Notion Of Logic Research Articles

Research on the Accuracy of Machine Learning-Based AI Grading Systems in Handling High School Math Function Problems: A Comparative Study of MathGPTPro and Zuoyebang

As artificial intelligence (AI) technology becomes more prevalent in education, AI automatic grading systems have emerged as essential tools for enhancing homework grading efficiency and alleviating teachers' workloads. The two leading platforms, Zuoyebang and MathGPTPro, are widely utilized in mathematics education. This study employs an experimental research method to compare the performance of these platforms in automatically grading function solution problems. The sample consists of 30 questions from the Function Solution Problems section of China's National College Entrance Examination. The focus will be on four key dimensions: logical steps, final answers, expression symbols, and analysis feedback to assess accuracy rates. A t-test will then examine differences in their handling of complex solution steps. The results show that MathGPTPro can achieve higher accuracy in complex reasoning, and its AI system has more potential to be applied to homework correction and math learning. However, there are still problems of inaccurate identification and wrong judgment in the process of Zuoyebang step recognition. This study offers insights into the application of AI automatic grading systems in education and suggests areas for system optimization.

A Study on Introducing Logical Symbols with Stories to Improve Critical Thinking with a Comparative Experiment

Critical thinking is becoming more and more important in modern society. Logical thinking is one of the core abilities of critical thinking. However, teaching logic to children faces some challenges especially when introducing logical symbols such as the implication symbol. Using stories to introduce logical symbols will address this problem and improve critical thinking.

Complementarity or substitution? The impact of the coexistence of corporate and independent venture capitalists on innovation in Chinese firms

ABSTRACT Research into corporate innovation generally focuses on the specific effects of corporate and independent venture capitalists (CVCs and IVCs). We explore whether CVCs and IVCs complement or substitute each other in innovative firms and how their interactions affect firm innovation, based on the notions of complementary assets and institutional logic. Using data from innovative firms listed in China, we find evidence of a complementary relationship between CVCs and IVCs and show that their coexistence significantly enhances firm innovation. Furthermore, our results show that the coexistence of government CVCs (GCVCs) and government IVCs (GIVCs) leads to better innovation performance, although their individual support also facilitates firm innovation. We also find that the coexistence of CVCs and IVCs contributes more to innovation in non-state-owned firms. Moreover, we find that their coexistence promotes firm innovation by mitigating agency problems. These findings contribute to a deeper understanding of the interactions between CVCs and IVCs.

Inferential-connexive mixed logics

Abstract In this article, we present a new type of connexive-like logics. We call them inferential-connexive mixed logics, as they satisfy inferential versions of the main four connexive principles: AT, AT’, BT and BT’. We focus first on some Strong-Kleene type of mixed and inferentially connexive logics that cannot be interpreted as truth-preserving, but that can receive other interpretations in terms to falsity-preservation and related features. We introduce afterwards the notion of inferential-connexive Boolean logic, and present some logics that fall in this ballpark. We also explain the relation between inferentially-connexive Boolean logics and some inferentially-connexive Strong-Kleene logics, and show how they can also be interpreted in epistemic (or attitudinal)-related terms.

Frege’s Begriffsschrift: On the Visual Basis of Logical Articulation and Understanding

One of Gottlob Frege’s most original contributions to logic and philosophy was his logical notation, his ‘Begriffsschrift’. While long criticized, dismissed, or simply ignored, the recent secondary literature contains some helpful re-evaluations and partial defenses of it. These rely largely on technical, pragmatic, or cognitive-psychological considerations. In this paper, we reconsider Frege’s own reasons for valuing his notation highly. We argue that there is a further semiotic dimension, one that matters epistemologically. This dimension becomes evident once one takes seriously, partly also literally, some striking visual metaphors Frege uses. The result is an interpretation highlighting a side of Frege’s position that is not widely known. It involves his views about the indispensable role that language, or sign systems more generally, play for human thought, and especially, for logic and mathematics. More particularly and as we read Frege, a good logical notation allows for expressing conceptual/inferential relations in a ‘visually inscribed’, thus ‘perspicuous’ way, and this leads to a special kind of ‘insight’ in mathematics. Or as we elaborate this point further, it involves a kind of articulation and understanding hardly possible without it. Frege designed his Begriffsschrift with that specific goal in mind.

