Formal Reasoning Research Articles

Redesigning geometry assessments to promote advanced geometric thinking: A case study on formal deduction and rigor

Many geometry problems at the university level, particularly in analytic geometry courses, tend to prioritize procedural tasks to foster deeper geometric thinking. This study aims to analyze and redesign existing geometry problems to enhance pre-service mathematics teachers' formal deductive reasoning and rigor in accordance with the Van Hiele model. Employing a case study approach, four geometric problems were analyzed in relation to their alignment with various levels of geometric thinking. The study involved a detailed examination of pre-service mathematics teachers’ responses and the structure of their problems to identify aspects that require improvement to better support higher-order thinking. The methodology included a content analysis of problem design and pre-service mathematics teachers’ answers, focusing on their engagement in formal deduction and generalization. The findings indicate that the current problems insufficiently promote the development of formal deduction and rigor, as they are primarily centered on formula applications without requiring proof or generalization. Specific recommendations are provided in the form of redesigned analytic geometric problems aimed at fostering advanced geometric thinking. These redesigns are expected to help pre-service mathematics teachers tackle more complex mathematical problems by encouraging logical reasoning and argumentation.

Reasoning About Exceptional Behavior At the Level of Java Bytecode with ByteBack

A program’s exceptional behavior can substantially complicate its control flow, and hence accurately reasoning about the program’s correctness. On the other hand, formally verifying realistic programs is likely to involve exceptions—a ubiquitous feature in modern programming languages. In this paper, we present a novel approach to verify the exceptional behavior of Java programs, which extends our previous work on Byte Back . Byte Back works on a program’s bytecode, while providing means to specify the intended behavior at the source-code level; this approach sets Byte Back apart from most state-of-the-art verifiers that target source code. To explicitly model a program’s exceptional behavior in a way that is amenable to formal reasoning, we introduce Vimp: a high-level bytecode representation that extends the Soot framework’s Jimple with verification-oriented features, thus serving as an intermediate layer between bytecode and the Boogie intermediate verification language. Working on bytecode through this intermediate layer brings flexibility and adaptability to new language versions and variants: as our experiments demonstrate, Byte Back can verify programs involving exceptional behavior in all versions of Java, as well as in Scala and Kotlin (two other popular JVM languages).

Exploration of Chemical Space Through Automated Reasoning

AbstractThe vast size of composition space poses a significant challenge for materials chemistry: exhaustive enumeration of potentially interesting compositions is typically infeasible, hindering assessment of important criteria ranging from novelty and stability to cost and performance. We report a tool, Comgen, for the efficient exploration of composition space, which makes use of logical methods from computer science used for proving theorems. We demonstrate how these techniques, which have not previously been applied to materials discovery, can enable reasoning about scientific domain knowledge provided by human experts. Comgen accepts a variety of user‐specified criteria, converts these into an abstract form, and utilises a powerful automated reasoning algorithm to identify compositions that satisfy these user requirements, or prove that the requirements cannot be simultaneously satisfied. In contrast to machine learning techniques, explicitly reasoning about domain knowledge, rather than making inferences from data, ensures that Comgen's outputs are fully interpretable and provably correct. Users interact with Comgen through a high‐level Python interface. We illustrate use of the tool with several case studies focused on the search for new ionic conductors. Further, we demonstrate the integration of Comgen into an end‐to‐end automated workflow to propose and evaluate candidate compositions quantitatively, prior to experimental investigation. This highlights the potential of automated formal reasoning in materials chemistry.

Exploration of Chemical Space Through Automated Reasoning.

The vast size of composition space poses a significant challenge for materials chemistry: exhaustive enumeration of potentially interesting compositions is typically infeasible, hindering assessment of important criteria ranging from novelty and stability to cost and performance. We report a tool, Comgen, for the efficient exploration of composition space, which makes use of logical methods from computer science used for proving theorems. We demonstrate how these techniques, which have not previously been applied to materials discovery, can enable reasoning about scientific domain knowledge provided by human experts. Comgen accepts a variety of user-specified criteria, converts these into an abstract form, and utilises a powerful automated reasoning algorithm to identify compositions that satisfy these user requirements, or prove that the requirements cannot be simultaneously satisfied. In contrast to machine learning techniques, explicitly reasoning about domain knowledge, rather than making inferences from data, ensures that Comgen's outputs are fully interpretable and provably correct. Users interact with Comgen through a high-level Python interface. We illustrate use of the tool with several case studies focused on the search for new ionic conductors. Further, we demonstrate the integration of Comgen into an end-to-end automated workflow to propose and evaluate candidate compositions quantitatively, prior to experimental investigation. This highlights the potential of automated formal reasoning in materials chemistry.

