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Focused Counterfactuals
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作者 Da Fan 《逻辑学研究》 2025年第3期67-95,共29页
It has long been noticed that focus is able to influence the truth-conditions of coun-terfactual conditionals.Namely,stressing different parts of a counterfactual leads to distinct interpretations.However,existing the... It has long been noticed that focus is able to influence the truth-conditions of coun-terfactual conditionals.Namely,stressing different parts of a counterfactual leads to distinct interpretations.However,existing theories,such as those by von Finte1 and Rooth,fail to ad-equately account for this phenomenon.In this paper,I exposit the drawbacks of these theories and then propose a novel account,ie.the Good Question-Answer(GQA)view.The GQA account posits that focus triggers question-answer pairs,and pragmatic pressures conceming the adequacy of such question answer pairs in contexts are able to affect the truth-conditions of counterfactuals.I also argue for the GQA account by appeal to its theoretical virtues. 展开更多
关键词 truth conditions counterfactualS focus different parts counterfactual good question answer view pragmatic pressures
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MMGCF: Generating Counterfactual Explanations for Molecular Property Prediction via Motif Rebuild
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作者 Xiuping Zhang Qun Liu Rui Han 《Journal of Computer and Communications》 2025年第1期152-168,共17页
Predicting molecular properties is essential for advancing for advancing drug discovery and design. Recently, Graph Neural Networks (GNNs) have gained prominence due to their ability to capture the complex structural ... Predicting molecular properties is essential for advancing for advancing drug discovery and design. Recently, Graph Neural Networks (GNNs) have gained prominence due to their ability to capture the complex structural and relational information inherent in molecular graphs. Despite their effectiveness, the “black-box” nature of GNNs remains a significant obstacle to their widespread adoption in chemistry, as it hinders interpretability and trust. In this context, several explanation methods based on factual reasoning have emerged. These methods aim to interpret the predictions made by GNNs by analyzing the key features contributing to the prediction. However, these approaches fail to answer critical questions: “How to ensure that the structure-property mapping learned by GNNs is consistent with established domain knowledge”. In this paper, we propose MMGCF, a novel counterfactual explanation framework designed specifically for the prediction of GNN-based molecular properties. MMGCF constructs a hierarchical tree structure on molecular motifs, enabling the systematic generation of counterfactuals through motif perturbations. This framework identifies causally significant motifs and elucidates their impact on model predictions, offering insights into the relationship between structural modifications and predicted properties. Our method demonstrates its effectiveness through comprehensive quantitative and qualitative evaluations of four real-world molecular datasets. 展开更多
关键词 INTERPRETABILITY Causal Relationship counterfactual Explanation Molecular Graph Generation
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What-If XAI Framework (WiXAI): From Counterfactuals towards Causal Understanding
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作者 Neelabh Kshetry Mehmed Kantardzic 《Journal of Computer and Communications》 2024年第6期169-198,共30页
People learn causal relations since childhood using counterfactual reasoning. Counterfactual reasoning uses counterfactual examples which take the form of “what if this has happened differently”. Counterfactual exam... People learn causal relations since childhood using counterfactual reasoning. Counterfactual reasoning uses counterfactual examples which take the form of “what if this has happened differently”. Counterfactual examples are also the basis of counterfactual explanation in explainable artificial intelligence (XAI). However, a framework that relies solely on optimization algorithms to find and present counterfactual samples cannot help users gain a deeper understanding of the system. Without a way to verify their understanding, the users can even be misled by such explanations. Such limitations can be overcome through an interactive and iterative framework that allows the users to explore their desired “what-if” scenarios. The purpose of our research is to develop such a framework. In this paper, we present our “what-if” XAI framework (WiXAI), which visualizes the artificial intelligence (AI) classification model from the perspective of the user’s sample and guides their “what-if” exploration. We also formulated how to use the WiXAI framework to generate counterfactuals and understand the feature-feature and feature-output relations in-depth for a local sample. These relations help move the users toward causal understanding. 展开更多