Cognitive frailty in older adults: examining the impact of frailty criteria on neuropsychological profile, functional outcomes, activity levels, and quality of life.

Cognitive frailty (CF) is the co-existence of cognitive impairment and physical frailty without dementia, conferring greater risks of adverse clinical outcomes compared to either condition alone. However, the impact of physical frailty components on cognitive performance remains unclear. This study aims to evaluate CF by determining the neuropsychological profiles, functional outcomes, activity levels, and quality of life across the Fried Frailty Phenotype (FFP) and its components. Cross-sectional study involving 120 community-dwelling older adults without dementia, but with subjective cognitive complaints (SCC, defined as AD8 ≥ 1). Participants were stratified into three groups to assess CF: SCC-Robust, SCC-Prefrail, and SCC-Frail, and further categorized by individual FFP components. Cognitive performance was assessed by comparing neuropsychological test battery (NTB) Z-scores between CF and non-CF groups with Cohen's d for effect sizes. We performed linear regression to examine the relationships between both groups with NTB scores, Instrumental Activities of Daily Living (IADL), Frenchay Activities Index (FAI), and quality of life scores. NTB scores showed no differences between individuals with CF when classified according to FFP criteria. Individuals with SCC-slow gait speed exhibited reduced processing speed (d = 0.62) and memory (d = 0.61); SCC-fatigue was associated with decreased working memory (d = 0.55). Regression analyses, adjusted for demographic and clinical variables, identified significant associations: slow gait speed with logical memory (-0.42; 95% CI -0.79 to -0.038]) and symbol search (-0.28; 95% CI -0.56 to -0.006]); fatigue with digit span backwards (-0.66; 95% CI -1.19 to -0.14) and color trails 2 (-0.67; 95% CI, -1.15 to -0.20). SCC-slow gait speed and SCC-fatigue were associated with reduced quality of life scores, but not with IADL and FAI scores. Specific frailty components, notably slow gait speed and fatigue, influence cognitive function and quality of life. Our findings provide greater insights into characterizing CF. Further longitudinal studies are required to determine the cognitive and functional trajectories of CF.

Pompeiu-Hausdorff Fuzzy <i>b</i>-metric Spaces Are Associated with a Common Fixed Point and Multivalued Mappings

The notion of fuzzy logic was introduced by Zadeh. Unlike traditional logic theory, where an element either belongs to the set or does not, in fuzzy logic, the affiliation of the element to the set is expressed as a number from the interval [0, 1]. The study of the theory of fuzzy sets was prompted by the presence of uncertainty as an essential part of real-world problems, leading Zadeh to address the problem of indeterminacy. The theory of a fixed point in fuzzy metric spaces can be viewed in different ways, one of which involves the use of fuzzy logic. Fuzzy metric spaces, which are specific types of topological spaces with pleasing ”geometric” characteristics, possess a number of appealing properties and are commonly used in both pure and applied sciences. Metric spaces and their various generalizations frequently occur in computer science applications. For this reason, a new space called a Pompeiu-Hausdorff fuzzy <i>b</i>-metric space is constructed in this paper. In this space, some new fixed point results are also formulated and proven. Additionally, a general common fixed point theorem for a pair of multi-valued mappings in Pompeiu-Hausdorff fuzzy <i>b</i>-metric spaces is investigated. The findings obtained in fuzzy metric spaces, such as those discussed in Remark 3.1, are generalized by the results in this paper, and additional specific findings are produced and supported by examples. The study of denotational semantics and their applications in control theory using fuzzy <i>b</i>-metric spaces and Pompeiu-Hausdorff fuzzy <i>b</i>-metric spaces will be an important next step.

Aspects of a logical theory of assertion and inference

AbstractThe aim here is to investigate assertion and inference as notions of logic. Assertion will be explained in terms of its purpose, which is to give interlocutors the right to request the assertor to do a certain task. The assertion is correct if, and only if, the assertor knows how to do this task. Inference will be explained as an assertion equipped with what I shall call a justification profile, a strategy for making good on the assertion. The inference is valid if, and only if, correctness is preserved from the premiss assertions to the conclusion assertion. Most of this is a spelling out of views on assertion and inference presented by Per Martin‐Löf in lectures since 2015.

