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Journal articles on the topic 'Logical tasks'

Author: Grafiati

Published: 5 June 2025

Last updated: 16 July 2025

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Taiboldina, K. R., K. R. Ramazanova, and G. R. Churbaeva. "LOGICAL TASKS." Vestnik of M. Kozybayev North Kazakhstan University, no. 2 (51) (December 29, 2021): 34–38. http://dx.doi.org/10.54596/2309-6977-2021-2-34-38.

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This article discusses non-standard logical problems encountered in the mathematical Olympiad and methods of their solution. Special attention is paid to familiarization with the ways of solving logical problems and the peculiarities of teaching this topic. Forming the skills of solving logical problems, we develop in the student the qualities of curiosity, perseverance, versatility. The main purpose of setting logical problems at the Mathematical Olympiad is the independent solution of problems and the development of students' curiosity.At the mathematical Olympiad, it is rather more difficult for schoolchildren to solve logical problems. Therefore, a professionally qualified teacher should be able to teach his students effective methods of solving problems.

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Pulatova, Manzura Iskhakovna, and Zilola Kahramonovna Khamroeva. "METHODS FOR SOLVING LOGICAL PROBLEMS FOR THE DEVELOPMENT OF THE MIND IN MATHEMATICS." GOLDEN BRAIN 1, no. 11 (2023): 68–75. https://doi.org/10.5281/zenodo.7865623.

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<em>Whatever the type of learning activity, it is the "tasks" that engage the student and encourage him to think. The ability to recall and apply new knowledge in various learning processes, to generalize and assimilate the acquired knowledge is directly related to learning tasks, and tasks are a means of developing the student’s knowledge (these ideas are not copied from anywhere). I came to this conclusion by observing students when I was in schools for experimental testing and work with teachers. Indeed, in order to gain new knowledge, the student uses his previous knowledge, applies and reinforces the acquired knowledge with examples and tasks.</em>

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Sapazhanov, Y., Y. Sapazhanov, T. Manap, and K. Uderbayeva. "DEVELOPING STUDENTS’ LOGICAL THINKING BY SOLVING NON-STANDARD TASKS." Педагогика и Методы Обучения, no. 3 (56) 2021 (September 15, 2021): 75–83. https://doi.org/10.47344/sdu20bulletin.v56i3.601.

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One of the priority tasks of the modern education system is the formation of a logically thinking, research-oriented personality. The ability to think logically is a necessary condition for the successful assimilation of educational material. The article deals with the use of various non-standard tasks for this purpose, which forces us to abandon the stereotypes of thinking. The paper considers some pedagogical conditions that must be followed when learning to solve non-standard problems, and partially reveals the work at the stages of their solution. However, it should be noted that when learning to solve non-standard tasks, you can and should follow the same pedagogical conditions as when working with standard tasks. The article also deals with the development of logical thinking in the process of teaching mathematics. The key point of studying this problem is the study of the levels of logical thinking: the identification of cause-and-effect relationships, the formation of mental operations in the course of solving non-standard problems.

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Ibragimov, R., B. Kalimbetov, and Zh Khabibullaev. "Features of Preparing Future Mathematics Teachers for the Implementation of Logical Tasks." Iasaýı ýnıversıtetіnіń habarshysy 129, no. 3 (2023): 239–52. http://dx.doi.org/10.47526/2023-3/2664-0686.18.

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This article describes the types of logical tasks in Mathematics textbooks of the main school according to the updated program and the characteristic features of the methodological training of future mathematics teachers in their implementation. The issue of preparing students for the implementation of logical tasks is considered. Methods and techniques for improving the logical thinking of students studying in the specialty of a mathematics teacher are outlined. The main task of teaching mathematics is the development of logical thinking and logical training of students. Accounting in the ability to think logically, along with the interest of a student who comes to school, is the main task of a mathematics teacher. Therefore, it is necessary to train future teachers of mathematics as young specialists capable of developing logical literacy of students using effective teaching technologies. This leads to the need to increase the requirements for the quality of teaching students in general schools and, accordingly, the quality of training of future teachers in pedagogical universities. However, only supplementing the process of training students with new content, increasing the amount of knowledge communicated to students is not able to solve the task of raising the quality of teacher training to the level of modern requirements. The solution to this problem, in our opinion, lies in the systematization of fundamental training of future teachers, should be logical training that allows students to be confident in critical thinking, analysis, reasoning and reasoning, maintain and justify their point of view.

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Ontuganova, Sh Sh, and A. Zhapbarov. "FORMATION OF LOGICAL THINKING AND SPEECH SKILLS OF ELEMENTARY CLASS STUDENTS." Bulletin of Kazakh National Women's Teacher Training University, no. 2 (July 16, 2021): 31–41. http://dx.doi.org/10.52512/2306-5079-2021-86-2-31-41.

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Only with logically correct thinking and understanding, we distinguish between cause-and-effect relationships, dependence on each other, the origin and path of development of things around us. The process of logically correct thinking expands the student's ability to treat his assumptions skeptically and critically, thereby deepening and expanding his understanding of the world, existence and being. The logical process is the result of scientific knowledge of the world, memorization of objects and phenomena of the external world in the human brain, consideration of the correct forms and laws, rules of this image. Logical methods of thinking cannot be formed independently from the day children come to school, for this the teacher must lay the foundations of logical knowledge and skills. It is necessary to work out the material, describing each action taking into account the age capabilities of children, hence the use of a large number of logical tasks in teaching is an important factor in quality learning. And the assimilation of logical techniques, forms of thinking, concepts, judgments to primary school students by conclusions is provided by the primary school program. This article discusses the pedagogical prerequisites for performing a system of tasks in the main subjects of primary school as a way of forming logical thinking skills of younger schoolchildren, skills and means of practical study of logical concepts.

