Logical Problems Research Articles

ŞAGİRDLƏRİN RİYAZİ NİTQİNİ İNKİŞAF ETDİRİLMƏSİNDƏ İNKİŞAFETDİRİCİ ÇALIŞMALARDAN İSTİFADƏ YOLLARI

Man must acquire certain necessary knowledge, skills and habits to get what he needs from nature. For this purpose, the concepts of school, education and training were created and the content and tasks of each of them were defined. Developmental studies in mathematics mean the following: when solving these problems, the student must observe, compare, draw independent conclusions, find possible solutions, justify his opinion, and discover certain regularities. There are many opportunities to develop students' speech in the process of solving games, fun, interesting, logical problems in the mathematics education of primary classes. In the article, the ways of using developmental studies in the development of mathematical speech in mathematics education are widely investigated.

Fuzzy Linear Temporal Logic with Quality Constraints

As an extension of quantitative temporal logic, uncertain temporal logic essentially describes the temporal behavior of uncertain and incomplete systems, thus better solving search and decision-making problems in such systems. Fuzzy linear temporal logic (FLTL) is a focal point in uncertain temporal logic research. However, there are evident shortcomings in the current research outcomes. First, in previous FLTL studies, the practice of obtaining path reachability and formula satisfaction values independently and subsequently selecting the smaller of the two as the satisfaction value metric led to information loss. Furthermore, this simplistic information fusion approach fails to reflect the varying importance of these two types of information to the requirements. Second, computing path reachability and temporal logic formula satisfaction values separately may result in a mismatch between the two pieces of information with respect to the same path segment. Thus, the primary challenge lies in accurately integrating the satisfaction values of temporal logic formulas with the path reachability of the segments that yields these satisfaction values, utilizing various reasonable information synthesis methods, to ensure synchronization between path reachability and formula satisfaction values without incurring information loss. Additionally, it is crucial to reflect the different preference requirements for these two types of information. Moreover, the temporal logic formula characterizes system properties, with its sub-formulas delineating distinct sub-properties. Consequently, considering the varying importance preferences of sub-formulas is also significant. To address these deficiencies, we introduced quality constraint operators into FLTL, resulting in quality-constrained fuzzy linear temporal logic (QFLTL). This incorporation enables the synchronization and comprehensive fusion of path-reachability information and formula satisfaction values within the final semantic metric, thereby resolving the issues related to information synchronization and loss. Furthermore, it can accommodate the differing preference requirements between the two types of information and sub-properties during the information synthesis process. We defined the syntax and semantics of QFLTL and examined its expressive power and properties. Notably, we investigated the decidability of logical decision problems in QFLTL, encompassing validity, satisfiability, and model-checking issues. We proposed corresponding solution algorithms and analyzed their complexities.

On increase of land tax in Kazakhstan

Land tax is one of the sources of formation of local budgets, filling their revenue part. The aim is to analyze the legal framework of the existing system of land taxation, to substantiate the need to increase mandatory payments for land. The following methods were used - monographic - to study the foreign experience of land taxation, statistical - to collect data on tax revenues, the state of the land fund, analytical - in the study of methods of tax payment, on the basis of abstract-logical method problems were identified and ways of their solution were proposed. Results - foreign experience of tax regulation has shown that fiscal policy is aimed at creating favorable preferential conditions for agricultural producers and improving soil quality. The existing domestic methodology of tax payments depending on the purposes of application is considered. The analysis of tax payments in dynamics for 7 years is presented. Land tax rates and rent in the context of target use are calculated. It is revealed that the tax for peasant (farm) farms in accordance with the income from the sale of agricultural products is not quite acceptable, as the costs of its production are not taken into account. Conclusions - it is established that a 40-fold increase in the land tax is premature, since to date such a measure is legislatively approved in the amount of 20-fold. It is recommended to increase the tax burden on residential lands for individual residential construction, shopping and entertainment centers and industrial facilities. Involvement in agricultural turnover of 62.5 million hectares of pastures, concentrated in the category of reserve lands, will make it possible to improve their quality level and receive additional money for the state budget.

