Basic Logic Research Articles (Page 1)

Mathematics learning plays an essential role in developing students’ logical, systematic, and analytical thinking skills. One of the higher-order thinking abilities that serves as a main focus in mathematics education is mathematical reasoning. This ability is closely related to the process of mathematical proof, which functions to justify the truth of a statement logically. This study aims to examine the relationship between the understanding of proof concepts and the development of mathematical reasoning among junior high school students through a library research approach. Data were obtained from various sources such as textbooks, journal articles, research findings, and relevant educational documents. The analysis was conducted using the content analysis method to review both conceptual and empirical findings from the literature. The results indicate that understanding the concept of proof not only helps students comprehend the logical structure of mathematics but also contributes to the development of deductive and reflective reasoning skills. Engaging in proof activities enables students to shift from merely imitative reasoning toward independent logical construction (creative reasoning). However, teaching proof at the junior high school level still faces several challenges, such as students’ limited understanding of basic logic, time constraints, and the lack of teacher training in teaching proof effectively. Therefore, learning strategies that emphasize students’ thought processes, provide opportunities for exploration, and integrate proof activities into meaningful learning contexts are needed.

Abstract Neutral atom qubit is a promising candidate platform for realizing quantum information processing in recent years due to its natural scalability, long coherence time, and reconfigurable array structure. However, the fidelity of basic logic operations such as the ‘NOT’ gate is still not high enough at present, which is constrained by noise. In this paper, we propose a new pulse optimization scheme for neutral atom qubits. We studied the composite pulses by introducing multi-phase superposition to enhance their noise robustness, achieving a fidelity up to 99.99 % in a noisy environment. The composite pulses improve the fidelity of the ‘NOT’ gate of neutral atom qubit and promote the neutral atom platform towards high-fidelity and scalable quantum information processing.

Particle-like chiral magnetic skyrmions can flow in nanotracks and behave like chiral fluids. Using interacting flows to perform logical operations is an important topic in microfluidics and nanofluidics. Here, we report a basic nanofluidic logic computing system based on chiral magnetic skyrmions flowing in parallel pipelines connected by an H-shaped junction. The flow behaviors could be manipulated by adjusting the spin polarization angle, which controls the intrinsic skyrmion Hall angle. We demonstrate that within certain range of the spin polarization angle, fully developed skyrmion flows could lead to fluidic logical operations, which significantly reduce the complexity of skyrmion logic as there is no need for deterministic creation, precise control, and detection of a single isolated skyrmion. Our results suggest that the chiral flow behaviors of magnetic quasiparticles may offer possibilities for spintronic and nanofluidic functions.

The article is devoted to the construction of fast neurons and neural networks for the implementation of two complete logical bases and modeling of computing devices on their basis. The main idea is to form a fast activation function based on semi-parabolas and its variations that have effective computational support. The constructed activation functions meet the basic requirements that allow configuring logical circuits using the backpropagation method. The main result is obtaining complete logical bases that open the way to constructing arbitrary logical functions. Models of such elements as a trigger, a half adder, and an adder, which form the basis of various specific computing devices, are presented and tested. It is shown that the new activation functions allow obtaining fast solutions with a slight decrease in quality compared to reference outputs. To standardize the outputs, it is proposed to combine the constructed circuits with a unit jump activation function.