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Kozyriev, Andrii, and Ihor Shubin. "The method of linear-logical operators and logical equations in information extraction tasks." INNOVATIVE TECHNOLOGIES AND SCIENTIFIC SOLUTIONS FOR INDUSTRIES, no. 1 (27) (July 2, 2024): 81–95. http://dx.doi.org/10.30837/itssi.2024.27.081.

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Relational and logical methods of knowledge representation play a key role in creating a mathematical basis for information systems. Predicate algebra and predicate operators are among the most effective tools for describing information in detail. These tools make it easy to formulate formalized information, create database queries, and simulate human activity. In the context of the new need for reliable and efficient data selection, a problem arises in deeper analysis. Subject of the study is the theory of quantum linear equations based on the algebra of linear predicate operations, the formal apparatus of linear logic operators and methods for solving logical equations in information extraction tasks. Aim of the study is a developing of a method for using linear logic operators and logical equations to extract information. This approach can significantly optimize the process of extracting the necessary information, even in huge databases. Main tasks: analysis of existing approaches to information extraction; consideration of the theory of linear logic operators; study of methods for reducing logic to an algebraic form; analysis of logical spaces and the algebra of finite predicate actions and the theory of linear logic operators. The research methods involve a systematic analysis of the mathematical structure of the algebra of finite predicates and predicate functions to identify the key elements that affect the query formation process. The method of using linear logic operators and logical equations for information extraction is proposed. The results of the study showed that the method of using linear logic operators and logical equations is a universal and adaptive tool for working with algebraic data structures. It can be applied in a wide range of information extraction tasks and prove its value as one of the possible methods of information processing. Conclusion. The paper investigates formal methods of intelligent systems, in particular, ways of representing knowledge in accordance with the peculiarities of the field of application and the language that allows encoding this knowledge for storage in computer memory. The proposed method can be implemented in the development of language interfaces for automated information access systems, in search engine algorithms, for logical analysis of information in databases and expert systems, as well as in performing tasks related to object recognition and classification.

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De Neys, Wim. "The freak in all of us: Logical truth seeking without argumentation." Behavioral and Brain Sciences 34, no. 2 (2011): 75–76. http://dx.doi.org/10.1017/s0140525x10002827.

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AbstractMercier and Sperber (M&S) sketch a bleak picture of logical reasoning in classic, nonargumentative tasks. I argue that recent processing data indicate that despite people's poor performance they at least seek to adhere to traditional logical norms in these tasks. This implies that classic reasoning tasks are less artificial–and logical reasoning less exceptional–than M&S's framework suggests.

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Fakhertdinova1, D. I., and A. L. Zolkin. "LOGICAL-FORMING TASKS IN THE DEVELOPMENT OF LOGICAL COMPETENCE OF IT FOREIGN APPLICANTS." Izvestiya of the Samara Science Centre of the Russian Academy of Sciences. Social, Humanitarian, Medicobiological Sciences 25, no. 90 (2023): 47–53. http://dx.doi.org/10.37313/2413-9645-2023-25-90-47-53.

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The article introduces the definition logical competence of the context of future IT professionals. The difference between existing approaches to the definition of logical competence and logical competences is considered. The importance of logical competence as a main competence on the formation and development of the professional competence of future IT specialists is presented. Difficulties in the process of formation and development of logical competence and ways to solve them are described. An overview of various educational systems of the world aimed at the formation of the logical competence of applicants for IT areas is presented. Also, the difficulties arising in the development of logical competence among foreign applicants of future IT specialists in Russian universities are considered. Despite the seemingly obvious problem of insufficient knowledge of the Russian language for learning, the main difficulty is the difference in programs and methods of learning in different countries. If the Russian educational system in the training of future IT specialists attaches great importance to the fundamental serious mathematical base, then even the best IT education systems in various countries focus on the applied part of disciplines. As you know, in the development of any kind of competencies, the foundation, the basic subjects on the basis of which the competencies are formed, is of paramount importance. The article describes tasks that form and develop the logical competence of applicants for future IT specialists. The proposed definition of logical competence, as well as the ways of its formation and development among applicants for IT areas, can be extended to other technical areas with appropriate refinement and recommended for work with applicants or undergraduate students.

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Bronkhorst, Hugo, Gerrit Roorda, Cor Suhre, and Martin Goedhart. "Logical Reasoning in Formal and Everyday Reasoning Tasks." International Journal of Science and Mathematics Education 18, no. 8 (2019): 1673–94. http://dx.doi.org/10.1007/s10763-019-10039-8.

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AbstractLogical reasoning is of great societal importance and, as stressed by the twenty-first century skills framework, also seen as a key aspect for the development of critical thinking. This study aims at exploring secondary school students’ logical reasoning strategies in formal reasoning and everyday reasoning tasks. With task-based interviews among 4 16- and 17-year-old pre-university students, we explored their reasoning strategies and the reasoning difficulties they encounter. In this article, we present results from linear ordering tasks, tasks with invalid syllogisms and a task with implicit reasoning in a newspaper article. The linear ordering tasks and the tasks with invalid syllogisms are presented formally (with symbols) and non-formally in ordinary language (without symbols). In tasks that were familiar to our students, they used rule-based reasoning strategies and provided correct answers although their initial interpretation differed. In tasks that were unfamiliar to our students, they almost always used informal interpretations and their answers were influenced by their own knowledge. When working on the newspaper article task, the students did not use strong formal schemes, which could have provided a clear overview. At the end of the article, we present a scheme showing which reasoning strategies are used by students in different types of tasks. This scheme might increase teachers’ awareness of the variety in reasoning strategies and can guide classroom discourse during courses on logical reasoning. We suggest that using suitable formalisations and visualisations might structure and improve students’ reasoning as well.

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Prokhorova, Tatiana Pavlovna. "The logical question as a method of development logical universal educational actions." KANT 40, no. 3 (2021): 280–84. http://dx.doi.org/10.24923/2222-243x.2021-40.53.