Trial selection criteria should not be used for clinical decisions and recommendations: the thrombectomy trials example

BackgroundDespite multiple calls for more inclusive studies, most clinical trial eligibility criteria remain too restrictive. Thrombectomy trials have been no exception. MethodsWe review the landmark trials that have shown the benefits of thrombectomy, their eligibility criteria, and consequences on clinical practice. We discuss the rationale behind various reasons for exclusions. We also examine the logical problem involved in using eligibility criteria as indications for treatment. ResultsMost thrombectomy trials have been too restrictive. This has been shown by a plethora of follow-up studies that have refuted most of the previously recommended trial eligibility restrictions. Meanwhile, the effect of clinical recommendations based on restrictive eligibility criteria is that treatment has been denied to the majority of patients who could have benefitted. Trial eligibility criteria cannot be used to make clinical decisions or recommendations unless, like any other medical diagnosis, they have been shown capable of reliably differentiating patients into those that will, and those that will not benefit from treatment. This goal can only be achieved with all-inclusive pragmatic trials. ConclusionRestrictive eligibility criteria render clinical trials incapable of guiding medical decisions or recommendations.

Divine Contradiction: some snippets

Abstract Two doctrines (or axioms) of christian theology sharply distinguish christian monotheism from its traditional monotheistic siblings (viz. jewish and islamic monotheism): the incarnation of God and the triunity of God. Both doctrines, as many have long observed, face a conspicuous so-called logical problem – namely, apparent contradiction. How should the strong appearance of such fundamental contradiction be explained? Beall's answer: the incarnation and trinity appear to be contradictory because God is a contradictory being – a being of whom some contradictions are true. The full truth of God is expressed only via contradiction, which is why the fundamental axioms of christian theology have long appeared to be contradictory. Divine Contradiction presents the target contradictory account of the trinity; its predecessor The Contradictory Christ presents the contradictory account of the incarnation.

The Construction of “Mental Models”: Its Essence and Use in Various Fields of Psychology

Introduction. Mental models are a scientific psychological construct, which means that people create models of the external world in their minds and operate them to plan their activities. Today, mental models have found application in various fields: explaining the principles of human thinking and solving logical problems, creating models about time, sets, causes and effects, as well as in the field of learning, social relations, teamwork. However, in Russian, the subject of the study of mental models is practically not presented.Purpose. To examine works devoted to the study of mental models in various fields of psychology.Mental models in the field of thinking process research. A leading expert in the field of human thinking mechanisms P. N. Johnson-Laird put forward and substantiated idea, that in the process of reasoning, people actively create mental models that accompany logical operations and can influence them. Mental models are iconic, reflecting the meaning of objects of the external world, are deployed in a sequence corresponding to external events, and reflect external operations schematically.Mental models in learning. Mental models can be useful tools for constructing the educational process. Understanding and competent use of the natural mechanisms of the psyche of students can improve the process of modeling their knowledge of the world around them.Mental models in socio-psychological processes. The interaction of an individual with other people generates the process of forming their reflections in the internal space, creating models of behavior and possible reactions of others. In team interaction, an important factor in the effectiveness and viability of the team is the presence of common (team) mental models.Discussion. The use of the concept of mental models in various fields and a large number of conceptual and empirical works on this topic may indicate the universality of the phenomenon of models. Mental models as an explanatory principle are built into existing theories and enrich them.

The Holy Spirit as “the Gift” in Charles Nyamiti's Trinitarian Theology: A Pentecostal-Lutheran Dialogical Perspective

This article starts from the theology of the Tanzanian-born Charles Nyamiti (1931–2020), as one of the most creative in his generation of African theologians. Nyamiti proposed that ancestral veneration is a foundational human relationship which reflects divine realities. Thus, he proposed an understanding of the Trinity where the Father is the Ancestor, the Son is the Descendant, and the Holy Spirit is the mutual Oblation connecting the two. Because an ancestor does not exist as an ancestor without sacred ritual communication, the Holy Spirit becomes thus absolutely necessary for the Godhead. We maintain that Nyamiti's ancestral approach describes an African logic of gift-giving. Translating his theological contribution into gift-language preserves the theological insights while solving some of the logical problems with the ancestral imaginary, such as how the Father who never died is supposed to be the Ancestor. Through gift-language, Nyamiti's theological insights, which are based on African relational ontologies, become more readily applicable in World Christianity and have potential to transform ecumenism into a vibrant and inclusive embodied pneumatic action for abundant life. In other words, Nyamiti's theological heritage invites theologians to envision Christian faith beyond the confines of Hellenistic-based philosophy.

The Power Dynamical Dissolution of the Logical Problem of Evil and a Foundational “Substance” for Metaethics

Abstract This paper aims to show that the traditional problem of evil can be logically dissolved by a more thorough analysis of what love (Agape, Eros, Philia) and evil actually are. When investigated this analysis reveals that they are manifestations and evaluations of power dynamical relations leading to a conclusion that it would be logically impossible for God to be all-loving and at the same time prevent evil as all-loving constitutes an unlimited, unjudgmental, empowerment and good and evil are simply evaluations or perspectives on that power use. To stop evil God would have to disempower in some way and that would not be Agape and thus logically impossible as Agape is part of the very nature of God. This paper reveals the “form” of good to be empowerment and the “form” of bad/evil to be disempowerment.