Из истории гонений на Русскую Православную Церковь на территории Северной Осетии: дело кафедрального собора

The article examines the issue of persecution of the Russian Orthodox Church in North Ossetia using the case of the Vladikavkaz Cathedral as an example. Based on the first published documentary sources, the mechanism of pressure exerted by the Soviet government on church employees is shown. The author concludes that arrests and trials of the clergy and church workers were made for formal reasons in order to deprive parishioners of the clergy before the impending destruction of churches. The materials of the Archives FSB of the Russian Federation for the Republic of North Ossetia-Alania were used to write this work.

Socio-political Struggle and the Problem of State Building in Ukraine in the 60's of the XVII Century

60-80s of the 17th century. entered the history of Ukraine as the "Age of Ruin". Unfortunately, the heirs of B. Khmelnytskyi could not successfully complete his endeavors. The beginning of the Age of Ruin was the removal of Yu. Khmelnytskyi from power in the fall of 1657. I. Vyhovskyi and his supporters actually carried out a coup d'état. In the post of hetman, I. Vyhovsky pursued an anti-Moscow policy, defeated the pro-Moscow uprising of the Cossacks (1658), and sent Russian troops to Konotop (1659). He concluded an agreement with the Polish-Lithuanian Commonwealth in Hadiachy (1658), which was ratified by the Polish Diet. This agreement too limited the rights of Ukraine, which reduced Vyhovsky's support among the Cossacks. In October 1659 he was removed from the hetmanship at the "Black Council" and returned power to Yuri Khmelnytskyi. After that, he was in the Polish civil service. In 1664, by order of his personal enemy - the then hetman of Right Bank Ukraine, Pavlo Teteri - he was arrested, baselessly accused of treason against the Polish king and shot. The formal reason for these actions was Yu. Khmelnytskyi's youth, illness, and weakness. The real reasons are the deterioration of the state's geopolitical situation, the strengthening of social opposition in society, the struggle of individual elite groups for power, weak support for the idea of hereditary monarchy, etc.

Sequential merging and construction of rankings as cognitive logic

Sequential merging and construction of rankings as cognitive logic

Assisted suicide in Switzerland (part 2): the «invisible» old age suicide

According to the Swiss Federal Statistical Office (FSO), there were 6608 assisted suicides in Switzerland in the 5-year period 2018-2022; of these, 4766 cases (72%) were assisted by team members of EXIT, the largest Swiss right-to-die organization. According to EXIT-data, age-related multimorbidity is the second most common disease group in assisted dying, accounting for 27 % of all cases. For formal reasons, these symptom-oriented cases of old age assisted suicide cannot be adequately recorded in the FSO's ICD-based cause of death statistics. This «statistical weakness» implies that Switzerland is unable to provide reliable data on the phenomenon of old age assisted suicide, which is the subject of controversial debate in medical ethics and social policy. It would therefore be advisable to set up a national registry that carefully documents all cases of assisted suicide and could also critically monitor certain cases.

New trends in didactic research in university mathematics education

Recent research in university mathematics education has moved beyond the traditional focus on the transition from secondary to tertiary education and students' understanding of introductory courses such as pre-calculus and calculus. There is growing interest in the challenges students face as they move into more advanced mathematics courses that require a shift toward formal reasoning, proof, modeling, and problem-solving skills. This survey paper explores emerging trends and innovations in the field, focusing on three key areas: innovations in teaching and learning advanced mathematical topics, transitions between different levels and contexts of mathematics education, and the role of proof and proving in advanced university mathematics. The survey reflects the evolving landscape of mathematics education research and addresses the theoretical and practical challenges of teaching and learning advanced mathematics across various contexts.