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The purpose of the study is to determine the actual problems of the formation and further development of logical universal educational actions and historical thinking of schoolchildren. The article emphasis is placed on the problems of teaching school students the subject "History" at the initial stage, including the problem of forming historical thinking, and the directions for solving them. The thesis is argued that one of the most effective methods of forming and development logical universal educational actions, and therefore the possibility of forming historical thinking, are logical tasks. The scientific novelty of the study lies in the formation of a new approach to the development of logical universal educational actions through the methodology of constructing logical questions as a type of logical tasks. As a result of the study, the practice-oriented conditions of the organization of the pedagogical process were identified and an author's model of teacher's work for different age groups is offered.

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Ruesga, P., J. Giménez, and M. Orozco. "Logical relations diagrams in transformation tasks for preschoolers." Enseñanza de las Ciencias. Revista de investigación y experiencias didácticas 23, no. 3 (2005): 403. http://dx.doi.org/10.5565/rev/ensciencias.3831.

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Pavlygina, R. A., V. I. Davydov, D. S. Sakharov, M. V. Tutushkina, and A. A. Pryamonosova. "The EEG during Solution of Mathematical Logical Tasks." Neuroscience and Behavioral Physiology 42, no. 1 (2011): 28–35. http://dx.doi.org/10.1007/s11055-011-9528-0.

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Liberman, Dov, and Michael K. Meyerhoff. "Differential Conformity Rates to Perceptual and Logical Tasks." Journal of Social Psychology 126, no. 2 (1986): 273–75. https://doi.org/10.1080/19401183.1986.12461529.

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Hayitovna, Aminova Feruza. "Development of The Competence of Clear Expression of Thoughts in Students During the Completion of Academic Tasks: Methods for Ensuring Logic and Sequence of Presentation." European International Journal of Pedagogics 5, no. 5 (2025): 40–44. https://doi.org/10.55640/eijp-05-05-09.

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This article is devoted to the development of methods and approaches to the enhancement of students' competence in the logical and sequential expression of their thoughts during the completion of academic tasks. In modern education, an important aspect is the ability of students to clearly and accurately present their ideas, argue them, and logically connect different elements of information. The article discusses the main principles of forming this competence, as well as practical recommendations for educators aimed at improving the quality of education and enhancing the level of students' communication skills. Special attention is paid to the importance of logical and sequential explanations and their role in successful academic activity.

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Abdullaeva, L., and М. Koshanova. "Improving students’ thinking abilities by solving logical problems." Q A Iasaýı atyndaǵy Halyqaralyq qazaq-túrіk ýnıversıtetіnіń habarlary (fızıka matematıka ınformatıka serııasy) 25, no. 2 (2023): 7–17. http://dx.doi.org/10.47526/2023-2/2524-0080.01.

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In the article, the authors consider the topical issue of improving students’ thinking skills in the school curriculum. This issue has not been sufficiently studied in our country and requires additional research in this area. The article sets a lot of tasks to improve students’ thinking skills. A pedagogical analysis of textbooks on the development of students’ logical thinking skills has been developed and advantages have been identified. In the course of the study, literature analysis, pedagogical analysis of non-standard tasks, questionnaires, control, pedagogical experiment were carried out. As a result of the research, tasks aimed at improving students’ thinking skills were developed. In the course of the study, the survey showed that the majority of students have poor mathematical thinking in the process of completing tasks. It is concluded that in order to improve the logical thinking of students, it is necessary to introduce additional mathematical material in the form of non-standard tasks, which will increase the efficiency of reading and attract all students to the educational process. The authors give practical suggestions to teachers on the development of logical and intuitive thinking of students in the classroom. This article and the results of the study will be of interest to teachers of secondary schools, young scientists, and those who want to improve their IQ in the future.

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İbrahimova, Xoşqədəm. "APPLICATION TECHNOLOGY OF LOGICAL PROBLEMS IN BIOLOGY LESSONS." Scientific Works 92, no. 1 (2025): 157–61. https://doi.org/10.69682/arti.2025.92(1).157-161.

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The article describes the technology of applying tasks that develop logical thinking in biology lessons. During the application of tasks that develop logical thinking, new knowledge, skills and habits are formed, activity, interest, erudition, creative thinking and other personal qualities develop. Activation of thinking plays a major role in improving the quality of students' knowledge, their intellectual development and the formation of a scientific worldview.

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Kumashova, A. "The Significance of Special Tasks in Forming Children’s Logical Competence." Bulletin of Science and Practice 10, no. 4 (2024): 531–36. http://dx.doi.org/10.33619/2414-2948/101/66.

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This article discusses the importance of special tasks in shaping children’s logical competence. Logical thinking plays a crucial role in developing children’s cognitive skills and serves as a foundation for successful learning and adaptation in modern society. Special tasks serve as effective tools that stimulate the development of analytical abilities, critical thinking, and the ability to make reasoned decisions. The article highlights the significance of using special tasks in the educational process, their role in stimulating student interest, and the individual development of each child.

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Shukla, Yash, Abhishek Kulkarni, Robert Wright, Alvaro Velasquez, and Jivko Sinapov. "Automaton-Guided Curriculum Generation for Reinforcement Learning Agents." Proceedings of the International Conference on Automated Planning and Scheduling 33, no. 1 (2023): 605–13. http://dx.doi.org/10.1609/icaps.v33i1.27242.

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Despite advances in Reinforcement Learning, many sequential decision making tasks remain prohibitively expensive and impractical to learn. Recently, approaches that automatically generate reward functions from logical task specifications have been proposed to mitigate this issue; however, they scale poorly on long-horizon tasks (i.e., tasks where the agent needs to perform a series of correct actions to reach the goal state, considering future transitions while choosing an action). Employing a curriculum (a sequence of increasingly complex tasks) further improves the learning speed of the agent by sequencing intermediate tasks suited to the learning capacity of the agent. However, generating curricula from the logical specification still remains an unsolved problem. To this end, we propose AGCL, Automaton-guided Curriculum Learning, a novel method for automatically generating curricula for the target task in the form of Directed Acyclic Graphs (DAGs). AGCL encodes the specification in the form of a deterministic finite automaton (DFA), and then uses the DFA along with the Object-Oriented MDP (OOMDP) representation to generate a curriculum as a DAG, where the vertices correspond to tasks, and edges correspond to the direction of knowledge transfer. Experiments in gridworld and physics-based simulated robotics domains show that the curricula produced by AGCL achieve improved time-to-threshold performance on a complex sequential decision-making problem relative to state-of-the-art curriculum learning (e.g, teacher-student, self-play) and automaton-guided reinforcement learning baselines (e.g, Q-Learning for Reward Machines). Further, we demonstrate that AGCL performs well even in the presence of noise in the task's OOMDP description, and also when distractor objects are present that are not modeled in the logical specification of the tasks' objectives.