Problems Of Many-Valued Logic from The Point of View of The Theory of Socio-Cultural Code

It is shown that there are prerequisites for returning to the original interpretation of logic as the science of the laws of thought. Using the methods of the neural network theory of the noosphere, it is proved that the nature of thinking is significantly influenced by the socio-cultural code of the ethnic/social system. A connection is revealed between philosophical categories as basic undefined concepts and archetypes, understood according to Jung. It is proved that the formalization of the laws of thinking, built on multi-valued logic, should operate not only and not so much with the concepts of natural language, but with “reflection quanta” lying on the archetypal level of consciousness. It is shown that the category of truth underlying classical logic can also be interpreted as a “reflection quantum”, but which has undergone a formalization procedure. It is demonstrated how exactly the apparatus of multi-valued logic can be applied to identifying links between the "quanta of reflection", which can be considered as a generalization of the rules of reasoning established in classical logic, dating back to Aristotle. The category “Qi”, which underlies ancient Chinese philosophy and is inseparable from the Chinese sociocultural code, was used as an example. Meaning of this category in the version that is assimilated by European and Eurasian sociocultural codes is revealed.

Quantum temporal logic and reachability problems of matrix semigroups

We study the reachability problems of a quantum finite automaton. More precisely, we introduce quantum temporal logic (QTL) that specifies the time-dependent behavior of quantum finite automaton by presenting the time dependence of events temporal operators ◊ (eventually) and □ (always) and employing the projections on subspaces as atomic propositions. The satisfiability of QTL formulae corresponds to various reachability problems of matrix semigroups. We prove that the satisfiability problems for □∨impi, ◊□∨impi and □◊∨impi with atomic propositions pi are decidable. This result solves the open problem of Li and Ying 2014. Notably, the decidability of □◊p can be interpreted as a generalization of Skolem-Mahler-Lech's celebrated theorem based on additive number theory. This paper's last part shows how the quantum finite automaton can model the general concurrent quantum programs, which may involve an arbitrary classical control flow.

Варианты взаимосогласования индивидов со сходными и различающимися психологическими характеристиками

<p>The article considers the problem of coordination of individual experience in the situation when individuals achieve a collective result. In terms of the system-evolutionary approach, such coordination is described as mutual-co-operation. The aim of the study was to evaluate possible variants of individual experience coordination in the conditions of joint solution of textual tasks (in dyads). Analytical logical ("Knights and Liars", "Grid-logic") and holistic ("Anagrams", "Moral Judgements") textual problems were used. Two criteria for distinguishing dyads were tested: 1. "Analytic-Holistic" of individuals and 2. "Groups representing different ways of solving". It was hypothesized that if individuals had different psychological characteristics ("analytic-holistic"), they would be more effective on both analytic and holistic tasks due to inter-individual complementarity, and if they were similar ("analytic-analytic" or "holistic-holistic"), they would be more effective on either analytic or holistic tasks. Although the relationship of performance with complementarity in problem solving according to the criterion "Analytic-Holistic" was found, the relationship with complementarity according to the criterion "Groups representing different ways of solving" turned out to be more pronounced. The belonging of individuals in the dyad to groups similar in the ways of problem solving may contribute to the mentioned performance to a greater extent. Thus, complementarity can be both for different and similar characteristics, which is consistent with the position on the necessity of mutual co-interaction of the degrees of freedom of individuals to achieve a collective result.</p>

G. H. von Wright on Logical Empiricism

Georg Henrik von Wright (1916–2003) started his studies in theoretical philosophy at the University of Helsinki in 1934. His teacher, Professor Eino Kaila (1890–1958), was an associate of the Vienna Circle who had changed the course of Finnish philosophy with his own version of logical empiricism. Under Kaila’s supervision, von Wright wrote his early studies on probability and defended his doctoral thesis The Logical Problem of Induction in 1941. Von Wright met Ludwig Wittgenstein in Cambridge in 1939 and 1947 and eventually became his successor there in 1948–1951. Later, von Wright characterized these two philosophers as his “father figures”: “Kaila had turned me into a logical positivist or empiricist. Wittgenstein, on the other hand, thoroughly eradicated this personality of mine.” This article studies von Wright’s changing relation to logical empiricism. The main sources include his correspondence with Kaila in 1937–1958 and his books Den logiska empirismen (in Swedish in 1943; in Finnish in 1945) and Logik, filosofi och språk (in Swedish in 1957, in Finnish in 1958). In his “Intellectual Autobiography” (1989), von Wright described the former book as “a farewell to the philosophy of my student years”. Wittgenstein’s influence can be seen in von Wright’s denial of the unity of science and his cool cultural pessimism as expressed in his critical essays. But it is also evident that logic and exact thinking continued to be central tools and ingredients of his subsequent and highly appreciated work as an analytic philosopher.