Design and Simulation of Balanced Ternary Priority Encoder

The priority encoder is a frequently used circuit in binary logic and is mostly used for interrupt handling and other priority resolving tasks. On the other hand, Ternary computing has tremendous potential for handling a wide variety of functions involving large range of numbers, whereas, the literature is confined to very basic functions. The proposed balanced priority encoder circuit that uses three logic symbols i.e.−1,0 and 1. In this study, we develop the design and architecture of a Ternary Priority Encoder circuit with an estimation of its time complexity. The intricacy of the circuit under consideration is supposed to highlight the capabilities of the ternary logic system. The flexibility of the circuit lies in its implementation using simple binary counterparts. As there is no simulator available for Ternary Logic, we have developed a Balanced Ternary Logic Simulator which is freely available from https://github.com/Aggtur11/Ternary-Logic-Simulator. The logic behaviour of the proposed priority encoder circuits is verified using the developed simulator.

Observing logics: revisiting reason in The Brothers Karamazov

AbstractVery often in frameworks for and presentations of The Brothers Karamazov, the modern reading public attempts to divide characters by their ability to reason. Usually Ivan is remembered for his reason, pitted against Dmitri’s passion. Adapting some terminology from mathematical logic, I propose and trace a different approach to reason in Dostoevsky’s text, to recast its canonical characters into alternative, though still fluid, categories. This exercise aims not to reinscribe or to reinterpret Dostoevsky’s novel but rather to reconsider an aspect of reasoning, specifically modes or forms of logic. With an admittedly imperfect mapping of characters onto these logical structures, this article encourages the ways in which we can trouble notions of stable reason and sound logic as they operate in the novel.

Bimorphisms and attribute implications in heterogeneous formal contexts

Formal concept analysis is a powerful mathematical framework based on mathematical logic and lattice theory for analyzing object-attribute relational systems. Over the decades, Formal concept analysis has evolved from its theoretical foundations into a versatile methodology applied across various disciplines. A heterogeneous formal context provides a feasible generalization of a formal context, enabling diverse truth-degrees of objects, attributes, and fuzzy relations. In our paper, we present extended theoretical results on heterogeneous formal contexts, including bimorphisms, Galois connections, and heterogeneous attribute implications. We recall the basic notions and properties of the heterogeneous formal context and its concept lattice. Moreover, we present extended results on bimorphisms and Galois connections in a heterogeneous formal context, including a self-contained proof of the main result. We include examples of introduced notions in heterogeneous formal contexts and two-valued logic. We propose the extension of attribute implications for heterogeneous formal contexts and explore their validity. By embracing heterogeneity in Formal concept analysis, we enrich its extended theoretical foundations and pave the way for innovative applications across diverse domains, including personal data protection and cybersecurity.

Reading indigenous signs: The wisdom of nagari communities toward natural disaster in Pasaman Barat

This study examines local wisdom regarding natural disasters of communities in traditional villages (nagari) in Pasaman Barat, Indonesia, through indigenous signs of disaster and interpretations. We analyze these signs through indigenous history and knowledge and a three-way communications framework of disaster interpretation in Indonesia. We collected data by conducting in-depth interviews with eight traditional figures and distributing questionnaires to 94 local residents in Pasaman Barat impacted by the 2022 earthquake through descriptive analysis. Our findings revealed that communities in Pasaman Barat have traditionally preserved indigenous knowledge about natural disasters, including architectural practices, logical and spiritual symbols, and a wide range of social mores and taboos. The people of the area improvised some valuable skills, such as the use of sandi tiang (the baseboard of a stilt) and bamboo barricades. Rituals and taboos associated with disasters include the tolak bala (warding-off ritual) and the banda larangan (forbidden fish), and distinctive signs of disaster observed by the community including the sounds of jirek (sacred grave), the appearance of tiger and uyia-uyia (forest beetles), and rivers flowing downstream during rain. These customs, mostly shared with Minangkabau customs despite some differences, are influenced by religious tradition, especially Sufistic tradition. Communities in Pasaman Barat continue to teach their children about these traditions, even as they adapt to modern life. Despite a dearth of established, traditional knowledge in this area, this study contributes to the future of disaster mitigation management by emphasizing rational and practical considerations in the face of natural disasters.

