Mathematical Logic Research Articles

Islamic Integrated Maths: Mathematical Logic in the Qur'an

One of the goals of national education is to form students who are faithful and devoted to God Almighty. Islamic-integrated mathematics learning is a bridge to achieving this goal. This study aims to explore the verses in the Quran related to the concept of mathematical logic. A literature review using qualitative research was conducted in this research. Data were obtained from the Quran, the Book of Tafsir, and relevant journal articles. The results showed the concept of mathematical logic in the Quranic verses. The conjunction form is found in surah Al-Baqarah verse 25, the disjunction form is found in surah Al-Balad verses 12 to 16, and the negation form is found in surah Al-Kafirun verses 2 to 5. Implication form is found in surah Al-Fatihah verses 6 and 7. The results of this study can be a reference for learning resources in mathematical logic and logic and set integrated with Islam at the school and lecture levels.

Forming the competence of physics and mathematics students using information technology

Relevance. The relevance of the study arises as computers in educational institutions have ceased to be a mere subject of study and have become a tool for learning. The main purpose of using computer-based learning technologies is to increase the efficiency of the learning process. This task is also solved by increasing the motivation of students to study technical graphics. Graduates should be able to use graphics systems to create both blueprint and design documentation and to solve three-dimensional graphic modelling tasks. Purpose. The purpose of the study was to identify the features of the formation of professional competence of non-humanitarian specialities through information technology. Methodology. The methodological basis of the study was general theoretical methods, through which it was possible to determine the fact that the use of information and communication technologies in the classroom allows raising the level of information culture, realising the potential of each student, and forming the professional skills of future specialists. Results. This article covered the main methods of using information technology in mathematics and physics classes, the features of the competency-based approach, the advantages of using innovative computer technology, and the types of technologies used. It has been found that the use of information technology in mathematics and physics classes affects: the activation of students' cognitive activity, development of mathematical logic, variability of reasoning, and concentration of students' intellectual activity on research and investigation. Conclusions. The practical significance of the study lies in the fact that its findings and conclusions improve the training in the development of competence of students of physics and mathematics specialities using information technology in educational activities.

НЕЗАКРЫТЫЕ ВОПРОСЫ ПО НЕКЛАССИЧЕСКОЙ ЛОГИКЕ (ПАМЯТИ ПРОФЕССОРА Д. В. ПИВОВАРОВА)

As a methodological tool of sorts in the memorial paper makes use of reconstruction of professor Pivovarov’s talks, which often displayed genuine, persevering and always critical interest in non-classical logic. The questions at hand are the question of scientific status and philosophical consistency of deuniverslization of classical logic. The various types of logical systems, whose co-existence was brought about during the XX century, has become an actual phenomenon, insistently calling for a broader philosophical, scientific, and even cultural reflection on the nature of contemporary logic as a body of knowledge. Among the questions three touch upon the problem of the status of non-classical logic, considered as the part of humanities: Should non-classical logic be taken as a response to mathematical logic’s absolute «inhumanity»? Mathematization of logic is related to another crisis of the foundations of mathematics – could one imply the crisis of ultimate methodological principles of social studies and humanities to be the reason for deuniversalization of classical logic? Does non-classical logic fit the natural reasonings? Three other questions address the philosophy of logic: Does contemporary logic – whether classical or not – build upon mathematics still belong to philosophy? Is there distinctive philosophy of non-classical logic yet? Could non-classical logic still serve as the normative discipline, as the «canon of thinking»? The very character of the questions doesn’t lead to any closed, definitive answers. Be that as it may and, having the current scientific studies philosophically reflecting on the logical pluralism backing us up, we aim here at a coherent and a consistent examination of philosophical aspects and problems of non-classical logic. The examination resulted in formulating several key results: non-classical logic’s development effectively was a response to semantic and metatheoretical problems of mathematical logic, that was coming to be, but a kind of «humanistic» aspect is the fundamental non-elimination of the subject in the semantics of the corresponding intensional logics; the actuel stance is supported that various types of reasoning do not correspond to the subject of logic, but can be (and traditionally are) objects of application of various logics as intellectual tools; extrological stimulations and especially intrological resources of logical investigations affect significantly the current understanding of philosophical nature of logic; the question of alterations of ontological and epistemological premises, which underlie the various logical systems – an essential one for the philosophy of logic – is reformulated as in effect being the question of correctness and efficiency of some particular tools in the logical arsenal; logical analysis in general is to be methodologically receptive to different contexts, their specifics in order to avoid destructive conflicts, threatening to eliminate the uniqueness of said contexts. The author voices a hope, that the critical assessment of the results presented as to their being valuable and sound will make the work a proper incentive for perspective and productive discussion of diversity of logic.