关键词 XAI AI WiXAI Causal Understanding counterfactualS counterfactual Explanation
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Embodied Meaning in Comprehending Abstract Chinese Counterfactuals
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作者 Xueyan LI Yahui ZHAO +1 位作者 Huili WANG Xue ZHANG 《Chinese Journal of Applied Linguistics》 2024年第3期414-432,524,共20页
Embodied cognition theories propose that language comprehension triggers a sensorimotor system in the brain.However,most previous research has paid much attention to concrete and factual sentences,and little emphasis ... Embodied cognition theories propose that language comprehension triggers a sensorimotor system in the brain.However,most previous research has paid much attention to concrete and factual sentences,and little emphasis has been put on the research of abstract and counterfactual sentences.The primary challenges for embodied theories lie in elucidating the meanings of abstract and counterfactual sentences.The most prevalent explanation is that abstract and counterfactual sentences are grounded in the activation of a sensorimotor system,in exactly the same way as concrete and factual ones.The present research employed a dual-task experimental paradigm to investigate whether the embodied meaning is activated in comprehending action-related abstract Chinese counterfactual sentences through the presence or absence of action-sentence compatibility effect(ACE).Participants were instructed to read and listen to the action-related abstract Chinese factual or counterfactual sentences describing an abstract transfer word towards or away from them,and then move their fingers towards or away from them to press the buttons in the same direction as the motion cue of the transfer verb.The action-sentence compatibility effect was observed in both abstract factual and counterfactual sentences,in line with the embodied cognition theories,which indicated that the embodied meanings were activated in both action-related abstract factuals and counterfactuals. 展开更多
关键词 action-sentence compatibility effect EMBODIMENT ABSTRACT counterfactualS language comprehension
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Security proof of counterfactual quantum cryptography against general intercept-resend attacks and its vulnerability 被引量:3
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作者 张盛 王剑 唐朝京 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第6期33-40,共8页
Counterfactual quantum cryptography, recently proposed by Noh, is featured with no transmission of signal parti- cles. This exhibits evident security advantages, such as its immunity to the well-known photon-number-sp... Counterfactual quantum cryptography, recently proposed by Noh, is featured with no transmission of signal parti- cles. This exhibits evident security advantages, such as its immunity to the well-known photon-number-splitting attack. In this paper, the theoretical security of counterfactual quantum cryptography protocol against the general intercept- resend attacks is proved by bounding the information of an eavesdropper Eve more tightly than in Yin's proposal [Phys. Rev. A 82 042335 (2010)]. It is also shown that practical counterfactual quantum cryptography implementations may be vulnerable when equipped with imperfect apparatuses, by proving that a negative key rate can be achieved when Eve launches a time-shift attack based on imperfect detector efficiency. 展开更多
关键词 quantum cryptography quantum counterfactuality quantum information
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Graph CA: Learning From Graph Counterfactual Augmentation for Knowledge Tracing
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作者 Xinhua Wang Shasha Zhao +3 位作者 Lei Guo Lei Zhu Chaoran Cui Liancheng Xu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第11期2108-2123,共16页
With the popularity of online learning in educational settings, knowledge tracing(KT) plays an increasingly significant role. The task of KT is to help students learn more effectively by predicting their next mastery ... With the popularity of online learning in educational settings, knowledge tracing(KT) plays an increasingly significant role. The task of KT is to help students learn more effectively by predicting their next mastery of knowledge based on their historical exercise sequences. Nowadays, many related works have emerged in this field, such as Bayesian knowledge tracing and deep knowledge tracing methods. Despite the progress that has been made in KT, existing techniques still have the following limitations: 1) Previous studies address KT by only exploring the observational sparsity data distribution, and the counterfactual data distribution has been largely ignored. 2) Current works designed for KT only consider either the entity relationships between questions and concepts, or the relations between two concepts, and none of them investigates the relations among students, questions, and concepts, simultaneously, leading to inaccurate student modeling. To address the above limitations,we propose a graph counterfactual augmentation method for knowledge tracing. Concretely, to consider the multiple relationships among different entities, we first uniform students, questions, and concepts in graphs, and then leverage a heterogeneous graph convolutional network to conduct representation learning.To model the counterfactual world, we conduct counterfactual transformations on students’ learning graphs by changing the corresponding treatments and then exploit the counterfactual outcomes in a contrastive learning framework. We conduct extensive experiments on three real-world datasets, and the experimental results demonstrate the superiority of our proposed Graph CA method compared with several state-of-the-art baselines. 展开更多