Herbrandized modified realizability

Realizability notions in mathematical logic have a long history, which can be traced back to the work of Stephen Kleene in the 1940s, aimed at exploring the foundations of intuitionistic logic. Kleene’s initial realizability laid the ground for more sophisticated notions such as Kreisel’s modified realizability and various modern approaches. In this context, our work aligns with the lineage of realizability strategies that emphasize the accumulation, rather than the propagation of precise witnesses. In this paper, we introduce a new notion of realizability, namely herbrandized modified realizability. This novel form of (cumulative) realizability, presented within the framework of semi-intuitionistic logic is based on a recently developed star combinatory calculus, which enables the gathering of witnesses into nonempty finite sets. We also show that the previous analysis can be extended from logic to (Heyting) arithmetic.

Characterising Context-Independent Quantifiers and Inferences

Abstract Context is essential in virtually all human activities. Yet some logical notions seem to be context-free. For example, the nature of the universal quantifier, the very meaning of “all”, seems to be independent of the context. At the same time, there are many quantifier expressions, and some are context-independent, while others are not. Similarly, purely logical consequence seems to be context-independent. Yet often we encounter strong inferences, good enough for practical purposes, but not valid. The two types of examples suggest a general problem: how to characterise the context-free logical concepts in their natural environment, that is, in the field of their context-dependent associates. A general Thesis on Quantifiers is formulated: among all quantifiers, the context-free ones are just those definable by the universal quantifier. The issue of inferences is treated following the approach introduced by Richard L. Epstein: valid ones are an extreme case, the result of the disappearance of context-dependence. This idea can be applied to an analysis of a form of abduction, called “reductive inference” in Polish literature on logic. A tentative Thesis on Inferences identifies the validity of a strong inference that is context-independent.

A Language-independent Quantitative Analysis Method on Conformance between Legal Contract and Smart Contract

The analysis on conformance between legal contracts and smart contracts is necessary and precondition for constructing the secure blockchain. Currently, the analysis method is the language-dependent single qualitative analysis. There doesn't exist quantitative metrics and quantitative analysis methods. Hence the quantitative metric and language-independent quantitative analysis method are proposed to analyze the conformance between legal contract and smart contract. First, the definitions and metrics of partial conformance and complete conformance are proposed, and then rewrite logic and language-independent symbol execution are used to construct a language-independent quantitative method; Then, the executable formal semantic for legal contract description language Business Process Model and Notation2.0 (BPMN2.0) is presented. Finally, the conformance of the five main methods for mapping BPMN2.0 legal contracts to Solidity smart contracts is analyzed. The results show that three methods have partial conformance, one method has complete conformance, and one method hasn't complete conformance and partial conformance.

Generating Novel Leads for Drug Discovery Using LLMs with Logical Feedback

Large Language Models (LLMs) can be used as repositories of biological and chemical information to generate pharmacological lead compounds. However, for LLMs to focus on specific drug targets typically requires experimentation with progressively more refined prompts. Results thus become dependent not just on what is known about the target, but also on what is known about the prompt- engineering. In this paper, we separate the prompt into domain-constraints that can be written in a standard logical form and a simple text-based query. We investigate whether LLMs can be guided, not by refining prompts manually, but by refining the logical component automatically, keeping the query unchanged. We describe an iterative procedure LMLF (“Language Model with Logical Feedback”) in which the constraints are progressively refined using a logical notion of generalisation. On any iteration, newly generated instances are verified against the constraint, providing "logical-feedback" for the next iteration's refinement of the constraints. We evaluate LMLF using two well-known targets (inhibition of the Janus Kinase 2; and Dopamine Receptor D2); and two different LLMs (GPT-3 and PaLM). We show that LMLF, starting with the same logical constraints and query text, can be used to guide both LLMs to generate potential leads. We find: (a) Binding affinities of LMLF-generated molecules are skewed towards higher binding affinities than those from existing baselines; (b) LMLF results in generating molecules that are skewed towards higher binding affinities than without logical feedback; (c) Assessment by a computational chemist suggests that LMLF generated compounds may be novel inhibitors. These findings suggest that LLMs with logical feedback may provide a mechanism for generating new leads without requiring the domain-specialist to acquire sophisticated skills in prompt-engineering.