Strategic Decision-Making Enhancement Framework (SDE-Framework): Leveraging Neutrosophic Logic and Fuzzy Mathematics for Optimized Outcomes in IT Management and Computational Systems

The created SDE-Framework combines neutronosophic logic and fuzzy mathematics in a novel method, aiming at facilitating more informed decision outcomes in computational systems and information technology management. This method hopes to aid in determining strategic solutions by controlling the expected sophistication and ambiguity in these two technologically dynamic industries. Neutronosophic logic divides data into three components: truth, indeterminacy, and falsity, build an exhaustive technique for addressing contradiction and indeterminacy. This significantly increases the method by enabling a more complete exploration of potential options with ambiguous and inadequate data. Second, the fuzzy mathematics gives a valuable contribution. It offers a refined method for managing the levels of probability and certainty through membership features, resulting in more exact and flexible evaluations. By the usage of such compared sophisticated mathematics concepts, SDE-Framework addresses potential decision-making scenarios by letting the computer formulates do the judgements for the determinable and in determinable explicit data. The subsequent crucial parameters are adopted to tolerance values: validity and responsibility, falseness foreach, indeterminacy magnitude to each, and truth value. This guarantees its combination of complexity supportive rand reading of actual surroundings.

Cognitive and social adaptation in autism spectrum disorder: A prospective cohort study.

During development, children face a number of demands and cognitive, behavioral, and social challenges necessary for growth. Cognitive skills make individuals competent and allow them to interact with their environment. To identify the cognitive skills that promote better social insertion in children with autism spectrum disorder within 12 months. Prospective cohort study. In this study, 21 children aged 3-12 years were assessed, and their mothers were interviewed. Children were enrolled in regular or special autistic schools. Twelve months after the first assessment, the same children participated in the second assessment. In individual interviews, mothers provided data by answering the Vineland Adaptive Behavior Scale. Each child was assessed individually using the fourth edition of the Stanford Binet Intelligence Scale 4th Edition. In the first assessment, the Stanford Binet areas and total scores correlated with the communication domains, daily life abilities, socialization, and total score of the Vineland Scale. After 12 months, a correlation was observed between the Stanford Binet areas and the total and communication domains, daily life abilities, socialization, motor abilities, and total score on the Vineland Scale. Logic mathematics and memory promote better social insertion in children with autism spectrum disorder. General cognitive ability promotes communication.

Resolving Conflicts and Strengthening International Relations with Investment: Game Theory Approach

Today, investors pay more attention to the international concept of investment than ever before. In addition, countries intend to use their domestic capital to fulfill domestic goals and prevent capital outflow as much as possible. The present article, while referring to objective examples of international relations, has tried to provide a different answer to the important question of "economic cooperation in the form of international investment while maximizing" by using game theory. The main question is whether investment at the international level can avoid war and build? For this purpose, by using game theory and game design between governments and investors as the main openers, three different modes have been discussed. To this end, in section one a state where two countries are indifferent has been considered. The second state includes two competing (enemy) countries, and in the third state, three countries are assumed, one being competitor and the other indifferent. In the second section, first a situation where two countries are indifferent to each other is considered. Then, in the second case, two countries are considered to be rivals (enemies), and in the third case, three countries are assumed: one of them is a competitor and the other is indifferent. Concerning the obtained equilibrium in the three states and for each of the two sections, the main conclusion is that the investor achieves the best consequence (Nash equilibrium) by constituting portfolio and investing in various markets, and the countries achieve the best outcome through cooperation and establishing peace. On the other words, the results of the research in the language of logic (mathematics) confirm the effect of economic cooperation on the development of peace.