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Auni, Anggita, and Ahmad Wachidul Kohar. "Comparing Students' Problem-Solving Processes on Probability Tasks: Well-Structured and Ill-Structured Tasks." Journal of Mathematical Pedagogy (JoMP) 4, no. 2 (2023): 57–73. http://dx.doi.org/10.26740/jomp.v4n2.p57-73.

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This study aims to describe the differences in the problem-solving abilities of well-structured problems and ill-structured problems models related to the concept of opportunity for Grade VIII junior high school students. Two students with the same mathematical abilities were selected to be subjects according to our research objectives. The results show that the two samples find it more difficult to solve well-structured problems than ill-structured problems. When at the stage of understanding the problem students need to read the questions repeatedly and when asked to retell the students can't do it well. In the questions of the type of well-structured problems subject 1 can only mention what is asked, but it is not appropriate to state the conditions needed to solve the problem and in subject 2 it is found otherwise, while in ill-structured problems it is not appropriate to write down what is known but write down what is asked with precise and knowing the requirements to solve the problem. Subject 1 uses logical and logical reasoning strategies. Then, subject 2 uses a trial and error strategy with logical reasoning. The two subjects carried out problem solving according to plan, carried out the re-checking stage, and were able to find solutions to problems that did not require calculations in them but could not find solutions to problems that contained calculations and had to be solved by utilizing the probability theorem. These results can be used as an evaluation in the learning process or a reference for further research.

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Polovikova, O. N., V. V. Shiryaev, N. M. Oskorbin, and L. L. Smolyakova. "Features of Software Implementation of Logical Tasks in Prolog." Izvestiya of Altai State University, no. 1(117) (March 17, 2021): 116–20. http://dx.doi.org/10.14258/izvasu(2021)1-20.

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One of the promising areas for using Prolog-systems is to solve logical tasks. This study outlines a solution approach based on the state generation procedure and the verification procedure. A solution to a logical task is presented, which demonstrates in practice the proposed approach and method of specifying a procedure for generating states. In the proposed example, a bit chain is generated that defines the code of a particular letter in the solution of the applied problem. Building a solution by means of code generation with verification allows not storing in the knowledge base a binary tree of all possible codes. The process of generating new states can be associated with the training of the program, with the dynamic formation of the knowledge base. The approach is based on the capabilities of software environments for adding facts and rules to existing ones, which were obtained as the results of the program or its stages. In this case, the entire program is the generating rule. An analysis of the constructed and tested procedures for the dynamic generation of states and the generation of facts allows us to talk about the applicability of such a solution for certain applied problems.

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Wu, Xin, Yuqi Bu, Yifei Chen, and Yi Cai. "Content-free Logical Modification of Large Language Model by Disentangling and Modifying Logic Representation." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 24 (2025): 25507–15. https://doi.org/10.1609/aaai.v39i24.34740.

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Despite extensive training on diverse datasets and alignment with human values, large language models (LLMs) can still generate fallacious outputs. Additionally, the validity of LLM's outputs varies significantly depending on the content. It is crucial to ensure LLMs' logical consistency across different contexts. Drawing inspiration from cognitive psychology studies, we propose a Logic Control Framework (LCF) that disentangles LLMs' hidden representations into separate content and logic spaces. Within the logic space, we use logically valid and invalid samples to construct distinct regions through contrastive learning. By moving logic representations to logically valid regions and fusing them with unchanged content representations, we significantly reduce logical fallacies in LLM outputs while maintaining content coherence. We demonstrate the effectiveness of LCF through experiments on conclusion generation and fallacy identification tasks, showing a significant improvement in logical validity and a reduction in fallacious outputs.

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Baroni, Giulia, Motonori Yamaguchi, Jing Chen, and Robert W. Proctor. "Mechanisms Underlying Transfer of Task-Defined Rules Across Feature Dimensions." Experimental Psychology 60, no. 6 (2013): 410–24. http://dx.doi.org/10.1027/1618-3169/a000214.

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The Simon effect can be reversed, favoring spatially noncorresponding responses, when people respond to stimulus colors (e.g., green) by pressing a key labeled with the alternative color (i.e., red). This Hedge and Marsh reversal is most often attributed to transfer of logical recoding rules from the color dimension to the location dimension. A recent study showed that this transfer of logical recoding rules can occur not only within a single task but also across two separate tasks that are intermixed. The present study investigated the conditions that determine the transfer of logical recoding rules across tasks. Experiment 1 examined whether it occurs in a transfer paradigm, that is when the two tasks are performed separately, but provided little support for this possibility. Experiment 2 investigated the role of task-set readiness, using a mixed-task paradigm with a predictable trials sequence, which indicated that there is no transfer of task-defined rules across tasks even when they are highly active during the Simon task. Finally, Experiments 3 and 4 used a mixed-task paradigm, where trials of the two tasks were mixed randomly and unpredictably, and manipulated the amount of feature overlap between tasks. Results indicated that task similarity is a determining factor for transfer of task-defined rules to occur. Overall, the study provides evidence that transfer of logical recoding rules tends to occur across two tasks when tasks are unpredictably intermixed and use stimuli that are highly similar and confusable.

