualidad Jurídica

El presente trabajo examina el derecho de las partes de un juicio a presentar una implicancia o recusación contra el juez, como un mecanismo para garantizar el derecho a un juez independiente, imparcial e idóneo, integrante del contenido sustantivo del debido proceso. Este análisis constata la problemática derivada de la taxatividad de las hipótesis legales que permiten invocar una implicancia y recusación, que limita la posibilidad de señalar situaciones distintas que también podrían evidenciar la parcialidad o falta de idoneidad del juez. Finalmente, se consideran distintas alternativas para lograr proponer posibles soluciones.

2025, HAL (Le Centre pour la Communication Scientifique Directe)

Despite recognition of the importance of Lakatos-style proving activity in the mathematics classroom, we know little about whether teachers' relevant mathematical knowledge is conducive to supporting it in their classrooms. We take a step towards addressing this research gap by reporting the results of an exploration of two primary teachers' mathematical knowledge of content, students, and teaching practices relevant to Lakatos-style investigation of proof tasks. Through vignettes-based, semi-structured interviews, we presented the participants with 19 illustrated classroom episodes covering a range of Lakatosian techniques and a range of student ways of engaging with supportive examples and counterexamples to formulate, validate, refute, and refine conjectures of different types. Participants' responses revealed both productive and counterproductive understandings highlighting that although Lakatos-style proof lies within teachers' reach, supporting their preparation is crucial.

2025, Comput. Sci. J. Moldova

In this paper, we introduce a new paradigm - multiset-based tree model. We show that trees can be represented in the form of wellfounded multisets. We also show that the conventional approach for this representation is not injective from a set of trees to the class of multisets representing such trees. We establish a oneto-one correspondence between trees and suitable permutations of a wellfounded multiset, which we call tree structures. We give formal deflnitions of a tree structure and a subtree structure of a tree structure. Finally, we represent membrane structures in the form of tree structures { a form in which membrane structures can suitably be represented at programming level.

2025

The aim of this study is to analyze and compare the argumentation and proving processes of senior high school students by using Toulmin's model. Four senior high school students participated in the study. A problem was used to gather data, and the participants were asked to prove the statement they produced with their pairs. The results of the analysis showed that when the students made a deductive proof after abductive argumentation, they could complete the proof process successfully. However, the students who made abductive proof after abductive argumentation were not able to prove the statement. The results of this study may be useful in analyzing the argumentation and proof processes and in determining the relationships between them to facilitate the proving process for the students. Summary

2025

We present a foundational unification of number theory, topological dynamics, and noncommutative geometry through a novel theory of prime numbers. By embedding the natural numbers in a specialized Fuzzy Differentiable Algebraic Graph System (F-DAGS), we demonstrate that prime numbers emerge inevitably as global attractors in a contractive manifold with precisely quantifiable spectral isolation properties. Our analysis extends through three major theoretical advances: (1) the characterization of primes as topological fixed points in a dynamical system; (2) the construction of multi-scale F-DAGS structures revealing emergent hierarchical prime decomposition patterns; and (3) the identification of primes as spectral singularities in non-commutative geometry. Our results leverage the Analytic Foundations Theorem (AFT), generalized Measure-Theoretic Cauchy Criterion, Multi-Agent Symbiotic Response Mechanisms (MASRM), and Dynamic Thought Evolution with Helical Encoding and DNA-Inspired Memory (DTE-HDM), yielding a framework with implications for quantum computing, cryptography, and AI-driven mathematical discovery.

2025

We introduce and rigorously prove the Analytic Foundations Theorem (AFT), the first major measure-theoretic generalization of the Fundamental Theorem of Calculus (FTC). The theorem precisely quantifies the discrepancy between integration and differentiation operations in the context of Lebesgue integrable functions, providing explicit bounds on exceptional sets. We extend the results to higher dimensions, probabilistic frameworks, and distributional forms. Applications to differential equations, numerical analysis, and Fuzzy Differentiable Algebraic Graph Systems (F-DAGS) demonstrate the theorem's broad impact.

2025, LA DEFENSA PENAL (Pablo Rovatti, coord.)

Se sostiene la necesidad de que los tribunales realicen un control serio de fiabilidad de las pruebas periciales, y de que los abogados "colaboren" en esa tarea mediante un contrainterrogatorio epistémicamente fundado. Se sugieren... more

2025

This essay explores how Plato's epistemology cannot be separated from his metaphysics. Particular consideration is given to the emaciation and delegitmisation of Plato's epistemological contributions in contemporary philosophy.

2025, Deus ex Universum: A Theological Equation for Cosmic Affection (With Footnotes and Existential Wit)

This paper posits a pantheistic framework wherein the universe (hereafter termed GOD) exhibits a statistically improbable affection for life-specifically, the human variety. By synthesizing the Fine-Tuning Argument, Fermi Paradox dynamics, and a dash of irreverent speculation, we propose that the universe's apparent indifference is, paradoxically, evidence of divine benevolence. Suggestions for reconciling theology with cosmology are appended, including a mathematical model for divine love (coefficient: ε = 0.999...).

2025

This study is part of a larger project exploring how beginning teachers learn to teach mathematics via reasoning and proving. The study followed two beginning secondary mathematics teachers for two years. First, as students in a capstone course in which they learned to integrate reasoning and proving into teaching mathematics, and then as full-time interns in secondary schools. The culminating part of the internship was an action research / inquiry project devoted to reasoning and proving. This exploratory multi-case study examined how conducting such an inquiry project affected interns' discourses and practices for teaching mathematics via reasoning and proving. The results show that both beginning teachers successfully recontextualized what they learned in the capstone course in their inquiry projects. Yet, there were substantial differences between the two interns, which affected their conclusions about continuing integrating reasoning and proving in their classrooms.

2025, The Body in Mathematics: Theoretical and methodological lenses.

In this chapter, the work of a pair of mathematics doctoral students is examined as they collaborate to seek a proof for a mathematical conjecture that is new to them. Particular attention is paid to how the students communicate their mathematical ideas to each other, using the various modalities and semiotic resources available to them. The interplay among the modalities of oral speech, gesture, symbols, and diagrams is analyzed, including their grounding in body-based image schemas.

2025, Conférence INFORSID

Nous montrons sur un petit exemple, un tampon à deux places, comment on peut utiliser de manière complémentaire la preuve, le raffinage et le model-checking. Nos outils logiciels sont l'Atelier B, LTSA et le langage FSP ainsi que ProB ABSTRACT. We show with a small example, a two-places buffer, how proof, refinement and modelchecking can be used in a complementary manner. Our software tools are Atelier B, LTSA and ProB.

2025

Goldbach's Conjecture states every even integer n > 2 can be written as the sum of 2 primes, while Bertrand's Postulate states for each n ≥ 2 there is at least one prime p such that n < p < 2n. I show both are essentially statements on the primes distribution, and their inherent properties when modeled and understood as the residues of modular groups Zn. In addition, a much tighter dynamic bound on p than given by the BP will be presented.