ABSTRACT In this paper, I attempt to show that Joseph Butler's conception of forgiveness presents a viable, even attractive alternative to contemporary views about forgiveness. I first describe the recent change in the interpretation of Butler's view of forgiveness and then spell out the consequences of Butler's understanding of forgiveness. Among them is that forgiveness requires self-criticism on the part of the forgiver and that it is compatible with ‘settled’, i.e. impartial resentment. Moreover, forgiveness, according to Butler, is a requirement of rationality rather than of morality. While it paves the way to exercising moral virtues, it cannot be seen as a moral virtue itself. Butler's account implies that there is no victim prerogative for forgiving but also provides an explanation for why such a victim prerogative is often taken for granted. I argue that, although some of these consequences may appear counterintuitive at first sight, they turn out to be plausible upon closer inspection and can be supported by good arguments.

Approaching for Manipulation: Robot Termination Pose Generation via Active Object Detection and Task-oriented Logical Reasoning

This study aims to explore how Artificial Intelligence (AI) technology can empower inquiry-based learning in high school mathematics. Addressing issues such as limited resources, insufficient guidance, and simplistic evaluation in traditional inquiry activities, this research proposes a design framework for AI-assisted inquiry-based learning activities, with the core concept of "invisible technology, visible thinking". This framework organically integrates AI technologies like big data analysis, intelligent tutoring, and knowledge graphs into the entire inquiry process: "context creation - question posing - collaborative inquiry - outcome generation - reflective evaluation". Through practical implementation in multiple classes of a high school, focusing on topics such as "functions", "geometry", and "probability and statistics", this study collected students' activity outcomes, classroom observation data, and learning feedback. The results indicate that AI technology can provide dynamic, visual learning scaffolds and personalized cognitive support for inquiry-based learning, effectively fostering students' higher-order mathematical thinking skills like question posing, logical reasoning, and collaborative inquiry, thereby enhancing the depth and efficiency of inquiry activities. This study offers an operable practical paradigm for the deep integration of "AI + Education" in subject-specific teaching.

It has been widely demonstrated that primary school students face cognitive obstacles in scientific argumentation and often employ ineffective strategies. Scaffolding can effectively guide the scientific argumentation process, enhance its logical rigor, and facilitate students’ reflective thinking during argumentation. The purpose of this study is to examine the effects of question prompts and worked examples on primary school students’ scientific argumentation skills, alongside their scientific achievement, learning motivation and cognitive load. Using a quasiexperimental design, this study involved 68 fourth-grade students and compared the effects of two types of scaffolding: question prompts and worked examples. The results show that both scaffolding strategies exerted positive effects on students’ scientific argumentation skills, scientific achievement and learning motivation. More importantly, the worked examples were significantly more effective than the question prompts in enhancing scientific argumentation skills, particularly in terms of evidence integration and logical reasoning, and they provided greater assistance to students with low levels of prior knowledge. Finally, the worked examples group exhibited significantly lower extraneous cognitive loads than the question prompts group did. This study provides empirical evidence for optimizing the scaffolding design of primary scientific argumentation teaching, confirming that worked examples offer more efficient and adaptive support for novice learners in primary schools in a short time period. From a long-term developmental perspective, it is necessary to gradually fade the support of worked examples and transition to question prompts in scientific argumentation instruction, so as to prompt students to invest more cognitive effort and foster their independent argumentation and critical thinking abilities. These findings have important implications for advancing science curriculum reform and designing targeted instructional interventions.

Critical thinking, an essential competency for the 21st century, denotes the ability for logical and rational reasoning. Critical thinking underpins science, especially in chemistry; both field investigations and prior research indicate that students’ critical thinking regarding reduction and oxidation reactions remains underdeveloped. In order to improve conceptual comprehension, foster students’ critical thinking, and connect the three levels of representation in chemistry, visualization tools are essential. This research evaluates how effectively the Redox Animation program helps students develop their critical thinking skills regarding oxidation-reduction processes. To perform normalized gain, correlation, and regression analyses, the study used a one-group pre-test and post-test preexperimental design. It also assessed improvements in students’ critical thinking abilities, examined how the Redox Animation application affected these improvements, and looked into other influencing factors. The results demonstrated that the Redox Animation program effectively enhanced students’ critical thinking abilities, with N-gain ratings classified as medium and high. Correlation and regression analysis revealed a statistically significant correlation and substantial contribution.