State of scientific research problems of judicial proceedings in civil jurisdiction

The article reveals current problems and the state of scientific research on judicial proceedings in civil proceedings. In particular, special attention is paid to the issue of justice. The definitions and content of justice given by both scientists and its normative basis are analyzed. It is established that some scientists define justice as the main function of the court, while others define it as a form of activity of the court itself. The proposed author’s definition of the concept of «justice». Issues of access to justice are highlighted. It is suggested that the issue of access to justice be classified as one of the main principles of the civil process. The availability of justice and access to court is considered in the context of the concept of basic human rights and freedoms. Access to justice is defined as a combination of such interrelated elements as unconditional freedom, state- guaranteed opportunity and equality of a person whose rights have been violated to apply for judicial protection of his rights and legitimate interests to a competent court; the duty of the court to accept the case for its proceedings, without applying formal reasons for refusal. Application of universal and unlimited court jurisdiction; guarantees of competitiveness, proper judicial procedures, which ensure reasonable terms of consideration of the case. Particular attention is paid to the main principles recommended by the Committee of Ministers of the Council of Europe to member states regarding measures that facilitate access to justice. The opinions of scientists revealing the meaning of such principles as simplification of court proceedings, acceleration of proceedings and court costs are established. The work analyzes official statistical data for 2020 - 2023, regarding the number of cases that were considered in the order of simplified legal proceedings in all courts on the territory of Ukraine. It was concluded that, in minor cases, it would be appropriate to develop and implement national standards that would allow individuals to independently fill out understandable standard forms of procedural documents and submit them to the court, without consulting legal experts. It is proposed to use a differentiated approach to determine the size of the court fee depending on the person’s income or depending on the degree of difficulty of the case, taking into account the procedural costs and time for consideration of the case.

Reasons and root causes: Conventional characterizations of doctoral engineering attrition obscure underlying structural issues

AbstractBackgroundAlthough most engineering graduate students are funded and usually complete their degrees faster than other disciplines, attrition remains a problem in engineering. Existing research has explored the psychological and sociological factors contributing to attrition but not the structural factors impacting attrition.Purpose/HypothesisUsing systems theory, this study seeks to understand nuance in how underlying structural causes affect engineering graduate students' attrition experiences in ways that may differ from their official reasons for departure.Design/MethodsData were collected through semi‐structured interviews with seven departing or already departed engineering doctoral students from R1 graduate programs across the United States. Using thematic analysis, root cause analyses were conducted to understand participants' attrition experiences to explore how structures influence causes of departure.ResultsThe ways participants discuss root causes of their departure indicate differences in formal reasons for departure and underlying causes of departure. We highlight the role of informal and formal policy as root causes of a different attrition rationale often passed off as interpersonal issues. When interpreted as evidence of structural issues, the causes of departure show ways in which action–inaction, policy–“null” policy serve as structural features governing student attrition decision processes. We also highlight a form of benign neglect toward struggling graduate students.ConclusionThis study reveals important nuances underlying face‐value reasons of attrition indicating foundational structural issues contributing to engineering graduate student attrition. Coaching faculty in team management and encouraging close revision of departmental policies could help mitigate students' negative graduate experiences and decrease unnecessary attrition.

Level of students' proportional reasoning in solving mathematical problems

This study aimed to evaluate the level of proportional reasoning among middle school students in their ability to solve mathematical problems involving proportions. Proportional reasoning is essential for understanding and mastering various mathematical concepts, serving as a fundamental skill for higher-level mathematics. A qualitative case study design was employed, involving 28 eighth-grade students from a school in Bandung, Indonesia. The participants were assessed using a set of proportion-related problems, including numerical comparison, non-proportional (additive), direct proportion, and inverse proportion tasks. The analysis focused on categorizing the students' problem-solving strategies into distinct levels of proportional reasoning, ranging from non-proportional to formal proportional reasoning. Additionally, three students representing high, moderate, and low mathematical performance were selected for in-depth interviews to explore their reasoning processes when addressing proportion problems. Data analysis included administering tests, reviewing students' problem-solving strategies, conducting in-depth interviews, and evaluating their proportional reasoning abilities. The findings revealed that students with high and moderate mathematical performance exhibited proportional reasoning levels ranging from 0 to 3, whereas low-performing students displayed levels ranging from 0 to 2. Moreover, students generally faced difficulties distinguishing between proportional and non-proportional problems. Even when correct answers were provided, many lacked a deep understanding of direct and inverse proportion concepts. The study also discusses several implications for enhancing students' proportional reasoning skills.