关键词 Contrastive learning counterfactual representation graph neural network knowledge tracing
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Quantum counterfactuality with identical particles
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作者 Vinod N Rao Anindita Banerjee R Srikanth 《Communications in Theoretical Physics》 SCIE CAS CSCD 2023年第6期59-65,共7页
Quantum self-interference enables the counterfactual transmission of information,whereby the transmitted bits involve no particles traveling through the channel.In this work,we show how counterfactuality can be realiz... Quantum self-interference enables the counterfactual transmission of information,whereby the transmitted bits involve no particles traveling through the channel.In this work,we show how counterfactuality can be realized even when the self-interference is replaced by interference between identical particles.Interestingly,the facet of indistinguishability called forth here is associated with first-order coherence,and is different from the usual notion of indistinguishability associated with the(anti-)commutation relations of mode operators.From an experimental perspective,the simplest implementation of the proposed idea can be realized by slight modifications to existing protocols for differential-phase-shift quantum key distribution or interaction-free measurement. 展开更多
关键词 quantum cryptography counterfactuality INDISTINGUISHABILITY
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Confounding of Three Binary-Variable Counterfactual Model with DAG
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作者 Jingwei Liu Shuang Hu 《Applied Mathematics》 2013年第10期1397-1404,共8页
Confounding of three binary-variable counterfactual model with directed acyclic graph (DAG) is discussed in this paper. According to the effect between the control variable and the covariate variable, we investigate t... Confounding of three binary-variable counterfactual model with directed acyclic graph (DAG) is discussed in this paper. According to the effect between the control variable and the covariate variable, we investigate three causal counterfactual models: the control variable is independent of the covariate variable, the control variable has the effect on the covariate variable and the covariate variable affects the control variable. Using the ancillary information based on conditional independence hypotheses and ignorability, the sufficient conditions to determine whether the covariate variable is an irrelevant factor or whether there is no confounding in each counterfactual model are obtained. 展开更多
关键词 CAUSAL Effect INDEPENDENCE Hypothesis counterfactual Model CONFOUNDING Bias Irrelevant Ancillary Information Directed ACYCLIC Graph
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Logical Difficulty from Combining Counterfactuals in the GHZ-Bell Theorems
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作者 Louis Sica 《Applied Mathematics》 2013年第10期90-94,共5页
In eliminating the fair sampling assumption, the Greenberger, Horne, Zeilinger (GHZ) theorem is believed to confirm Bell’s historic conclusion that local hidden variables are inconsistent with the results of quantum ... In eliminating the fair sampling assumption, the Greenberger, Horne, Zeilinger (GHZ) theorem is believed to confirm Bell’s historic conclusion that local hidden variables are inconsistent with the results of quantum mechanics. The GHZ theorem depends on predicting the results of sets of measurements of which only one may be performed. In the present paper, the noncommutative aspects of these unperformed measurements are critically examined. Classical examples and the logic of the GHZ construction are analyzed to demonstrate that combined counterfactual results of noncommuting operations are in general logically inconsistent with performed measurement sequences whose results depend on noncommutation. The Bell theorem is also revisited in the light of this result. It is concluded that negative conclusions regarding local hidden variables do not follow from the GHZ and Bell theorems as historically reasoned. 展开更多
关键词 HZ-Theorem Bell-Theorem Noncommutation counterfactual Hidden Variables LOCALITY NONLOCALITY
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The Effect of Counterfactual Thinking on the Sunk Cost Effect