ABSTRACT This study addresses the imperative goals of enhancing academic performance and increasing graduation rates within a Finance graduate program. By analysing data from all 790 students who took the Financial and Capital Markets graduate program at a business school in Brazil, the study employs linear and quantile regressions for performance prediction and logistic regression for graduation rates prediction. Findings reveal a significant positive correlation between logical reasoning and core course scores with overall student performance, with core course scores proving useful in predicting program completion. The study establishes criteria for identifying students likely to face challenges in graduating and employs a logistic regression model, correctly classifying 86% of the sample, to predict those at risk of dropping out from a Brazilian business school. We recommend using a mediator variable midway through the 18-month program to implement proactive measures, including individual interventions and collective initiatives, effectively addressing academic challenges and improving graduation rates.

The exponential growth of medical data and complexity in Pulmonary and Critical Care Medicine (PCCM) necessitates a paradigm shift in clinical reasoning and education. This paper proposes a structured framework for collaborative decision-making between physicians and artificial intelligence (AI) that emphasizes the integration of critical thinking with AI-enhanced capabilities. Critical thinking is defined as the systematic and objective analysis of information accompanied by logical reasoning and evidence‑based judgment. Traditional medical education often neglects explicit instruction in these cognitive skills, leaving clinicians vulnerable to diagnostic error and cognitive biases. Meanwhile, AI excels at data aggregation, pattern recognition, and predictive analytics, offering complementary capabilities that can support evidence-based decision-making. By distinguishing two modes of interaction AI‑assisted tools that provide recommendations and AI‑enhanced systems that simulate complex scenarios, we propose a conceptual model in which AI reinforces rather than replaces physician judgment. The article outlines how critical‑thinking skills map onto phases of diagnostic and management reasoning and illustrates the roles of physicians and AI. We discuss applications of AI in diagnosis, radiology, pulmonary function interpretation and decision support, and outline ethical considerations including algorithmic bias, data privacy and HIPAA compliance. This framework reimagines the physician-AI relationship as a cognitive partnership essential for the future of PCCM.

Abstract Background College students are at high risk for schizophrenia spectrum–related thought disorders, which are often manifested by loose logic, reduced language coherence, and impaired situational judgment. Current mental health education relies mainly on subjective questionnaires and static interviews, limiting dynamic identification and intervention under realistic cognitive load. Virtual simulation offers a controllable and immersive assessment environment, but evidence for its synergistic use with mental health education remains limited. This study constructs and evaluates a virtual simulation–based synergistic mechanism for thought disorder assessment and mental health education. Methods A total of 220 undergraduate students from three universities were recruited (mean age: 20.4 ± 1.3 years) and classified into a high-risk group (n = 106) and a control group (n = 114) based on mental risk screening results. A pretest–posttest controlled experimental design was adopted. Logical reasoning, situational decision-making, and language organization tasks were implemented on a virtual simulation platform, and indicators including response time, decision-path deviation rate, and language coherence index were collected. In addition to routine mental health education, the high-risk group received an 8-week virtual simulation–assisted intervention, while the control group received routine courses only. Thought disorder assessment scales and mental health questionnaires were administered. Statistical analyses were conducted using t-tests, analysis of variance, and correlation analysis, with the significance level set at p<.05. Results Baseline results showed that the high-risk group exhibited significantly longer response times than the control group (3.79 ± 0.68 s vs. 2.91 ± 0.64 s, p<.001) and significantly lower language coherence indices (69.15 ± 7.92 vs. 77.04 ± 8.01, p<.001). After the intervention, response time in the high-risk group was reduced by 18.7%, and the decision-path deviation rate decreased from 22.14% to 15.03% (p=.001). The total score of the thought disorder scale decreased by 11.86 ± 3.94 points (p<.001). Analysis of variance revealed a significant main effect of group (F = 19.62, p<.001), while no significant interactions with gender or academic year were observed. Correlation analysis indicated a significant negative correlation between improvements in language coherence and reductions in thought disorder scale scores (r = −0.48, p<.01), and a significant positive correlation between improvements in task performance and increases in overall mental health scores (r = 0.52, p<.01). Following the intervention, classroom participation and course completion rates increased by 24.9% and 19.8%, respectively. Discussion The results indicate that the synergistic mechanism integrating thought disorder assessment and mental health education within a virtual simulation context can effectively identify abnormalities in thought processing among college students and significantly improve cognitive and mental health outcomes in high-risk individuals. The significant associations between assessment indicators and intervention effects support the practical value of an integrated assessment–feedback–intervention framework in campus mental health education. This study provides a novel pathway for early identification and precise intervention of schizophrenia spectrum–related thought disorders. Future research should incorporate multimodal behavioral data and longitudinal follow-up to further validate the stability and predictive utility of this mechanism. Funding No. 24C17.