A Knowledge Graph-Based Consistency Detection Method for Network Security Policies

Network security policy is regarded as a guideline for the use and management of the network environment, which usually formulates various requirements in the form of natural language. It can help network managers conduct standardized network attack detection and situation awareness analysis in the overall time and space environment of network security. However, in most cases, due to configuration updates or policy conflicts, there are often differences between the real network environment and network security policies. In this case, the consistency detection of network security policies is necessary. The previous consistency detection methods of security policies have some problems. Firstly, the detection direction is single, only focusing on formal reasoning methods to achieve logical consistency detection and solve problems. Secondly, the detection policy field is not comprehensive, focusing only on a certain type of problem in a certain field. Thirdly, there are numerous forms of data structures used for consistency detection, and it is difficult to unify the structured processing and analysis of rule library carriers and target information carriers. With the development of intelligent graph and data mining technology, the above problems have the possibility of optimization. This article proposes a new consistency detection approach for network security policy, which uses an intelligent graph database as a visual information carrier, which can widely connect detection information and achieve comprehensive detection across knowledge domains, physical devices, and detection methods. At the same time, it can also help users grasp the security associations with the real network environment based on the graph algorithm of the knowledge graph and intelligent reasoning. Furthermore, these actual network situations and knowledge bases can help managers improve policies more tailored to local conditions. This article also introduces the consistency detection process of typical cases of network security policies, demonstrating the practical details and effectiveness of this method.

A Formal Explainer for Just-In-Time Defect Predictions

Just-in-Tim e (JIT) defect prediction has been proposed to help teams prioritize the limited resources on the most risky commits (or pull requests), yet it remains largely a black box, whose predictions are not explainable or actionable to practitioners. Thus, prior studies have applied various model-agnostic techniques to explain the predictions of JIT models. Yet, explanations generated from existing model-agnostic techniques are still not formally sound, robust, and actionable. In this article, we propose FoX , a Fo rmal e X plainer for JIT Defect Prediction, which builds on formal reasoning about the behavior of JIT defect prediction models and hence is able to provide provably correct explanations, which are additionally guaranteed to be minimal. Our experimental results show that FoX is able to efficiently generate provably correct, robust, and actionable explanations, while existing model-agnostic techniques cannot. Our survey study with 54 software practitioners provides valuable insights into the usefulness and trustworthiness of our FoX approach; 86% of participants agreed that our approach is useful, while 74% of participants found it trustworthy. Thus, this article serves as an important stepping stone towards trustable explanations for JIT models to help domain experts and practitioners better understand why a commit is predicted as defective and what to do to mitigate the risk.

THE DESIGN OF AN INSTRUMENT TO ASSESS COGNITIVE LEVELS OF INFORMAL INFERENTIAL REASONING IN HIGH SCHOOL PHYSICS

Informal logical reasoning (English Informal Inferential Reasoning, IIR) is a cognitive process, the main characteristic of which is to take into account the student's environment, informal and formal reasoning, and the latter, as a rule, is promoted in high school science courses such as physics, and in courses that are developed and consolidated during adolescence. The study aims to consider the construction of methods for measuring IIR with elements based on the educational goals of the Marzano and Kendall taxonomy, which are detailed in terms of the performance that must be achieved in each cognitive process. Similarly, the key concepts of physics are considered from the topics of Uniform Rectilinear Motion (URM) and Uniformly Accelerated Rectilinear Motion (UARM). The method was evaluated by 12 experts for understanding and relevance, and a pilot test was conducted with a sample of 212 high school students aged 15 to 18 years. The results showed the reliability and reliability of the method (V Aiken = .73) to evaluate the cognitive processes necessary for the study of physics. This experiment is a useful method for teachers who want to adapt the thematic content of the curriculum to gradually encourage cognitive processes, ranging from recall to analysis and use of knowledge.

On being drawn to different types of arguments: a mouse-tracking study

How people distinguish well-justified from poorly justified arguments is not well known. To study the involvement of intuitive and analytic cognitive processes, we contrasted participants’ personal beliefs with argument strength that was determined in relation to established criteria of sound argumentation. In line with previous findings indicating that people have a myside bias, participants (N = 249) made more errors on conflict than on no-conflict trials. On conflict trials, errors and correct responses were practically equal in terms of response times and mouse-tracking indices of hesitation. Similarly to recent findings on formal reasoning, these findings indicate that correct reasoning about informal arguments may not necessitate corrective analytic processing. We compared findings across four argument schemes but found few differences. The findings are discussed in light of intuitive logic theories and the notion that evaluating informal arguments could be based on implicit knowledge of argument criteria.