THE VARIETY OF INVARIANCE IN FORMAL AND REGIONAL ONTOLOGIES

The paper examines the invariance principles proposed by the analytical and phenomenological traditions for demarcating the boundaries of formal and regional ontologies. The principle of invariance with respect to isomorphic transformations, generalizing Alfred Tarski’s criterion for logical concepts, is extended to formal ontology as the theory of manifolds in its phenomenological interpretation. Isomorphism types, which are abstract individuals of the highest order, hypostases of forms of all possible ontologies, are considered as model-theoretical analogs of manifolds. The correlativity of the phenomenological principles of demarcation of ontological regions and the criterion of invariance with respect to isomorphic transformations is demonstrated, leading to the convergence of logic and formal mathematics in both traditions and, at the same time, to the exclusion of geometry from formal ontology. Particular attention is paid to the discussion of the analytical and phenomenological traditions of the synthetic (material) a priori and the contribution that Wittgenstein’s doctrine on internal relations at different stages of its evolution makes to this discussion. The paper reveals the basis for later Wittgenstein’s criticism of his earlier project of creating a phenomenological language for expressing internal regional relations (such as the colours exclusion). The paper shows how Wittgenstein’s doubts about the possibility of an ideal notation based on the dichotomy of the logical and phenomenological led him to the study of invariants arising in language games. These invariants are not determined by the special properties of the categorical objects of formal ontology or the structures of regional subject matter, but are stable equilibria generated by the “consensus of actions.” New perspectives are outlined that are opened for logic and phenomenology by switching focus from the invariants of ontological structures to the invariants of structured interactions of various agents.

Interactive experience of sculpture design based on virtual reality technology

Abstract The application of computer technology provides new ideas for the design of sculpture works. In this paper, with the support of virtual reality technology, the pixel set of each color block is extracted from the actual image to determine the location of the center point of the color block. Based on the extracted information, a visual color marking method is used to realize the 3D registration of the sculpture scene. In the virtual scene, through the virtual modeling of the sculpture work, a spline surface model was generated by applying sparse image sequences and optimally adjusted to transform the surface piece control point problem into a quadratic function of the network vertices. The mathematical logic properties of the virtual reality sculpture work wind direction improved by 22.5 points, the mathematical logic properties of the light design improved by 25.8 points, and the mathematical logic properties of the shadow design improved by 23.1 points. The virtual reality technology provides an interactive experience for the design of sculpture works.

The Current Situation, Problems and Development Concepts of Korean Language Education in Chinese Universities under the Integration of Information Technology

Abstract The use of information technology in classroom teaching has become a common trend. This paper proposes a mathematical model for the dynamic measurement of the level of informatization of Korean language education, which adopts a mathematical logic method to comprehensively examine the attributes, functions, and values of each part of the construction of informatization of Korean language education, and dynamically regulate the relationship between the whole and the parts. The index value of the assessment system is obtained by the weighted average of the factor loading coefficients of each index variable, and the weighting coefficients are determined by the difference assignment method to maximize the differences between the objects being assessed. Finally, the differences in informatization of Korean language education in colleges and universities are measured through the concentrated trend, discrete degree, skewed and peak indicators, and the optimization path is proposed. The results show that the differences in the level of informatization of Korean language education in colleges and universities between regions are all less than 0.1, and the degree of contribution to the total difference is all around 15%, which indicates a relatively small situation of differences between colleges and universities in each region. In this paper, the in-depth measurement of the difference in the level of informatization of Korean language education among Chinese universities in various regions is of great value and significance in promoting the development of Korean language education informatization in Chinese universities.