Logical reasoning is often presumed to require effortful cognition. However, there is evidence that reasoners may have access to a form of intuition that relies on variations in the availability of semantically related information. This may provide intuitive cues for judgments of conclusion validity or invalidity, allowing for very rapid forms of reasoning that do not rely on belief-based heuristics. We examined very rapid reasoning with formally identical syllogisms where the major premise was characterized by having relative Few or Many alternative antecedents. In four studies, we examined premises that had identical formal structure and syntax, with minimal differences in content, using two forms of invalid inferences: ("All A are B. X is B. X is A."; "All A are B. X is not A. X is not B."), and one valid form ("All A are B. X is not B. X is not A."). All studies showed that under severe time constraint reasoners judged that the putative conclusion was invalid more often for premises with Many alternative antecedents than for those with Few alternatives. These results support the conclusion that semantically activated information can serve as a cue for intuitive, rapid inferences.

Abstract Background Schizophrenia is a severe psychiatric disorder, and most patients show cognitive impairments that affect social functioning and quality of life. About 70%–80% of patients have deficits in working memory, attention, verbal fluency, and thinking. Medication can reduce symptoms but has limited effects on cognition. In recent years, cognitive training and language rehabilitation have gained attention. English story reading blends language learning with cognitive stimulation. Second-language learning activates multiple brain regions, and story content can support logical thinking and social cognition. However, systematic studies on its effects in schizophrenia remain lacking. This study assesses how English story reading influences language and cognitive functions to offer new ideas for rehabilitation. Methods The study includes 120 stable patients who meet DSM-5 criteria for schizophrenia. Patients are 18–55 years old, have a disease duration of 2–10 years, and have a Positive and Negative Syndrome Scale (PANSS) total score ≤ 60. Patients are randomly assigned to an intervention group (n = 60) or a control group (n = 60). The intervention group receives 12 weeks of English story reading education, three sessions per week, each lasting 60 minutes, guided by English teachers and psychiatrists. Reading materials include short English stories about daily life and social interaction. The sessions include vocabulary learning, sentence comprehension, story retelling, and plot discussion. The control group receives routine rehabilitation, including occupational therapy and social skills training. After the intervention, the Verbal Fluency Test (VFT) assesses language function. The Wisconsin Card Sorting Test (WCST) assesses executive function. The Digit Span Test and the Trail Making Test assess working memory and attention. Class participation, interaction frequency, and learning progress are also recorded. Results After 12 weeks, semantic fluency scores in the intervention group increased from 12.3 ± 3.1 to 17.8 ± 3.5, while the control group increased from 12.5 ± 2.9 to 13.9 ± 3.2 (p<.001, d = 1.15). Phonemic fluency scores in the intervention group increased from 9.8 ± 2.6 to 14.2 ± 3.1, while the control group increased from 9.5 ± 2.7 to 10.8 ± 2.9 (p<.001, d = 0.98). WCST results showed that the intervention group had fewer perseverative errors (p=.003, d = 0.67), indicating improved executive function and cognitive flexibility. In the Digit Span Test, forward and backward scores improved significantly in the intervention group (p=.012 and p=.005), while the control group showed no clear changes. Subgroup analysis showed that patients with higher education levels and shorter disease duration had stronger intervention effects. Class participation in the intervention group correlated positively with cognitive improvement (r = 0.58, p<.001). Discussion The study showed that English story reading education improved language and cognitive functions in patients with schizophrenia. The intervention enhanced verbal fluency, executive function, working memory, and attention. These effects may stem from second-language learning activating coordinated activity in prefrontal, temporal, and parietal regions, supporting neuroplasticity. Story comprehension and discussion trained logical reasoning, causal judgment, and social cognition, while group activities improved social motivation and emotional expression. English story reading education could serve as a useful supplement to cognitive rehabilitation, especially for stable patients with higher educational backgrounds. Future studies should examine optimal intervention duration, individualized reading materials, and the long-term stability of cognitive gains, and neuroimaging may help clarify the neural mechanisms. Developing standardized programs could support clinical application.