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Horváth, Fruzsina, and László Pokorádi. "Graph-Demonstration of The Solutions of Engineering Tasks." Műszaki Tudományos Közlemények 9, no. 1 (2018): 103–6. http://dx.doi.org/10.33894/mtk-2018.09.21.

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Abstract During technical education it is a very difficult yet essential task to develop the good logical engineering thinking of students or pupils. One main part of this thinking is the determination of the optimal set of required input parameters for the calculation task mentioned above. The LogTreeMM (Logical Tree of Mathematical Modelling) method can help to solve this task. The aim of this paper is to show modification of the LogTreeMM method to determine the required parameters of a mathematical model by a simple case study.

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Dulatova, Zainep Asanalievna, Anna Ivanovna Kovyrshina, Elena Sergeevna Lapshina, and Nikolay Nikolaevich Shtykov. "Development of Synthesis as a General Logical Method of Cognition in the Process of Teaching Mathematics of Students and Future Teachers." Siberian Pedagogical Journal, no. 1 (February 26, 2024): 7–16. http://dx.doi.org/10.15293/1813-4718.2401.01.

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General logical cognitive actions form the basis of almost all cognitive methods. This determines the necessity of their purposeful formation in the process of subject teaching. A special role in the development of cognitive methods belongs to mathematics, in the process of teaching which these actions manifest themselves in the most explicit form. In the article we consider the formation of synthesis as a basic general logical method. The purpose of our study is to develop approaches to the organization of subject-based teaching aimed at the formation and development of synthetic thinking of school students and teacher education students. The methodology of the research is the theory of funding of logical constructions, developed on the basis of the concept of funding in education (V. D. Shadrikov, E. I. Smirnov). The results of the study. Examples demonstrating the main types of synthesis in mathematics learning are considered. These types include: synthesis as a leading action in the construction a mathematical model and synthesis as a representation of a logically justified solution to a problem. The problems of synthesis implementation by students in the process of solving mathematical problems are analyzed. The specificity of educational tasks that contribute to the formation of synthetic thinking is studied. The role of combinatorial tasks as tasks with prevailing logical component in the formation of synthetic thinking of students is described. In conclusion, on the basis of the theory of funding, the typification of types of synthesis in school mathematical education is proposed.

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Shi, Jihao, Xiao Ding, and Ting Liu. "Case-Based Deduction for Entailment Tree Generation." Mathematics 12, no. 18 (2024): 2893. http://dx.doi.org/10.3390/math12182893.

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Maintaining logical consistency in structured explanations is critical for understanding and troubleshooting the reasoning behind a system’s decisions. However, existing methods for entailment tree generation often struggle with logical consistency, resulting in erroneous intermediate conclusions and reducing the overall accuracy of the explanations. To address this issue, we propose case-based deduction (CBD), a novel approach that retrieves cases with similar logical structures from a case base and uses them as demonstrations for logical deduction. This method guides the model toward logically sound conclusions without the need for manually constructing logical rule bases. By leveraging a prototypical network for case retrieval and reranking them using information entropy, CBD introduces diversity to improve in-context learning. Our experimental results on the EntailmentBank dataset show that CBD significantly improves entailment tree generation, achieving performance improvements of 1.7% in Task 1, 0.6% in Task 2, and 0.8% in Task 3 under the strictest Overall AllCorrect metric. These findings confirm that CBD enhances the logical consistency and overall accuracy of AI systems in structured explanation tasks.

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Syafitri, Rani, Zetra Hainul Putra, and Eddy Noviana. "Fifth Grade Students’ Logical Thinking in Mathematics." JOURNAL OF TEACHING AND LEARNING IN ELEMENTARY EDUCATION (JTLEE) 3, no. 2 (2020): 157. http://dx.doi.org/10.33578/jtlee.v3i2.7840.

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The purpose of this study was to investigate fifth-grade students’ logical thinking in mathematics. Their logical thinking skills were categorized based on five levels, namely very low, low, medium, high and very high. This study used descriptive quantitative method, and it was conducted with 123 fifth-grade students from a public elementary school in Pekanbaru, Riau, Indonesia. The instruments used to collect data were logical thinking ability tests consisting of short answer tasks and mathematical reasoning for the given answers. The results of this study indicated that students have very low logical thinking within the average score of 22.76%. More than half of students could not give correct answers to the given tasks and also could not provide reasoning to their answers. The implication of this study is that teachers, teacher educators, curriculum developers, and government need to develop learning instruction that support students’ logical thinking in facing challenges in 21st century life.

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Nangue Tasse, Geraud, Steven James, and Benjamin Rosman. "Composition and Zero-Shot Transfer with Lattice Structures in Reinforcement Learning." Journal of Artificial Intelligence Research 82 (April 17, 2025): 2325–88. https://doi.org/10.1613/jair.1.16817.

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An important property of long-lived agents is the ability to reuse existing knowledge to solve new tasks. An appealing approach towards obtaining such agents is by leveraging logical composition over tasks, where new tasks are defined by applying logic operators to previously-solved ones. This composition is particularly powerful since it provides a human-understandable mechanism for task specification. However, no unifying formalism for applying logic operators to tasks and generalising combinatorially over them has yet been developed. We address the problem by formally defining logical composition as operators acting on a set of tasks in a lattice structure—the algebraic structure that generalises the study of Boolean logic. This provides a theoretically rigorous method for composing tasks, allowing us to formulate new tasks in terms of the negation, disjunction, and conjunction of a set of base tasks. We prove that by learning a new type of goal-oriented value function model free, called the world value function, an agent can solve composite tasks involving arbitrary logical operators with no further learning. We verify our approach in high-dimensional domains—including a video game environment and continuous-control task—where an agent first learns to solve a set of base tasks, and then composes these solutions to solve a super-exponential number of new tasks.