Understanding random resampling techniques for class imbalance correction and their consequences on calibration and discrimination of clinical risk prediction models

Class imbalance is sometimes considered a problem when developing clinical prediction models and assessing their performance. To address it, correction strategies involving manipulations of the training dataset, such as random undersampling or oversampling, are frequently used. The aim of this article is to illustrate the consequences of these class imbalance correction strategies on clinical prediction models' internal validity in terms of calibration and discrimination performances. We used both heuristic intuition and formal mathematical reasoning to characterize the relations between conditional probabilities of interest and probabilities targeted when using random undersampling or oversampling. We propose a plug-in estimator that represents a natural correction for predictions obtained from models that have been trained on artificially balanced datasets ("naïve" models). We conducted a Monte Carlo simulation with two different data generation processes and present a real-world example using data from the International Stroke Trial database to empirically demonstrate the consequences of applying random resampling techniques for class imbalance correction on calibration and discrimination (in terms of Area Under the ROC, AUC) for logistic regression and tree-based prediction models. Across our simulations and in the real-world example, calibration of the naïve models was very poor. The models using the plug-in estimator generally outperformed the models relying on class imbalance correction in terms of calibration while achieving the same discrimination performance. Random resampling techniques for class imbalance correction do not generally improve discrimination performance (i.e., AUC), and their use is hard to justify when aiming at providing calibrated predictions. Improper use of such class imbalance correction techniques can lead to suboptimal data usage and less valid risk prediction models.

Deductive Reasoning Based on the Valid Aristotelian Syllogism AEE-2

This paper firstly formalizes Aristotelian syllogisms based on the tripartite structure of categorical propositions, and then uses the truth definitions of categorical propositions to prove the validity of the Aristotelian syllogism AEE-2. Then, the remaining 23 valid syllogisms are derived from the syllogism AEE-2 with the help of relevant facts, inner and outer negation definitions of quantifiers, and deductive rules. In other words, this paper reveals the reducible relationship between/among these 24 syllogisms and establishes a succinct formal reason system for Aristotelian syllogistic. The deductive reasoning not only ensures consistency in its results, but also provides a concise mathematical paradigm for other types of syllogisms.

On Alternating-Time Temporal Logic, Hyperproperties, and Strategy Sharing

Alternating-time temporal logic (ATL*) is a well-established framework for formal reasoning about multi-agent systems. However, while ATL* can reason about the strategic ability of agents (e.g., some coalition A can ensure that a goal is reached eventually), we cannot compare multiple strategic interactions, nor can we require multiple agents to follow the same strategy. For example, we cannot state that coalition A can reach a goal sooner (or more often) than some other coalition A'. In this paper, we propose HyperATL*_S, an extension of ATL* in which we can (1) compare the outcome of multiple strategic interactions w.r.t. a hyperproperty, i.e., a property that refers to multiple paths at the same time, and (2) enforce that some agents share the same strategy. We show that HyperATL*_S is a rich specification language that captures important AI-related properties that were out of reach of existing logics. We prove that model checking of HyperATL*_S on concurrent game structures is decidable. We implement our model-checking algorithm in a tool we call HyMASMC and evaluate it on a range of benchmarks.

The Effect of Teaching Methods and Formal Reasoning Ability on Student Learning Outcomes

The purpose of this study is to examine the influence of teaching methods and formal reasoning abilities on students' learning outcomes. The research employs a quantitative research method and utilizes simple linear regression analysis with the assistance of SPSS version 16. Regression is a statistical technique used to analyze the relationship between one or more independent variables and a dependent variable. The population and sample size for this study consist of 50 students. The results of the research lead to the conclusion that the simple linear regression test yields a Sig. value of 0.001 < 0.05. Based on decision-making principles, it can be inferred that X1 and X2 have a simultaneous impact on the variable Y. Therefore, it can be concluded that both the teaching method (X1) and formal reasoning (X2) have an influence on the students' learning outcomes (Y). This finding further strengthens previous research findings by employing a better methodology and a larger sample size, demonstrating that formal reasoning affects learning outcomes, although there are still other factors that influence learning outcomes, such as motivation, environment, and so on.