Abstract Background The construction of the rule of law in the new era places higher demands on university students majoring in law. In addition to solid professional competence, positive psychological qualities such as stress resistance, empathy, and professional identity are core supports for their adaptation to legal practice. At present, university psychological assessments lack evaluation systems for cultivating positive psychology that are tailored to the characteristics of law majors, resulting in cultivation efforts that lack precise guidance and scientific feedback. Therefore, it is necessary to study in connection with the training goals of law professionals to establish a systematic and practical evaluation system for cultivating positive psychology, providing theoretical and practical support for improving the mental health of law students. Methods This study selected 240 participants, including law students and faculty from three universities at different levels, as well as legal practitioners. A literature review was used to identify the core dimensions of positive psychology, and evaluation indicators were initially drafted based on the characteristics of the legal profession. The Delphi method was used to optimize the indicator system through two rounds of expert consultation, ultimately determine ng four primary dimensions and twelve secondary indicators. A “Positive Psychological Cultivation Evaluation Scale for Law Students” was developed, and a pre-survey was conducted with 180 students. Exploratory factor analysis was used to test construct validity, Cronbach’s α coefficient was used to test reliability, and the analytic hierarchy process (AHP) was used to determine the weights of each indicator. Data are expressed as mean ± standard deviation (SD). Results As shown in Table 1, the evaluation system constructed in this study includes four primary dimensions: cognitive efficacy (weight 0.28), emotion management (0.25), professional identity (0.27), and social adaptation (0.20). In the pre-survey, the scores for each dimension were: cognitive efficacy 3.72 ± 0.58, emotion management 3.56 ± 0.61, professional identity 3.85 ± 0.53, and social adaptation 3.63 ± 0.59. Secondary indicators cover logical reasoning, stress management, and belief in the rule of law. The scale showed good reliability and validity, with a total Cronbach’s α coefficient of 0.89 and α coefficients for each dimension ranging from 0.78 to 0.85. Confirmatory factor analysis showed a fit index χ2/df = 2.31, RMSEA = 0.07, and CFI = 0.92, indicating good structural fit. Discussion The evaluation system developed in the study shows that professional identity and cognitive efficacy account for the highest proportions, aligning with the core needs of talent development in the field of law, and possessing good scientific validity and practicality. This system can help accurately identify gaps in cultivation, optimize training programs, and in the future, it can expand sample coverage and dynamically adjust indicator weights using longitudinal tracking data, enhancing the system’s adaptability across different universities and promoting the standardized development of positive psychological cultivation in the legal profession.

Large language models (LLMs) have shown remarkable progress in general reasoning and understanding, but their ability to perform formal logical reasoning remains under-explored. In this paper, we introduce DLReasonSuite, a novel benchmark designed to rigorously evaluate LLMs on reasoning tasks grounded in Description Logic (DL). DL-ReasonSuite comprises 4740 tasks spanning seven distinct task types and organized into three reasoning tracks: (1) DLCore, covering fundamental ontology reasoning tasks (consistency checking, subsumption, and instance checking); (2) DLQuery, focusing on answering entailment-aware SPARQL queries; and (3) DLBridge, bridging natural language and formal logic (bidirectional NL ↔ OWL translation and tool-augmented entailment resolution). We detail the methodology for designing and implementing this benchmark, including task construction, automatic evaluation metrics and validation using reliable OWL reasoners. Then, we present an empirical evaluation of five leading reasoning LLMs as stateofart models: Kimi k1.5, LlamaNemotron Ultra, DeepSeekR1, Phi4 Reasoning Plus, and Phi4 Reasoning on the full suite of tasks. Our results reveal significant variability in LLM performance on formal reasoning was observed. While the best model, Phi4 Reasoning Plus, achieves an overall accuracy of 85% and excels especially in tool-augmented tasks, other models struggle notably with complex query reasoning for DL and precise OWL translation. We analyze the strengths and weaknesses of each model across different DL metrics and task categories, providing insights into current limitations of LLM reasoning such as handling SPARQL queries and maintaining logical consistency and the benefits of neuro-symbolic techniques. DL-ReasonSuite is a comprehensive framework for assessing and advancing LLMs’ Description Logic reasoning capabilities aiming to bridge the gap between natural language understanding and formal knowledge representation.