Code-Aware Prompting: A Study of Coverage-Guided Test Generation in Regression Setting using LLM

Testing plays a pivotal role in ensuring software quality, yet conventional Search Based Software Testing (SBST) methods often struggle with complex software units, achieving suboptimal test coverage. Recent work using large language models (LLMs) for test generation have focused on improving generation quality through optimizing the test generation context and correcting errors in model outputs, but use fixed prompting strategies that prompt the model to generate tests without additional guidance. As a result LLM-generated testsuites still suffer from low coverage. In this paper, we present SymPrompt, a code-aware prompting strategy for LLMs in test generation. SymPrompt’s approach is based on recent work that demonstrates LLMs can solve more complex logical problems when prompted to reason about the problem in a multi-step fashion. We apply this methodology to test generation by deconstructing the testsuite generation process into a multi-stage sequence, each of which is driven by a specific prompt aligned with the execution paths of the method under test, and exposing relevant type and dependency focal context to the model. Our approach enables pretrained LLMs to generate more complete test cases without any additional training. We implement SymPrompt using the TreeSitter parsing framework and evaluate on a benchmark challenging methods from open source Python projects. SymPrompt enhances correct test generations by a factor of 5 and bolsters relative coverage by 26% for CodeGen2. Notably, when applied to GPT-4, SymPrompt improves coverage by over 2x compared to baseline prompting strategies.

Enhancing Brain Elasticity: Key Lifestyle Habits to Unlock Genius Potential at Any Age

The brain is a masterpiece, often referred to as the king organ, as it governs the entire body. When the brain ceases to function, it marks the end of an individual's vitality, essentially rendering them a "vegetable." This profound importance raises a crucial question: Are we adequately nurturing and caring for our brains? In today's fast-paced world, humans often subject their brains to relentless stress and negative impulses, leading to cognitive decline. However, enhancing brain elasticity can be remarkably simple by adopting specific daily habits. These habits not only pamper the brain but also make it sharper and stronger. Key factors in boosting brain capacity include maintaining optimal hydration, engaging in IQ-enhancing non-digital games like chess and Scrabble, solving logical math problems, regular exercise, and meditation. Additionally, incorporating fruits and vegetables into the diet, consuming foods rich in Omega-3 and DHA, ensuring 8 hours of sleep, reducing screen time, learning new languages, playing various musical instruments, and fostering a positive and resilient mindset are vital. One crucial yet often overlooked habit is regular reading. Reading stimulates the brain, improves concentration, enhances vocabulary, and fosters a deeper understanding of diverse subjects, all of which contribute to increased cognitive flexibility and brain elasticity. Another important factor is maintaining good gut health. Recent research has shown that good gut bacteria play a crucial role in increasing brain activity. The gut-brain axis, a complex communication network, connects the gut and brain, allowing gut bacteria to influence cognitive functions. Probiotics and a diet rich in fiber can enhance the diversity and health of gut microbiota, leading to improved brain function and mental health. This review explores how these lifestyle practices contribute to cognitive enhancement, potentially transforming ordinary individuals into geniuses. It posits that genius is not an inherent trait but a result of deliberate and consistent mental engagement and nurturing. By embracing these strategies, including the habit of regular reading and maintaining good gut health, individuals can significantly elevate their cognitive abilities and achieve exceptional intellectual growth.

Defying gravity and gadget numerosity: The complexity of the Hanano Puzzle and beyond

Using the notion of visibility representations, our paper establishes a new property of instances of the Nondeterministic Constraint Logic (NCL) problem (a PSPACE-complete problem that is very convenient to prove the PSPACE-hardness of reversible games with pushing blocks). Direct use of this property introduces an explosion in the number of gadgets needed to show PSPACE-hardness, but we show how to bring that number from 32 down to only three in the general case, and down to two in our specific case! We propose it as a step towards a broader and more general framework for studying games with irreversible gravity, and use this connection to guide an indirect polynomial-time many-one reduction from the NCL problem to the Hanano Puzzle—which is NP-hard—to prove it is PSPACE-complete.