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作者 YANG Fan-yu 《Psychology Research》 2019年第3期91-98,共8页
Counterfactual thinking is helpful to comprehend the mistakes made previously and to move toward by proposing future actions to facilitate the success of self-regulation.The sunk cost effect rationalizes a strategy,wh... Counterfactual thinking is helpful to comprehend the mistakes made previously and to move toward by proposing future actions to facilitate the success of self-regulation.The sunk cost effect rationalizes a strategy,which is the aim of studies on decision-making.However,few of them have discussed the influence of counterfactual thinking to the sunk cost effect.This study assumes that downward counterfactual thinking can regulate the unhappy mood at the moment for relief,which may reduce the sunk cost fallacy;upward counterfactual thinking,on the contrary,emphasizes the improvement of future behaviors,which may increase the sunk cost fallacy. 展开更多
关键词 counterfactual THINKING sunk COST EFFECT SELF-REGULATION
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Chinese Native Speakers' Counterfactuals Revisited
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作者 LIANG Zheng yu (Foreign Languages Departmen, Guilin University of Electronic Technology, Guilin 541004, China) 《广西师范大学学报(哲学社会科学版)》 2002年第S2期13-33,共21页
This paper examines whether or not Chinese native speakers (CNSs) have difficulties in understanding English counterfactuals, whether CNSs have counterfactual reasoning problems in their own language, what the causes ... This paper examines whether or not Chinese native speakers (CNSs) have difficulties in understanding English counterfactuals, whether CNSs have counterfactual reasoning problems in their own language, what the causes of these difficulties may be, and the problems in teaching English subjunctives. It also proposes on how to improve CNSs’ English counterfactual comprehension. 展开更多
关键词 Chinese native speakers counterfactualS COMPREHENSION
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Practical Stabilization of Counterfactual Quantum Cryptography
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作者 Musheng Jiang Shihai Sun Linmei Liang 《Journal of Quantum Information Science》 2011年第3期116-120,共5页
A novel counterfactual quantum key distribution scheme was proposed by T.-G. Noh and a strict security analysis has been given by Z.-Q.Yin, in which two legitimate geographical separated couples may share secret keys ... A novel counterfactual quantum key distribution scheme was proposed by T.-G. Noh and a strict security analysis has been given by Z.-Q.Yin, in which two legitimate geographical separated couples may share secret keys even when the key carriers are not traveled in the quantum channel. However, there are still plenty of practical details in this protocol that haven’t been discussed yet, which are of significant importance in physical implementation. In this paper, we will give a practical analysis on such kind of counterfactual quantum cryptography in the aspects of quantum bit error rate (QBER) and stabilization. Furthermore, modified schemes are proposed, which can obtain lower QBER and will be much more robust on stabilization in physical implementation. 展开更多
关键词 counterfactual QUANTUM CRYPTOGRAPHY QUANTUM BIT Error rate PRACTICAL STABILIZATION
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Counterfactual Learning on Graphs:A Survey
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作者 Zhimeng Guo Zongyu Wu +3 位作者 Teng Xiao Charu Aggarwal Hui Liu Suhang Wang 《Machine Intelligence Research》 2025年第1期17-59,共43页
Graph-structured data are pervasive in the real-world such as social networks,molecular graphs and transaction networks.Graph neural networks(GNNs)have achieved great success in representation learning on graphs,facil... Graph-structured data are pervasive in the real-world such as social networks,molecular graphs and transaction networks.Graph neural networks(GNNs)have achieved great success in representation learning on graphs,facilitating various downstream tasks.However,GNNs have several drawbacks such as lacking interpretability,can easily inherit the bias of data and cannot model casual rela-tions.Recently,counterfactual learning on graphs has shown promising results in alleviating these drawbacks.Various approaches have been proposed for counterfactual fairness,explainability,link prediction and other applications on graphs.To facilitate the develop-ment of this promising direction,in this survey,we categorize and comprehensively review papers on graph counterfactual learning.We divide existing methods into four categories based on problems studied.For each category,we provide background and motivating ex-amples,a general framework summarizing existing works and a detailed review of these works.We point out promising future research directions at the intersection of graph-structured data,counterfactual learning,and real-world applications.To offer a comprehensive view of resources for future studies,we compile a collection of open-source implementations,public datasets,and commonly-used evalu-ation metrics.This survey aims to serve as a“one-stop-shop”for building a unified understanding of graph counterfactual learning cat-egories and current resources. 展开更多