Campus placement preparation requires consistent practice in quantitative aptitude, logical reasoning, and analytical problem-solving. Traditional preparation methods often lack structure, performance tracking, and real-time feedback, making it difficult for students to evaluate their progress effectively. This paper presents the design and development of an Aptitude Portal integrated with an Android Application, aimed at providing a centralized and interactive platform for aptitude preparation. This system categorizes questions topic-wise and difficulty-wise (Easy, Medium, Hard), enabling progressive learning. It includes time- based quizzes, instant score evaluation, streak tracking, and performance monitoring to encourage consistent practice. The admin panel allows dynamic management of questions using Firebase Firestore, ensuring that content remains updated and relevant. The web application is built using Node.js, Express.js and EJS, while the Android app is developed using Kotlin and XML. By integrating web and mobile access, the system ensures flexibility, accessibility, and scalability. The proposed system enhances student engagement, supports self-assessment, and improves placement readiness through structured and gamified learning.

The objective of this paper is to assess the ambience of diverse learners practicing the contents in calculus with Microsoft Math Solver. Calculus problems involve abstract reasoning, particularly logical reasoning and abstract thinking, as well as equations as a platform. This study's primary goal is to evaluate conceptual learning in calculus in teacher education using an exploratory approach that prioritizes visuals over conventional math solvers. Aforementioned is primarily to assess how effectively student-teachers can develop a profound, long-lasting understanding of mathematical concepts through a preferred procedure. To help achieve the goals, an exploratory survey design is employed over a specified interval of time, known as a time-series approach. The convenience sampling technique is employed in this study. This approach seeks to explain phenomena, such as calculating derivatives in the advanced computational laboratory using Microsoft Math Solver, which forms the foundation for similar concepts carried out methodically in conventional classrooms. Additionally, the description refers to using a method that involved six math majors' student-teachers in various contexts. The Hawthorne effect is mitigated in this study, as the researcher can observe students in class while they receive instruction, allowing them to focus on problem-solving. As already stated, this is also possible in an advanced computing lab. The research yielded well-resourced, self-paced questions and answers, as well as an environment that facilitated the exposure of the concept of calculus in collaboration with Microsoft Math Solver. Learners save time, increase creativity and experience, and recapitulate solutions through visualization with updated, enhanced routines. This study captures the ambiance in the visualization of learning Calculus via MMS. The sample may include student teachers, who benefit significantly from applying the subject in this way, both in their teaching practice and in the early stages of their careers. Additionally, treating student-teachers as samples in this exploratory survey is a novel aspect of this study.

ABSTRACT Evidence remained conflicting regarding how the prefrontal cortex supported decision-making abilities, particularly in patients with focal prefrontal cortex lesions. While damage to this region was known to impair executive functioning, the precise contribution of such deficits to decision-making performance – especially under varying levels of uncertainty – remained debated. Moreover, cognitive estimation processes, which were associated with logical reasoning and prefrontal involvement, had rarely been examined in relation to decision-making tasks. To clarify these associations, we administered a cognitive estimation task and the Iowa Gambling Task (IGT), alongside a battery of executive function tests, to 30 patients with focal prefrontal damage and 30 matched control subjects. Our results indicated that patients showed consistent impairment across executive functions, cognitive estimation, and decision-making under risk. Furthermore, correlation and regression analyses revealed that performance on executive tasks and cognitive estimation predicted IGT outcomes, particularly under risk conditions. Finally, voxel-based lesion-symptom mapping identified a bilateral prefrontal network – spanning ventromedial, dorsomedial, and dorsolateral regions – associated with impaired IGT performance. These findings suggested that the multidimensional nature of the IGT was associated with complex executive and inferential reasoning demands and implicated diverse patterns of frontal dysfunction beyond the ventromedial prefrontal cortex

Driven by the intensifying mission to foster virtue through education within the Chinese higher education landscape, the strategic integration of value-based guidance into academic curricula has emerged as the primary vehicle for achieving a comprehensive and holistic instructional environment. Chemistry, as a discipline, is uniquely defined by its combination of rigorous scientific theory and extensive practical utility. Consequently, embedding ideological elements into chemistry courses is not merely a critical step in enhancing the caliber of professional training; it is also instrumental in nurturing students' logical reasoning, ethical standards, and civic accountability. By synthesizing domestic and international scholarly progress from the last five years, this study dissects the multi-layered theoretical framework that supports value-integrated chemistry education. It provides a detailed analysis of six essential pillars—including scientific integrity, patriotism, and cultural pride—and distills an operational model characterized by "six dimensions and four pillars" derived from current pedagogical practices. Furthermore, the paper addresses existing bottlenecks, such as undeveloped assessment tools and fragmented resource utilization, by proposing targeted optimization strategies. This research aims to offer a fresh theoretical benchmark for innovating and standardizing the practical implementation of ideological-political education in chemistry, ultimately laying a solid groundwork for preparing a new generation of chemical experts who possess both professional excellence and unwavering social convictions.