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Silliman, Elaine R., Sylvia F. Diehl, Ruth Huntley Bahr, Theresa Hnath-Chisolm, Catherine Bouchard Zenko, and Stephanie A. Friedman. "A New Look at Performance on Theory-of-Mind Tasks by Adolescents With Autism Spectrum Disorder." Language, Speech, and Hearing Services in Schools 34, no. 3 (2003): 236–52. http://dx.doi.org/10.1044/0161-1461(2003/020).

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Purpose: A hallmark of autistic spectrum disorder (ASD) is disruption in theory-of-mind development, including the understanding of false beliefs. Previous studies have typically assessed the development of first- and second-order false belief concepts in ASD, with tasks primarily emphasizing physical causality and logical inferencing. The present study investigated how preadolescents and adolescents with ASD performed on false belief tasks that included social inferencing of psychological states as well as logical inferencing of physical states. Method: Two categories of tasks were administered: four traditional logical inferencing tasks and four social inferencing tasks specifically developed for this study. In addition, a prompt hierarchy was included to ascertain if performance on both task types improved. Participants were 45 children and adolescents primarily selected from three urban school districts: 15 adolescents with a previous diagnosis of ASD (ASD group); 15 typically developing children matched for age, gender, and ethnicity (CA group); and 15 typically developing children matched for language age, gender, and ethnicity (LA group). Results: Three findings were pertinent. First, the CA group performed at higher levels than did the LA group and the ASD group on both task sets. Second, although the CA and the LA groups performed equally well on both the logical and the social inferencing tasks, the ASD group performed better on the social inferencing tasks. Finally, the prompt hierarchy significantly improved overall task performance for the ASD and LA groups. Clinical Implications: These findings indicate that task type, variations in vocabulary ability, and the provision of support influenced performance on the false belief tasks.

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Slavoljub, Hilčenko, Jakovljević Nebojša, and Nikolić Sanja. "Didactics: Logical Operation – Seration in Preschool." Journal of Education, Technology and Computer Science 32, no. 2 (2021): 11–17. http://dx.doi.org/10.15584/jetacomps.2021.2.1.

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The paper presents an example of processing a logical operation – SERATION in preschool. The didactic-methodical approach to processing is traditional which is recommended as a rule and the first step in adopting this topic. Examples of e-tasks using ICT can serve only in the second phase – the phase of determining this content.

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Sdobnikov, V. V. "New Tasks of Translation Teachers: the Challenge of Mosaic Thinking." Professional Discourse & Communication 3, no. 2 (2021): 43–54. http://dx.doi.org/10.24833/2687-0126-2021-3-2-43-54.

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The research is aimed to determine how the mosaic thinking of the younger generation affects the process of translator training. Development of the mosaic thinking results in the need to solve new tasks by translation teachers. They include: to teach students how to determine the communicative task of the source text, or ST; to teach students how to analyze the logical structure of the ST; to teach students how to determine the relevance of specific linguistic units used in the ST with due account of the text’s logical structure; to teach students to doubt their interpretation of the ST; to teach students to produce a logically coherent text in the target language. To solve the tasks, a comprehensive system of actions must be designed. The aim of the system is to make students’ thinking more professional, i.e. to transform the mosaic thinking into the professional translator’s mentality. The conclusions are based on the analysis of the provisions voiced in the research of the mosaic thinking from the philosophical, psychological and pedagogical perspective as well as on observations of how translation is taught in Russian universities. The present investigation is innovative since it highlights the factors that make it especially difficult to form professional translators’ mentality now.

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Журавлева, Н., N. Zhuravleva, М. Шашкина, and M. Shashkina. "Development of cognitive universal learning activities for students while solving tasks with a parameter." Standards and Monitoring in Education 5, no. 5 (2017): 42–47. http://dx.doi.org/10.12737/article_59ca544952a481.06451085.

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The article highlights the problem of developing universal learning activities of students at Mathematics lessons. It is proposed to use the didactic potential of tasks with a parameter developing cognitive universal learning activities while studying mathematics. By solving tasks with a parameter, students need to be able to show quite advanced logical reasoning, to work accurately with the range of permissible values of the variable and the parameter, i.e. they should demonstrate high level of logical thinking and mathematical culture. Therefore, it can be argued that when using such tasks in the process of teaching mathematics, it is possible to form and develop logical, symbolic and exploratory learning activities (according to A.G. Asmolov). The authors present a set of training exercises for the development of cognitive universal learning activities on the basis of various tasks with a parameter used during the Unifi ed State Examination mass testing in 2017.

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Rajabboyevich, Ibrat Atakav. "USE OF STUDY TASKS IN TEACHING THE SCIENCE OF EDUCATIONMETHODOLOGY." International Journal of Pedagogics 4, no. 10 (2024): 39–50. http://dx.doi.org/10.37547/ijp/volume04issue10-08.

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In the article, the use of pedagogical technology, interactive methods and educational games, modern information and communication technologies by teachers in the teaching of educational science in the 5th-6th grades allows students to think independently, expand the scope of creative research and logical thinking. ideas that help to connect what they learned in the lessons with life and increase their interest are stated.

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Hu, Ziyi, Jun Liu, Zhongzhi Liu, Yuzhong Liu, Zheng Xie, and Yiping Song. "RMath: A Logic Reasoning-Focused Datasets Toward Mathematical Multistep Reasoning Tasks." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 22 (2025): 24104–12. https://doi.org/10.1609/aaai.v39i22.34585.