Introduction. Logic and Politics

The aim of this special issue is to explore the intersections of logic, intended as the formal science of valid consequence, and politics, the practical science of associated life. The analyses here provided deal with the theme in two ways: by considering what logic can do for politics, so proposing possible formalizations of political arguments, or using logical notions and tools to interpret political facts and problems; by considering what politics can do for logic, so examining how logical choices are and have been affected or determined by extra-logical facts of political relevance. The two perspectives outline a territory of inquiry that is not so much frequented, in political and logical literature, but is becoming more and more interesting nowadays.

Concerning Multivariate Bernstein Polynomials and Stochastic Logic

Among the applications of the Bernstein polynomials in one variable is their use in solving problems associated with stochastic computing. Taking as a starting point the notion of stochastic logic in the sense of Qian-Riedel-Rosenberg, the aim of this paper is to investigate some necessary and sufficient conditions for guaranteeing whether polynomial operations can be implemented with stochastic logic based on multivariate Bernstein polynomials with coefficients in the unit interval.

Aspects of Indigenous Participation in Brazilian Literature

The article both presents how, from the end of the 1980s onwards, native peoples have begun to occupy certain spaces of textual production and circulation that they had not previously occupied in the Brazilian cultural scene (for social, linguistic, and cultural reasons, but also political and juridical) and discusses how this process has provoked a vigorous movement of dilation of traditional textual and discursive borders in Western culture. Texts deriving from indigenous peoples in the sphere of academic discourse are, in general, bilingual, and are structured in ways that combine aspects of intellectual production with those of artistic creation. Moreover, they are also structured around a rather complex conception of the notion of authorship (considering that they are written by an author but represent the voice of their people). As examples, the article analyzes the case of Os cantos tradicionais Ye’kwana [Traditional Ye’kwana Chants], by the indigenous teacher and researcher Fernando Ye’kwana Gimenes, winner of the 2020/2021 edition of the Dirce Cortes Riedel Masters Dissertation Award by the Brazilian Association of Comparative Literature, as a typical example of the cultural phenomenon discussed. The traditional Ye’kwana chants present significant transgressions in relation to the traditional notions of narrative logic and the dominant forms of narration in the fields of literature and history. The awarding of this academic prize to an indigenous inhabitant of the forest, on the border between Brazil and Venezuela, by the largest association of comparative literature in Latin America, in addition to being an important act in political terms, demonstrates how urgent it is to rethink processes of global literary dissemination beyond the restricted frameworks configured by the logic of hegemonic cultures, which are based on closed divisions and hierarchies. With this, we intend to contribute to the process of including Amerindian texts in the repertoire of Comparative Literature and World Literature.

Mixed inference machine reading comprehension method based on symbolic logic

With the rapid development of machine learning, challenging question and answer datasets have also emerged, and the machine reading comprehension technology has emerged. Traditional machine reading comprehension methods mostly focus on the understanding word level semantics, with the weak ability to extract logical relationships from text, resulting in the lower ability of logical reasoning. In order to strengthen the ability of machine reading comprehension method to extract the logical relationship of text and the ability of logical reasoning, a neural symbol model based on logical reasoning was proposed, and the logical expressions captured by the neural symbol model were converted into text input and trained in a mixed reasoning reading comprehension model based on symbolic logic. The mixed reasoning reading comprehension model based on symbolic logic is different from the traditional machine reading comprehension model. It uses symbolic definition and logical capture to extract logical symbols and generate logical expressions. The research results show that the accuracy and F-measure values of the neural symbol model based on the logical reasoning are 70.08% and 70.05%, respectively, when the training set sample size is 4000. The accuracy of the mixed reasoning reading comprehension model based on symbolic logic in the logical reasoning data set of the standard postgraduate entrance examination is 88.31%, which is higher than the 58.74% of the language perception map network model. The accuracy rate in the four-choice and one-choice question-and-answer data set is 40.92%, which is 1.58% higher than that of the language awareness graph network model. In summary, the neural symbol model and hybrid inference reading comprehension model proposed in the study have superior performance, which can capture the logical relationship of text in data sets well, improve the model feature abstraction and reasoning ability, effectively shorten the training time and improve the model efficiency.