This study aims to analyze and describe students' intuitive thinking abilities in solving mathematical problems on the topic of integers. This research employs a qualitative descriptive method. One research subject (S1) will be selected using purposive sampling based on their ability to demonstrate initial indications of intuitive thinking, such as the accuracy and speed of their initial response to a problem. The research instrument consists of one integer problem-solving test question designed to assess intuitive thinking abilities. Data is collected through triangulation using the think-aloud technique during the problem-solving process, followed by a semi-structured interview to explore the subject's (S1) reasoning and intuitive thought processes. Data is analyzed qualitatively through the stages of data reduction, data presentation, and conclusion drawing. The results reveal that intuition, specifically the common-sense type, acts as a cognitive bridge that accelerates the emergence of ideas and the formulation of problem-solving strategies. This intuitive thinking characteristic is demonstrated through the application of systematic strategies, logical reasoning, and a strong reliance on prior learning experiences. These findings indicate that learning experiences can serve as a crucial foundation in forming effective mathematical intuition. Therefore, mathematics instruction should be designed to enrich student experiences through a variety of problem-solving tasks to develop students' intuitive thinking abilitie

Green-synthesized nanomaterials have emerged as promising candidates for environmentally sustainable remediation; however, experimental evidence describing their synthesis routes, physicochemical properties, remediation performance, and sustainability-relevant attributes remains fragmented, inconsistently reported, and difficult to integrate across studies. This work addresses this challenge by proposing an ontology-based semantic framework for the interoperable integration of green-synthesized nanomaterials, contaminants, and remediation processes, incorporating explicit provenance metadata and structured sustainability descriptors. The ontology was developed using the Linked Open Terms (LOT) methodology and implemented in OWL 2 DL, with selective alignment to established vocabularies including eNanoMapper, ChEBI, ENVO, and PROV-O. Adsorption and photocatalysis were instantiated as representative remediation mechanisms to evaluate the framework’s capacity to accommodate structurally distinct processes. Logical reasoning and SHACL-based validation were applied to assess semantic consistency, provenance traceability, and data completeness. The results demonstrate that the proposed ontology effectively integrates heterogeneous experimental data within a unified, FAIR-compliant semantic framework, supports conservative and provenance-aware inference, and enables comparative analysis across mechanistically diverse remediation systems without structural modification. This ontology-based approach provides a robust foundation for sustainability-aware knowledge integration in environmental nanotechnology and establishes the basis for future extensions involving data quality assessment and explainable AI-driven analysis.

Objective: The research aimed to develop a scale for students' logical reasoning in football, prepare educational exercises for the idea filtering strategy and its application in physical education football lessons on outdoor fields, and identify its impact on logical reasoning and performance in the skills of forward shooting from dribbling and from side passes in football. Research methodology: The experimental method was adopted with a two-group design (experimental and control) with (58) students randomly selected and divided into the two groups, representing (65.909%). The researchers used (120) students to develop the scale under study, employing systematic steps and various sequential statistical analyses. They also prepared the forward shooting test from dribbling and the shooting test from side passes. Educational exercises for the idea filtering strategy were developed and applied in the research experiment, the results of which were systematically analyzed. Results: The results showed that the students in the experimental group outperformed their peers in the control group in all three dependent variables. The differences between the experimental and control groups in the reasoning tests were significant. The logical reasoning in football, scoring from a dribble, and scoring from a side pass (0.000) are statistically significant and positive, confirming the effectiveness of the idea filtering strategy on students. Conclusions: The most important conclusion is that implementing educational exercises using the idea filtering strategy helps improve the level of logical reasoning and improves the performance of students who study using this strategy in terms of scoring from a dribble and scoring from a side pass in football, making them outperform their peers who study without it.

Necessary and sufficient knowledge enhanced collaborative logical reasoning in LLMs.