It is indicated that the axiological function of human rights is a key element in the processes of formation, development and functioning of the legal system, creating a structured system of value orientations at both the individual and collective levels. This function provides a logical basis for understanding their fundamental importance and universal meaning in the context of human existence and social development, while determining the basic principles for law-making activity and law enforcement practice. The article defines the role of human rights in the legal system by analyzing and substantiating the relevant functions that are crucial for the existence of the legal system as a whole. The fundamental role of human rights in the legal system as basic guidelines for the formation, development and application of all legal norms and institutions, determining the content of legal regulation, and the fundamental basis of the legal system of a democratic state is substantiated. It is established that the study of the role of human rights in the legal system has not only theoretical, but also practical significance for the effective functioning of the legal system, ensuring the rule of law and legal certainty. The study of the role of human rights in the legal system through their functional analysis is proposed, based on a set of functions that are crucial for the existence of the legal system as a whole, and such functions as value-orientation, guarantee, integration, regulatory and control are defined. It is indicated that the integration function of human rights ensures the integrity of the legal system, its coherence and interconnection between various legal branches, contributing to its harmonization, unity and compliance with international standards. The regulatory function of human rights is characterized as providing a direct impact on the mechanism of normative and legal regulation of social relations, by determining the impact of the need to observe human rights on the formation of new legal norms, as well as creating a balance between individual freedom and the interests of society and the state by ensuring the relationship between human rights and their obligations. The role of the control function of human rights in guaranteeing the orientation of legal mechanisms towards the real protection of human rights and freedoms, by contributing to ensuring the compliance of national legislation with international human rights standards and the establishment of the rule of law and legal certainty, is emphasized.

Abstract Based on the synergistic effects of solid–liquid interfacial dewetting, Marangoni effect, and minimum energy principle, a novel method for fabricating Ni@Ag core–shell microspheres is proposed. The composition and size of microspheres can be effectively controlled by adjusting the precursor and dispersant ratio, respectively. Due to the excellent mobility of spherical particles, uniform distribution of microspheres in the magnetic liquid metal (MLM) is achieved through simple stirring. The highly conductive Ag shell not only enhances the electrical conductivity of MLM, but also significantly suppresses the corrosion of the magnetic Ni core by liquid metal. Experimental results identify 15 wt.% as the optimal filling ratio, at which the MLM retains good fluidity and exhibits superior magnetic and electrical properties. The MLM can be magnetically patterned on 2D and 3D surfaces, transported through confined channels, and employed as electrodes for flexible and stretchable LED arrays. Furthermore, a single MLM droplet can function as a basic logic unit, and multiple droplets can be integrated to construct complex logic devices. This work offers valuable guidance for the design of multifunctional liquid metal.

Abstract High‐density memory arrays are essential for neuromorphic computing, providing the massive parallelism and connectivity needed to emulate complex brain‐like functions with low energy consumption. Self‐rectifying memristors (SRMs), which combine rectification and resistive switching, effectively address the sneak‐path issue—a key challenge in large‐scale, high‐density 3D integration. However, lead‐free halide perovskite (LFHP)‐based SRMs remain largely unexplored, despite their mixed ionic–electronic conductivity and potential for ultralow‐power operation. Here, the first LFHP CsBi3I10‐based SRM with a self‐organizing heterostructure enabled by halide ion migration is reported. The device achieves ultralow SET power (≈16.8 fJ), a high rectification ratio (≈6.2 × 10⁴), and fast switching (30 ns), arising from Ag/iodide vacancy conductive channels and a spontaneously formed pn junction‐like heterojunction. Functionally, the device leverages its characteristics to enable versatile applications. It realizes basic logic gates (OR, AND, XOR), achieves image encryption and reconstruction using keys generated by voltage‐driven stochastic switching, and further exhibits excellent neuromorphic computing capabilities in array configuration, achieving a recognition accuracy of ≈92.08% and supporting real‐time image edge detection. This work establishes a new device/material paradigm for low‐power, multifunctional SRMs that unify storage, logic, encryption, and neuromorphic computing—paving the way for next‐generation AI‐oriented information technologies.

Abstract The fast development of artificial intelligence and brain‐like computing poses new challenges to data processing and storage, escalating the demand for novel computing and memory devices. Herein, inspired by the selective ion‐transport behavior of protein channels in biological synapses, a hydrous hexagonal tungsten trioxide (h‐WO3)‐based supercapacitor diode (CAPode) is designed and constructed. Benefiting from its hexagonal biomimetic proton channels and embedded single‐file water chains, the hydrous h‐WO3 exhibits outstanding selectivity and fast transport kinetics toward protons. As a consequence, the as‐built CAPode delivers an ultrahigh rectification ratio of 242, an unprecedented response frequency of 1745 Hz, and an excellent cycling stability over 20 000 charging/discharging cycles. Combining these unparalleled performances together, the hydrous h‐WO3‐based CAPode is demonstrated to be very competent for basic logic operations even at a frequency of over kilohertz. More attractively, it also demonstrates superior writing–erasing capability and excellent long‐term memory effect, validating great potential in the burgeoning computing‐in‐memory architecture and corresponding brain‐like computing.