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Mathematical reasoning ability objectively reflects a language model's understanding of implicit knowledge in contexts, with logic being a prerequisite for exploring, articulating and establishing effective reasoning. Large language models (LLMs) have shown great potential in complex reasoning tasks represented by mathematical reasoning. However, existing mathematical datasets either focus on commonsense reasoning, assessing the model's knowledge application ability, or arithmetic problems with fixed calculation rules, evaluating the model's rapid learning capability. There is a lack of datasets that require solving problems solely through logical reasoning. As a result, the performance of LLMs in accurately understanding the implicit logical relationships in problems and deriving conclusions based solely on given conditions is hindered. To address this challenge, we construct a dataset specifically for multiple step reasoning tasks: Reasoning-Math (RMath). This dataset focuses on evaluating logical reasoning abilities with mathematical reasoning problems, covering typical problem types, including direct reasoning problems, hypothetical reasoning problems, and nested reasoning problems. Additionally, we design a standardized annotation scheme that transforms natural language descriptions of conditions into formal propositions. Other annotation contents include problem categories, proposition truth values, and proposition relationship types. This not only reduces biases caused by semantic misunderstandings during problem-solving, but also facilitates the incorporation of theoretically grounded logical reasoning methods to enhance reasoning abilities. Furthermore, we propose a normalization problem-solving framework based on propositional logic for RMath and design the problem-solving process for prompt tuning to guide LLMs to absorb mathematical logical theories and improving reasoning abilities. Finally, we evaluate RMath on several popular LLMs and present the corresponding results.

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Best, John B. "Salience in Logical Deduction Tasks: Effects on Processing or Representation?" Journal of General Psychology 113, no. 3 (1986): 235–41. http://dx.doi.org/10.1080/00221309.1986.9711034.

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Pavlyugina, R. A., N. N. Karamysheva, D. S. Sakharov, and V. I. Davydov. "Influence of music on the solution of mathematical logical tasks." Human Physiology 38, no. 4 (2012): 354–60. http://dx.doi.org/10.1134/s0362119712030097.

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Ritz, Barbara M., and G. Ludwig Hofacker. "Informational properties of neural nets performing algorithmic and logical tasks." Biological Cybernetics 74, no. 6 (1996): 549–55. http://dx.doi.org/10.1007/bf00209426.

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Braüner, Torben. "Hybrid-Logical Reasoning in the Smarties and Sally-Anne Tasks." Journal of Logic, Language and Information 23, no. 4 (2014): 415–39. http://dx.doi.org/10.1007/s10849-014-9206-z.

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Bagotskaya, M. S., A. A. Smirnova, and Z. A. Zorina. "Corvidae Can Understand Logical Structure in Baited String-Pulling Tasks." Neuroscience and Behavioral Physiology 42, no. 1 (2011): 36–42. http://dx.doi.org/10.1007/s11055-011-9529-z.

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Arend, Udo, and Jens Wandmacher. "On the generality of logical recoding in spatial interference tasks." Acta Psychologica 65, no. 3 (1987): 193–210. http://dx.doi.org/10.1016/0001-6918(87)90049-7.

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Bobyr, M. V., S. G. Emelyanov, and N. A. Milostnaya. "Optimizing the Number of Passes in Logical Image Filtering Tasks." Scientific and Technical Information Processing 51, no. 5 (2024): 478–86. https://doi.org/10.3103/s0147688224700394.

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Mukhabbat, Mamasaidova, and Sobirova Saydiniso. "Analysis of Tasks Aimed at Developing an Interdisciplinary Approach to General Education Subjects in Mathematics Lessons." European International Journal of Pedagogics 5, no. 5 (2025): 17–21. https://doi.org/10.55640/eijp-05-05-05.

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This article analyzes the tasks used to form an interdisciplinary approach in mathematics classes. Based on theoretical sources and modern methodological approaches, the study examines the effectiveness, challenges, and prospects of these tasks. The aim of the article is to demonstrate the role of mathematical tasks in developing students’ logical thinking and problem-solving skills through an interdisciplinary approach.

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Jansson, Lars C. "Logical Reasoning Hierarchies in Mathematics." Journal for Research in Mathematics Education 17, no. 1 (1986): 3–20. http://dx.doi.org/10.5951/jresematheduc.17.1.0003.

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Ordering theory was used ro empirically determine hierarchies of developmental precedence for Piager's 16 logical combinations. In two studies carried out in the Netherlands, subjects were tested in individual interviews. In Study 1, 94 subjects responded to statements about odd and even numbers; in Study 2, 30 subjects responded to statements about line segments. For each study, a hierarchy of operations was produced from the responses. The two hierarchies were similar to each other and to a hierarchy from a previous study in which a nonmathematical task was used. Different linguistic forms for the same logical operation appeared to yield greater differences in performance than differences in tasks.

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Jalolov, Shavkat. "To enhance pupils’ and students’ spatial imagination and logical thinking skills." Общество и инновации 3, no. 4/S (2022): 222–26. http://dx.doi.org/10.47689/2181-1415-vol3-iss4/s-pp222-226.

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Every day we are faced with many tasks, the solution of which requires us to think logically. The ability to think and logic as a cause takes us in many cases, from sequentially and consistently finishing judgement interlocutors and shoppers, starting with complex technical and business tasks. But, despite the great need for this skill, we often make logical mistakes without knowing it. In fact, among many people the right mindset can be based on experience and so-called common sense, not on the idea, using laws and special methods, said “the official logic”. To perform simple logic operations, the initial proposal and statements of simple conclusions can lead to often errors in the general sense of closeness and common sense, and if you know or understand something more complex. In this article, ideas and feedback are made about how to increase the spatial imagination and logical thinking ability of students and students.

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Kumashova, A. "Integration of Gaming Tasks into the Educational Process for the Development of Logical Thinking in Elementary School Students." Bulletin of Science and Practice 10, no. 4 (2024): 537–42. http://dx.doi.org/10.33619/2414-2948/101/67.

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In modern pedagogy, the issue of developing logical thinking in elementary school students occupies one of the most important places. This work is dedicated to exploring the integration of gaming tasks into the educational process as an effective means of stimulating children’s logical thinking. The principles of selecting gaming tasks, taking into account the age characteristics of students, as well as methods of their implementation in educational practice, are examined. The article analyzes the role of the teacher in organizing gaming situations, identifies the main advantages of using games in education, and describes practical methods that contribute to the development of logical thinking in elementary school students. The presented abstract will assist educators and researchers in developing and implementing gaming tasks into the educational process to achieve more effective results in the development of students’ cognitive skills.