关键词 counterfactual learning graph-structured data graph neural networks FAIRNESS explainability
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Dynamical counterfactual inference under time-series model for waterflooding oilfield
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作者 Guoquan Wen Chao Min +1 位作者 Qingxia Zhang Guoyong Liao 《Petroleum》 2025年第1期113-124,共12页
The performances of numerical simulation and machine learning in production forecasting are severely dependent on precise geological modeling and high-quality history matching.To address these chal lenges,causal infer... The performances of numerical simulation and machine learning in production forecasting are severely dependent on precise geological modeling and high-quality history matching.To address these chal lenges,causal inference is an effective methodology since it can provide a causality for formalizing causality in history,not statistical dependence.In this paper,to dynamically predict oil production from causality existed in waterflooding oilfield,a dynamical counterfactual inference framework is built to predict oil production.The proposed framework can forecast the oil production under non-observation of engineering factors,i.e.,counterfactual,and provide the causal effect of engineering factors impacting on oil production.Meanwhile,combining with the practice exploitation in engineering factor impacting on production,a counterfactual experiment is designed to execute counterfactual prediction.Compared with general machine learning and statistical models,our results not only show better performance in oil production flooding but also guide the specific optimization in improving production,which holds more practical application significance. 展开更多
关键词 Waterflooding oilfield Single oil well counterfactual inference Time-series
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Analyses of Political Crisis Impact on Tourism:A Panel Counterfactual Approach with Internet Search Index
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作者 HUANG Bai SUN Yuying YANG Boyu 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2024年第4期1581-1603,共23页
Existing research has shown that political crisis events can directly impact the tourism industry.However,the current methods suffer from potential changes of unobserved variables,which poses challenges for a reliable... Existing research has shown that political crisis events can directly impact the tourism industry.However,the current methods suffer from potential changes of unobserved variables,which poses challenges for a reliable evaluation of the political crisis impacts.This paper proposes a panel counterfactual approach with Internet search index,which can quantitatively capture the change of crisis impacts across time and disentangle the effect of the event of interest from the rest.It also provides a tool to examine potential channels through which the crisis may affect tourist outflows.This research empirically applies the framework to analyze the THAAD event on tourist flows from the Chinese Mainland to South Korea.Findings highlight the strong and negative short-term impact of the political crisis on the tourists' intentions to visit a place.This paper provides essential evidence to help decision-makers improve the management of the tourism crisis. 展开更多
关键词 Composite search index counterfactual analysis political crisis search query data tourism demand
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Counterfactual discriminative micro-expression recognition
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作者 Yong Li Menglin Liu +2 位作者 Lingjie Lao Yuanzhi Wang Zhen Cui 《Visual Intelligence》 2024年第1期350-359,共10页
Micro-expressions are spontaneous,rapid and subtle facial movements that can hardly be suppressed or fabricated.Micro-expression recognition(MER)is one of the most challenging topics in affective computing.It aims to ... Micro-expressions are spontaneous,rapid and subtle facial movements that can hardly be suppressed or fabricated.Micro-expression recognition(MER)is one of the most challenging topics in affective computing.It aims to recognize subtle facial movements which are quite difficult for humans to perceive in a fleeting period.Recently,many deep learning-based MER methods have been developed.However,how to effectively capture subtle temporal variations for robust MER still perplexes us.We propose a counterfactual discriminative micro-expression recognition(CoDER)method to effectively learn the slight temporal variations for video-based MER.To explicitly capture the causality from temporal dynamics hidden in the micro-expression(ME)sequence,we propose ME counterfactual reasoning by comparing the effects of the facts w.r.t.original ME sequences and the counterfactuals w.r.t.counterfactually-revised ME sequences,and then perform causality-aware prediction to encourage the model to learn those latent ME temporal cues.Extensive experiments on four widely-used ME databases demonstrate the effectiveness of CoDER,which results in comparable and superior MER performance compared with that of the state-of-the-art methods.The visualization results show that CoDER successfully perceives the meaningful temporal variations in sequential faces. 展开更多