Down Syndrome Regression Disorder (DSRD) is a rare neuropsychiatric condition affecting individuals with Trisomy 21. Barriers to care for DSRD patients have not been studied. This research aimed to explore how demographic, socioeconomic, and geographic factors influence access to diagnosis, testing, and treatment for individuals with DSRD. A cross-sectional, online, REDCap survey was utilized to query caregivers of individuals with DSRD. Eligible caregivers answered questions regarding demographics, clinical features, and barriers to diagnosis and treatment. Statistical analysis was performed using R software, employing χ2, Mann-Whitney U, and Kruskal-Wallis H tests. A total of 397 participants were enrolled, most from the US (74%). Barriers to diagnosis (58.1%), treatment (52.6%), referral (52.0%), and testing (39.4%) were prevalent. Key barriers included physician unfamiliarity with DSRD and a lack of local specialists. Travel distances for diagnosis, testing, and treatment were significant, with 14.7% traveling over 500 miles for diagnosis and some requiring international travel. Factors influencing delays in diagnosis and treatment included household income, region, and demographic variables. Higher income was associated with shorter time to diagnosis (p = 0.004) and treatment (p < 0.001). Race, income, maternal education, and setting influenced delays in diagnosis. Delays in treatment were influenced by ethnicity, income, and location. This large international survey of caregivers of individuals with DSRD elucidates perceived barriers to accessing diagnosis, testing, and treatment, with demographic factors such as socioeconomic status and geography influencing these challenges. The directionality of these effects and their impact on clinical care and outcomes will be a logical basis for additional studies. Further studies are needed to explore these barriers in greater depth and assess their impact on healthcare outcomes.

The fact that the world requires to acquire the skills of computational thinking at a young age has worsened the search on the pedagogical techniques that can be applied to engage novice students in programming sufficiently. Text based or traditional methods are steep in learning curve and therefore lead to high attrition rates and low self efficacy amongst the students. To eliminate these problems, gamification or the application of game-related ideas to non-games context, has emerged as a feasible paradigm and is examined in the paper to trace the impact of gamification implemented via the interactive platforms Scratch and Python Turtle Graphics on the engagement, learning outcomes as well as on the psychological maturation of novice programmers. Under the conceptual framework approach, the study employs the concepts of education psychology including the Self-Determination Theory (SDT), the Flow Theory, Constructivism, and also the Cognitive Load Theory in determining the effectiveness of game-based learning environments. The analysis disaggregates the essential gamified characteristics of such platforms, such as real-time visual feedback, narrative creation and quest-based problemsolving and sequential challenges and tracks their effects on the key student outcomes. According to the findings, these factors are highly successful in shaping the inner drives of motivation which are fulfillment of the primary psychological needs of autonomy, competence and relatedness. Besides, these tools are visual and interactive, thus reducing redundant memory loading and the student is able to focus on learning and memory of the fundamentals of constructing basic logic. In its argument, the paper asserts that coding syntax could be taught using computer science platforms like Scratch and Python Turtle and that inculcate a tough and confident attitude that encourages long time learning in computer science. By considering the intricate interaction between the design and gamification, the role of students and inculcating confidence in the code, the present study can provide useful insights to teachers, curriculum developers and platform creators who, in the future, can create more promising and inclusive points of entry into the programming profession.