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Aladin, Dmitry, Anton Kotsenko, Radmir Kim, Mariia Peresypkina, and Oleg Varlamov. "Reasons for using parallel activation of logical rules in solving management tasks." E3S Web of Conferences 549 (2024): 08007. http://dx.doi.org/10.1051/e3sconf/202454908007.

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The complexity of the subject areas in which intelligent information systems operate is steadily increasing. The tasks set for such systems are increasingly aimed at automating and robotizing spheres of human activity. The solution of such problems requires adaptive and flexible methods capable of taking into account dynamic changes in the environment in real time. The mivar approach to creating intelligent decision-making systems allows working with adaptive discrete structures and provides methods for making management decisions based on adaptive active logical inference based on the knowledge base of mivar rules. The mivar machine of logical inference is the core of expert systems based on the mivar approach. As a result of the historical development of the mivar approach when working on different subject areas, various versions of mivar machines of logical inference with their algorithms for bypassing rules in the knowledge base were obtained. This paper discusses the reasons for the emergence of such options and demonstrates the need to use a parallel algorithm for activating rules in an adaptive network of logical rules when solving problems of action planning in technical systems.

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Marconi, Diego. "Introduction." Disputatio 12, no. 58 (2020): 199–208. http://dx.doi.org/10.2478/disp-2020-0009.

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Abstract This introduction is a short critical presentation of the topic and main arguments of Andrea Iacona’s book Logical Form. Furthermore, it summarizes the commentators’ views on two central issues: Iacona’s rejection of the uniqueness thesis, i.e. his claim that no single notion of logical form can be adequate to the tasks that logical form has been supposed to perform, and the relation between a sentence’s logical form and its truth conditions.

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Liashyk, Volodymyr, and Ihor Shubin. "The Method Of Logical Networks For Modeling Adaptive Knowledge Testing Systems." Innovative Technologies and Scientific Solutions for Industries, no. 4(26) (December 27, 2023): 45–57. http://dx.doi.org/10.30837/itssi.2023.26.045.

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The subject of the research is the development of mathematical and algorithmic support of the intellectual toolkit for the analysis of sets of test tasks and the modeling of the process of interpreting the quality of sets of test tasks, which allows for objective and comprehensive continuous control of the knowledge of subjects of training, subject to the implementation of the concept of virtual distributed training (retraining). The purpose of the research is to improve the effectiveness of monitoring the knowledge of subjects of education in the distance form of education through the use of adaptive computer testing methods based on models of logical networks and the algebra of finite predicates. The following tasks are solved in the article: the formation of a testing model in a distributed virtual learning environment and a model of validity assessment based on the content of sets of test tasks. The following methods are used: methods of logical networks and algebraic programming based on the algebra of finite predicates and predicate operations, intellectual analysis of information. The following results were obtained: the principles of intellectual analysis were formulated in the development of a model of a universal logical network and its application to actual tasks of artificial intelligence in the field of informal information processing, namely, in the construction of knowledge testing systems for distributed virtual learning Conclusions. Algorithms for optimal multi-stage adaptive testing of knowledge as part of distributed virtual learning models and methods for analyzing the success of training subjects have been improved. The use of conjunctive decomposition with binary predicates achieves the goal of the research, because in this way any multi-place predicate can be represented by a logical network simulating the process of knowledge testing, the model of the subject of learning is described.

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Li, Yuqian, Shuai Lu, Weiguo Xu, and Yingzhou Gao. "Logic-Driven and Technology-Supported Creativity Development Model in Open-Ended Design Tasks." Buildings 15, no. 6 (2025): 871. https://doi.org/10.3390/buildings15060871.

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The increasing reliance on digital tools in architectural education has transformed design workflows, offering new opportunities for creativity while posing challenges to students’ logical reasoning and structured problem-solving abilities. While digital tools facilitate automation and generative design, over-reliance on them can limit students’ ability to navigate design complexity independently. Addressing this issue, this study develops the Logic-Driven and Technology-Supported Creativity Development Model to examine the roles of logical frameworks, digital tools, and open-ended design tasks in fostering structured creativity. The findings reveal that logical frameworks provide essential cognitive scaffolding, helping students balance creative exploration with structured decision-making. Digital tools enhance form generation but introduce challenges such as automation bias and steep learning curves. Open-ended tasks promote design flexibility, yet their effectiveness depends on logical structures to maintain coherence. This study highlights the importance of curriculum design in supporting structured creativity, emphasizing the integration of technical training, interdisciplinary methods, and reflective learning. The findings contribute to design education theory and provide practical insights for improving course structures and pedagogical approaches in digital design environments.

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Ragulienė, Loreta, and Violeta Šlekienė. "DEMONSTRATION TASKS AND THEIR LOGICAL REASONING SCHEMES IN THE SECONDARY SCHOOL ELECTROSTATICS COURSE." GAMTAMOKSLINIS UGDYMAS / NATURAL SCIENCE EDUCATION 9, no. 1 (2012): 35–47. http://dx.doi.org/10.48127/gu-nse/12.9.35.

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The article discloses the importance of demonstration tasks in physics teaching in sec-ondary schools. The place of the demonstration tasks and the possibilities of applying them during physics teaching are analyzed. Four demonstration tasks of electrostatics phenomena in the secondary school are presented and analyzed. They are: Two types of electrical charge; Distribution of surface-charge density; Electric field of electrified sphere; Electric field of two electrically charged plates. Logical reasoning schemes to these physics demo tasks are developed. The proposed reasoning schemes designed to improve students' thinking, explaining the observed demonstrations of physical phenomena which help students to: un-derstand the essence of the demo task, determine cause - effect relationships and dependen-cies, compare the conditions and findings, summarize the results and do conclusions. Such using of demonstration tasks is useful to both of teacher and pupil: teacher manages the con-tent of teaching and a learning of pupils, pupils - are focused to self-activities, encouraged to think, analyze, summarize and do conclusions. Key words: demonstration task, electrostatics phenomena, logical reasoning schemes, phys-ics teaching,

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