Development of Mathematical Logic Pipeline Tools (Pilogmath) for Learning Mathematical on Logic Material

This development research aims to determine the feasibility of using Mathematical Logic Pipe teaching aid (Pilogmath) on mathematical logic material at SMA Negeri 1 Tanah Luas in terms of validity, practicality, and attractiveness. The development model used is the ADDIE development model which consists of the stages of analysis (analysis), design (design), development (development), implementation (implementation), evaluation (eveluation). The subjects of this research are class X SMA Negeri 1 Tanah Luas. The feasibility of learning media refers to the results of the assessment of teaching aids by experts, teachers and small group students. Feasibility can be seen from the results of the validator's assessment where all validators stated very valid, the results of the percentage of product ratings by media experts were 81% in the “Very Valid” category, the results of the percentage of product ratings by material experts were 87% in the “Very Valid” category, the results of the percentage of product assessment by the teacher were 92% in the “Very Practical” category, and the results of the percentage of product assessment by 6 small group students were 93 .6 % in the “Very Interesting” category. Based on product assessment by all validators who stated that it was very valid, the teachers assessment stated that it was very practical, and student assessment stated that it was very interesting, the Mathematical Logic Pipe teaching aid (Pilogmath) that was developed meeting the criteria of being very feasible to use for class X students of SMA Negeri 1 Tanah Luas.

ALGEBRA OF SOCIAL PHENOMENA

The characteristics of modern societies are central to discussions of various types of policy (social, economic, etc.) and are often seen as predictors of socio-economic processes. Any society can be studied through the lens of social phenomena. Hence, it seems fair to assume that the better one understands the nature of social matter and its impact on various processes, the better one's decisions will be able to meet today's challenges. The purpose of this paper is to explain and present the new framework for measuring social phenomena in the form of an algebra based on the definition of social phenomenon, its components, rationality and mathematical logic. Methodology. Using the example of social cohesion, the paper examines the current fundamental methodological approaches to interpreting the definition and, consequently, measuring social phenomena. In this paper, the authors use an analogy with probability space and event algebra to develop their mathematical method. As a result, the article presents and explains the basic terms of the algebra of social phenomena that make up the new concept. Practical implications. The authors' approach to formalisation provides a tool for deriving the measure of a complex phenomenon from the measures of its components (simple phenomena), as demonstrated in the example. Thus, this study enriches the range of methods suitable for deepening one's knowledge of the social characteristics of the society under study. Value/Originality. The concept of algebra as a methodology for measuring social phenomena and establishing dependencies between them on the basis of mathematical logic has not yet been the subject of public discussion. Therefore, this publication is also an invitation to a scientific discussion.

Similarities of Jonsson spectra’s classes

The study of syntactic and semantic properties of a first-order language, generally speaking, for incomplete theories, is one of the urgent problems of mathematical logic. In this article we study Jonsson theories, which are satisfied by most classical examples from algebra and which, generally speaking, are not complete. A new and relevant method for studying Jonson theories is to study these theories using the concepts of syntactic and semantic similarities. The most invariant concept is the concept of syntactic similarity of theories, because it preserves all the properties of the theories under consideration. The main result of this article is the fact that any perfect Jonson theory which are complete for existential sentences, is syntactically similar to some polygon theory (S-polygon, where S is a monoid). This result extends to the corresponding classes of Jonsson theories from the Jonsson spectrum of an arbitrary model of an arbitrary signature.

Teacher Performance in Developing Early Childhood Mathematical Logic Intelligence through Environmental Potential Educational Games

This study describes how the performance of teachers in developing mathematical logic intelligence of early childhood through Potential Environmental Educational Games. The purpose of this study is to know about : the performance of teachers, utilization potential environment as a learning media, and the impact of Potential Environmental Educational Games for Mathematical Logic Intelligence of children.
 Literature review in this study is the view of the concept of Non formal Education, education stream, learning theory and learning, teacher performance concepts, theories play, and educative games, and the concept of teacher performance.
 The research method used is descriptive outlines the results of the interview, observation, and study documentation in the field. Subjects in this study were teachers and early childhood at PAUD SPS Melati 01 Desa Tanjungwangi Kecamatan Cihampelas Kabupaten Bandung Barat .
 The analysis of data shows that the performance of a good teacher can achieve the goal of every learning, especially to improve the intelligence of children. Through the good performance, teachers able to implement learning activities with potential environmental Educational games can help children to improve mathematical logic intelligence . This can be observed by: ( 1 ) The performance of teachers through the activities of planning, implementation , and evaluation of learning, ( 2 ) Utilization of the potential environment as a learning through a variety of educative games that are made from raw material of the potential environment, ( 3 ) Impact of the use of educational games potential environment on children's mathematical logic intelligence can be seen from the ability to recognize more colors , have a good curiosity , is able to sort something , is able to know the size , love the game fiddle with numbers , able to sort the numbers , and were able to put something in accordance with the group. Utilization of the potential environment as educational games has many positive effects for children's intelligence and the solution of the problem a lack of APE owned by PAUD institutions.