Changes in splicing can mediate phenotypic variation, ranging from flowering time differences in plants to genetic diseases in humans. Splicing changes occur due to differences in splice-site strength, often influenced by genetic variation and the environment. How genetic variation influences splice-site strength remains poorly understood, largely because splice-site usage across transcriptomes has not been empirically quantified. Here, we quantify the use of individual splice-sites in Arabidopsis, Drosophila and humans and treat these measurements as molecular phenotypes to map variation in splice-site usage through GWAS. We carry out more than 130,000 GWAS with splice-site usage phenotypes, cataloguing genetic variation associated with changes in the usage of individual splice-sites across transcriptomes. We find that most of the common, genetically controlled variation in splicing is cis and there are no major trans hotspots in the three species analyzed. We group splice-sites based on GT[N]4 or [N]4AG sequence, quantify their average use, develop a ranking and show that these hexamer rankings provide a simple and comparable feature across species to explain most of the splice-site choice. Transcriptome analyses in several species suggest that hexamer rankings offer a rule that helps explain splice-site choices, forming a basis for a shared splicing logic in eukaryotes.

A series of molecular logic gates with multiple biocomputing capabilities have been successfully fabricated by using four antibiotic residues [tetracycline (TET), chloramphenicol (CHL), kanamycin (KAN), and streptomycin (STR)] as inputs. The lateral flow strip biosensor was utilized to realize the visual and portable sensing of logic events. Four basic logic gates (OR, AND, XOR, and INHIBIT) and three cascade logic circuits (OR-INHIBIT-AND, 3AND-OR, and XOR-INHIBIT-OR-AND) were constructed. The red band on the test zone of the strip is used to indicate the signal output. In the logic operation, the aptamer sequence in the DNA probes was used to distinguish different antibiotic residues. Two hairpin DNAs (H1 and H2) were used as the assembly probes to improve the detection signals. Using gold nanoparticles (AuNPs) as the signal tracers, the logic results can be readily visualized with the naked eye. Our constructed logic system exhibited high specificity and good robustness, enabling the logic strip to operate even in complex seawater samples with correct biocomputing functions. With the advantages of simplicity, portability, and multiple biocomputing capabilities, the disposable logic strip can provide a promising candidate for intelligent and on-site monitoring of antibiotic residues in a resource-limited setting.

The article sets the task to show how the dialectical form of thinking is con­cretized in the form of a new dialectical approach to mathematical creativity. Its philosophical basis is the fundamental ontology of Martin Heidegger, from which the operation of dialectical negation, called privation, is borrowed. Pri­vation in its ultimate expression finds a place in the paraconsistent (“Imagi­nary”) logic of N.A. Vasiliev, operating with logical antinomies and revealing their difference from logical contradictions (from logical absurdity). In logical and mathematical research, a clear example of the application of privation are the well-known Gödel incompleteness theorems, which establish the existence of positive integers with properties opposite to the properties of inductive numbers (N.N. Luzin). Within the framework of the task, the descriptive set theory of Luzin and the non-Euclidean (hyperbolic) geometry of Lobachevsky are analyzed. They are united by the problem of ordering the arithmetic conti­nuum. In this context, the question is posed as to why the set of real points of the continuum is not countably ordered, and an answer is given. The answer is provided by the dialectical approach to mathematical creativity described here as part of the logical discipline of thinking called complementary-dialecti­cal logic. The dialectical approach to mathematical creativity includes the trans­formation of mathematical logic developed on the basis of classical formal logic. This transformation is presented in the article as a synthesis of the exten­sional and intensional aspects of logical thinking, which are often called (for brevity) extensional and intensional logic. Key words: fundamental ontology, privation, paraconsistent logic, descriptive set theory, hyperbolic geometry, vir­tual points.

The purpose. Introduction into the bridge movement drive control system of a bridge support movement synchronization unit, developed in stages on the basis of fuzzy logic to eliminate bridge tilt arising as a result of the movement of a flexible suspension load along the bridge by a trolley.Methods. The objectives set in the study were achieved through the use of mathematical modeling in the Matlab Simulink environment and practical research.Results. The use of correction units, including those based on fuzzy logic, led to the elimination of the bridge tilt, reducing it to almost zero, and reducing the amplitude of elastic vibrations in the bridge truss to 45 percent.Conclusion. The use of control systems with correction units, including those based on fuzzy logic, allows eliminating the desynchronization of the speeds of movement of the bridge supports of the bridge crane, which reduces the load on the metal tructure of the crane, reduces the wear of the wheel flanges and crane tracks, and increases the reliability of the crane.