Identifying the use of artificial intelligence in math learning based on learning outcomes

In an era of rapidly developing technology, the need to simplify and improve the learning process of mathematics is increasingly urgent. One emerging solution is the utilization of Artificial Intelligence (AI) in mathematics education. AI provides learning content that is tailored to students' needs, creating a relevant and engaging learning experience. An understanding of AI and the ability to interact with technology is important, helping students face the challenges of the digital age. Understanding math concepts is the foundation for logical thinking, problem solving and critical thinking. Research shows that some students do not fully understand mathematical concepts. Therefore, this study aims to identify the impact of using AI in mathematics learning on student learning outcomes. The preliminary study data showed the prevalence of AI use in mathematics learning. The results show a very strong positive correlation between the use of AI and mathematics learning outcomes, where student learning activities observed during learning using AI (Artificial Intelligence) based on observation sheets include several indicators, with the following results: 1) Visual indicators of 88%, 2) Listening indicators of 84%, 3) Oral indicators of 72.5%, and 4) Mental indicators of 84.5%. The results showed that learning activities were in the high category with a percentage of 82.25%. This shows that during learning activities, there is a good stimulus for students.

Language models, like humans, show content effects on reasoning tasks.

reasoning is a key ability for an intelligent system. Large language models (LMs) achieve above-chance performance on abstract reasoning tasks but exhibit many imperfections. However, human abstract reasoning is also imperfect. Human reasoning is affected by our real-world knowledge and beliefs, and shows notable "content effects"; humans reason more reliably when the semantic content of a problem supports the correct logical inferences. These content-entangled reasoning patterns are central to debates about the fundamental nature of human intelligence. Here, we investigate whether language models-whose prior expectations capture some aspects of human knowledge-similarly mix content into their answers to logic problems. We explored this question across three logical reasoning tasks: natural language inference, judging the logical validity of syllogisms, and the Wason selection task. We evaluate state of the art LMs, as well as humans, and find that the LMs reflect many of the same qualitative human patterns on these tasks-like humans, models answer more accurately when the semantic content of a task supports the logical inferences. These parallels are reflected in accuracy patterns, and in some lower-level features like the relationship between LM confidence over possible answers and human response times. However, in some cases the humans and models behave differently-particularly on the Wason task, where humans perform much worse than large models, and exhibit a distinct error pattern. Our findings have implications for understanding possible contributors to these human cognitive effects, as well as the factors that influence language model performance.

El Cid: Can an Aesthetics Lens Save Transformational Leadership from Itself?

Countless articles and books have been written about transformational leadership theory since the late 1970s when it first appeared in the literature. The purpose of this conceptual paper is to illustrate that transformational leadership contains both logical and psychological problems when explaining the nature of leadership and as an empirically supportable and verifiable construct. It aims to show that its failure to garner evidence from a scientific methodological analysis may not invalidate its efficacy if it is viewed from an alternative lens, such as aesthetics. An aesthetic frame is one that recognizes sensuous ways of knowing since feelings and emotions are just as important as reason and logic. An aesthetic approach to leadership would see leadership as more of an art than a science. This paper is not arguing for the abandonment of transformational leadership theory; rather it is saying that an aesthetic lens is likely to yield a richer, more artistic, and more nuanced account of what is understood and enacted as transformational leadership. This way, the manifestations of transformational leadership may live on in the arts and continue to inspire and motivate us.

Logical thinking skills and problem solving skills of the Grade 12 STEM students of University of Northern Philippines: A basis for extension plan

Logical thinking skills and problem solving skills of the Grade 12 STEM students of University of Northern Philippines: A basis for extension plan

Initial state‐dependent implementation of logic gates with memristive neurons

AbstractThis study introduces a simple memristor cellular neural network structure, a minimalist configuration with only two cells, designed to concurrently address two logic problems. The unique attribute of this system lies in its adaptability, where the nature of the implemented logic gate, be it AND, OR, and XOR, is determined exclusively by the initial states of the memristors. The memristors' state, alterable through current flow, allows for dynamic manipulation, enabling the setting of initial conditions and consequently, a change in the circuit's functionality. To optimize the parameters of this dynamic system, contemporary machine learning techniques are employed, specifically gradient descent optimization. Through a case study, the potential of leveraging intricate circuit dynamics is exemplified to expand the spectrum of problems solvable with a defined number of neurons. This work not only underscores the significance of adaptability in logical circuits but also demonstrates the efficacy of memristive elements in enhancing problem‐solving capabilities.