The Effect of Fun Thinker’s Book Media on the Mathematical Logic Intelligence of 5 - 6-Year-Old Children

This study aims to determine the effect of fun thinker's book media on the mathematical logic intelligence of children aged 5-6 years at Nurul Taqwa Kindergarten. The research approach used is quantitative with the type of quasi-experimental design. The research design used is A non-equivalent control group design. The population of this study is children aged 5-6 years of Nurul Taqwa Pattunggalengang Kindergarten, Gowa Regency, with 30 children. The sampling technique used was purposive sampling, so the subjects in this study were 20 children aged 5-6 years. The data collection techniques used in this study were observation, tests, and documentation. The method used is descriptive and nonparametric statistical analysis using the Wilcoxon test. The results of hypothesis testing using the SPSS application show that the data is 2.271 and the sig value. (2- tailed) of 0.023 <0.05, then H1 is accepted and H0 is rejected. The results showed an effect of fun Thinkers book media on the mathematical logic intelligence of children aged 5-6 years at Nurul Taqwa Pattunggalengang Kindergarten, Gowa Regency.

Compensation Incentive of Executives under the Situation of Synergy or Mutual Exclusion of Corporate Profit and Innovation Tasks: Based on Incentive Game Model between Principal and Agent

Based on the synergistic or mutually exclusive relationship between corporate profits and innovation tasks, such that shareholders can predict these two scenarios, this study constructed a multitask principal-agent mode considering “the degree of synergy or mutual exclusion between profit and innovation,” “salary reduction penalty,” and other factors. Based on mathematical logic, we determined the correlation and influence of synergistic or mutually exclusive degrees on executive profitability compensation and salary reduction penalties. Based on the 2016–2022 annual reports of A-share listed companies registered in Shanghai and Shenzhen, China, this research empirically verifies the effects of the aforementioned degree of synergy and mutual exclusion on managers’ compensation incentives. The research conclusions are stated as follows: (1) If shareholders can predict the synergy between profitability and innovation activities, then the salary reduction penalty (representing executive compensation stickiness) exhibits a significant negative correlation with the degree of synergy μ, whereas if the coefficient of executive profitability compensation βi (compensation sensitivity) bears a moderately positive relationship with μ, the shareholders will, to a certain extent, improve the performance-sharing coefficient of senior executives and reduce the penalty coefficient of salary reduction to increase the overall income level of senior executives via the incentive effect. (2) If shareholders can predict the mutually exclusive effect of profitability and innovation activities, the salary reduction penalty (representing executive compensation stickiness) is significantly positively correlated with the degree of mutual exclusion μ, whereas the coefficient of executive profitability compensation βi (compensation sensitivity) negatively affects the degree of synergy μ to a certain extent; however, this negative relationship is not prominent. This indicates that to avert the short-sighted behaviour of executives, shareholders will drive them toward investing in innovation by reducing the profitability compensation coefficient as well as increasing the innovative compensation coefficient. Simultaneously, the shareholders will increase the penalty coefficient of salary reduction to urge the executives to strengthen the operation and management of other profitable activities of the enterprise to maintain short-term performance at a reasonable level. (3) If shareholders cannot predict the synergy between profitability and innovation activities, they will attribute the source of excess earnings to the efforts of the senior executives. In particular, a greater degree of synergy is more likely to reduce the penalty for the senior executives. If the shareholders cannot predict the mutually exclusive effect of profitability and innovation tasks, the correlation between the penalty coefficient of salary reduction and the degree of mutual exclusion is related to the decline in performance. In such a scenario, the shareholders attribute the short-term deterioration in corporate performance to the negligence of the senior executives in corporate operations. Consequently, they urge senior executives to seriously operate the enterprise by increasing the penalty for senior executives. If the decline in performance exceeds the critical value, the shareholders will effectively motivate the senior executives by reducing the penalty coefficient of their salary reduction and moderately increasing their profit-making compensation sharing coefficient to avoid negative investment or their resignation.