Interpolation in Hájek's basic logic

Thirty to seventy percent of proteins in any given genome have no assigned function and have been labeled as the protein "unknome." This large knowledge shortfall is one of the final frontiers of biology. Machine learning (ML) approaches are enticing, with early successes demonstrating the ability to propagate functional knowledge from experimentally characterized proteins. An open question is the ability of ML approaches to predict enzymatic functions unseen in the training sets. By integrating literature and a combination of bioinformatic approaches, we evaluated individually Enzyme Commission number predictions for over 450 Escherichia coli unknowns made using state-of-the-art ML approaches. We found that current ML methods not only mostly fail to make novel predictions but also make basic logic errors in their predictions that human annotators avoid by leveraging the available knowledge base. This underscores the need to include assessments of prediction uncertainty in model output and to test for "hallucinations" (logic failures) as a part of model evaluation. Explainable artificial intelligence analysis can be used to identify indicators of prediction errors, potentially identifying the most relevant data to include in the next generation of computational models.

The formation and evolution of China’s foreign policy as a global power are determined by the interaction of multidimensional factors. Based on the analytical hierarchy process (AHP), this study reveals the influencing mechanisms of four key variables: 1) the structural pressure of the international system (power, institutions), 2) the demands of national interests (security, development), 3) the structure of the domestic political system (par-ty-government, bureaucracy, think tanks), and 4) ideological and cultural factors (tradition, socialist ideology). The results show that these factors shape the external environment, the basic logic of decision-making, the institutional structure, and the perceived value coordinates, respectively. The constructed model systematically identifies the dynamic weights of various factors in the diplomatic decision-making process and their interrela-tions. This method overcomes the limitations of a single explanatory paradigm and provides a scientific tool for predicting the trajectory of China’s diplomacy.

The article presents a new alternative approach for determining the sensitivity of mathematical models. Mathematical models (MM) operate on the basis of input and output, which are transmitted to and extracted from embedded mathematical algorithms. These algorithms, which have parameters, change when these sensitivity parameters of mathematical models change. This change in sensitivity can lead for the better, or maybe for the worse. The construction of a mathematical model is usually accompanied by problems in calculating the influence of inputs (other names: argument or factor). These problems are solved in the field of mathematics, which is called sensitivity analysis of mathematical models. To solve the problem of finding the sensitivity of mathematical models, the author proposes to find a criterion that allows not directly, but indirectly to determine the sensitivity. This criterion is derived on the basis of mathematical logic, and its experimental confirmation is also carried out. Further in the article, using a new criterion, one example is the best sensitivity of computer systems. In the article there is a proof of the criterion using the Monte Carlo method.

In this paper, we present the design, fabrication and performance of metal-oxide-semiconductor field-effect transistors (MOSFETs) utilizing magnesium (Mg) metal as the metal interconnect layer. We review the material properties of magnesium that enable its use in transient electronics, discuss fabrication techniques for integrating magnesium into semiconductor platforms, and evaluate the degradation mechanisms under various environmental conditions. Furthermore, basic logic gates are fabricated and tested using magnesium-based MOSFET devices. Magnesium in water degrades, forming magnesium hydroxide and releasing hydrogen, [Formula: see text]. By addressing the challenges of scalability, stability, and degradation control, this work aims to contribute to the broader adoption of degradable electronics. The integration of magnesium interconnects not only aligns with the principles of green technology but also opens new avenues for innovation in fields such as bioelectronics and environmental monitoring.

Logical Basis for Teaching Schoolchildren Comparison Skills Summary Research has shown that comparison is an inextinguishable flame that enhances the sharpness of the mind, increases clarity of consciousness and gives the cognitive process the right direction. This inextinguishable flame creates a psychological environment that promotes deep understanding and strong memorization of the material being studied, and therefore its easy recall when necessary. First of all, during the comparison, the student gets used to looking for similarities in different phenomena (objects) and differences in similar ones. Secondly, comparison is fully consistent with the general laws of real life, processes occurring in the cerebral cortex, psychological and logical phenomena. Key words: comparative skills, logical foundations of education, mental education, central nervous system, scientific generalization