The Influence of Number Dice Games in Improving Early Childhood Mathematical Logic in Early Childhood Education

Purpose of the study: The aim of this research is to determine the effect of the number dice game in improving the mathematical logic intelligence of young children in Early Childhood Education.
 Methodology: The method used in this research is quantitative with an experimental research design, the sampling technique is purposive sampling, with post test and pre test research instruments, the data analysis used is inferential statistics.
 Main Findings: The results of this research show that Early Childhood Education Teachers use the number dice game media used in mathematics learning, which is a game that children like because it is very easy and interesting to play. In order to stimulate various areas of development such as cognitive, language and social. Social skills trained in this game include the willingness to follow and obey the rules of the game, playing in turns. Mathematical cognitive skills that are stimulated are stating the order of numbers, recognizing number symbols and number concepts.
 Novelty/Originality of this study: The use of a number dice game introduces a novel and engaging way for young children to interact with mathematical concepts. It offers an enjoyable learning experience that can potentially enhance children's motivation and interest in mathematics, establishing a positive foundation for learning.

On the main scientific achievements of Victor Selivanov

This survey paper summarizes the main results of Professor Victor Selivanov’s research, which together highlight the important advances he achieved in mathematical logic and theoretical computer science.

Giuseppe Peano in Germany, His Connections with German Mathematicians, and the First English Translation of Gottlob Frege’s Unpublished Letter to Adolph Mayer on Giuseppe Peano’s Mathematical Logic

The article aims to answer whether Gottlob Frege’s letter to Adolph Mayer, dated 8 July 1896, could help German mathematicians get acquainted with Giuseppe Peano’s mathematical work, including his mathematical logic. It is the first publication of this letter in English. At the beginning, I present the main characters of this story. Next, I refer to the letters concerning Peano and his mathematical results. Thus, I show the background of Frege’s letter to Mayer. In the last part, I collect information about Peano’s contacts with German mathematicians – where he was quoted and by whom, who was quoted by Peano, and in which period of his life. I conclude that Peano was known in Germany before Frege wrote to Mayer in 1896. However, the letter could have helped publish five of Peano’s articles in Germany, where Peano’s mathematical logic was hardly known then. Undoubtedly, the letter promoted that knowledge.

OPERATIONS ON BLOCK PREDICATE MATRICES

This article discusses the possibility of performing basic logical operations on matrices that are divided into rectangular blocks in an arbitrary manner. The results obtained are illustrated using the example of predicate logical matrices defined over a field of finite predicates of arbitrary arity. The possibility of extending the results obtained to Boolean matrices is also justified (they are considered to be defined over a field of finite predicates of zero arity). At the same time, using the apparatus of multivalued logic, starting from Boolean logical matrices, the results obtained can also be extended to the study of logical objects that are not Boolean. Block partitioning of matrices allows you to divide information specified in matrix form into parts, process these parts separately, and then combine them into a single whole, adhering to certain rules and restrictions described in this article. These methods can find their application in graph theory, in the theory of algorithms, programming and in other areas of theoretical and practical activity that are in one way or another related to mathematical logic.

Educational robotics with robocode as a teaching tool to reduce student dropout in engineering courses

Student evasion is a problem that affects institutions of higher education in general, causing impacts of social and economic nature. For this reason, it was adopted in the electrical engineering course, a mini course on using the Java programming language with robocode as a tool for learning education. This language has become increasingly popular for teaching students in universities in the areas of engineering because it has shown effectiveness regarding encouraging the teaching of programming with the open source educational game. This paper presents an efficient method to reduce the great escape of students. The mini course aims activities related to technologies in various aspects of computing: logical reasoning, mathematics, artificial intelligence, neural networks, and object-oriented programming through the integration with the Robocode software. The proposed activities were applied to students of higher education of the Universidade Federal do Ceará in the discipline of Introduction to Engineering. We also believe that these activities have shown the efficiency of educational Robotics as a tool for teaching and learning in object-oriented programming.