关键词 Affective computing Micro-expression recognition Temporal variation counterfactual reasoning Causal graph
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Nonreferential Uses of “I” and Its Perspectival Character
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作者 Minyao Huang 《逻辑学研究》 2025年第3期115-127,共13页
The English“T” is widely held as a well-behaved Kaplanian indexical that has a directly-referential content and a character which imples immunity to self misidentification.In this paper I present uses of“T”outside... The English“T” is widely held as a well-behaved Kaplanian indexical that has a directly-referential content and a character which imples immunity to self misidentification.In this paper I present uses of“T”outside attitudal contexts that are not directly referential yet exhibit immunity to self misidentification.They include uses of“I”for simulation and for counterfactual self portrait.I argue that they(i)challenge the non-shiftability and the rigidity arguments for the direct reference view,and(1)require a revision of the character of“T”to reflect the sensitivity of its content to the perspective from which the speaker identifies herself. 展开更多
关键词 Kaplanian indexical simulation counterfactual self portraiti perspectival character self misidentification counterfactual self portrait nonreferential uses
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Counterfactual Reasoning over Community Detection:A Case Study of the Public Science Day Community 被引量:1
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作者 Wenkang Jiang Hongbo He +2 位作者 Lei Lin Qirui Tang Runqiang Wang 《Journal of Social Computing》 EI 2023年第2期125-138,共14页
With the rapid rise of new media platforms such as Weibo and Tiktok,communities with science communication characteristics have progressively grown on social networks.These communities pursue essential objectives such... With the rapid rise of new media platforms such as Weibo and Tiktok,communities with science communication characteristics have progressively grown on social networks.These communities pursue essential objectives such as increased visibility and influence.For the success of the public understanding of science in China,case studies of science communication communities on social media are becoming increasingly valuable as a point of reference.The authenticity of user influence plays an important role in the analysis of the final outcome during the process of community detection.By integrating counterfactual reasoning theory into a community detection algorithm,we present a novel paradigm for eliminating influence bias in online communities.We consider the community of Public Science Day of the Chinese Academy of Sciences as a case study to demonstrate the validity of the proposed paradigm.In addition,we examine data on science communication activities,analyze the key elements of activity communication,and provide references for not only augmenting the communication impact of similar types of popular science activities but also advancing science communication in China.Our main finding is that the propagation channel for the science communication experiment exhibits multi-point scattered propagation and lacks a continuous chain in the process of propagation. 展开更多
关键词 causal inference counterfactual reasoning community detection science communication social networks
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Counterfactuals and Context-Sensitivity 被引量:1
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作者 SU Ching Hui 《Frontiers of Philosophy in China》 2015年第4期668-682,共15页
It is commonly agreed that when evaluating the validity of an argument involving context-sensitive expressions, the context should be held fixed. In their 2008 essay 'Counterfactuals and Context,' Brogaard and... It is commonly agreed that when evaluating the validity of an argument involving context-sensitive expressions, the context should be held fixed. In their 2008 essay 'Counterfactuals and Context,' Brogaard and Salerno argue further that context should be held fixed when evaluating an argument involving counterfactuals for validity, since, as many will agree, counterfactuals are context-sensitive. In the present paper, it will however be argued that Brogaard and Salerno fail to distinguish between two different roles that context plays in determining the meaning of a given counterfactual. If they were fully aware of the distinction between these two roles played by context, they might propose a contextualist approach to counterfactuals, as has been developed by Ichikawa in his 2011 paper 'Quantifiers, Knowledge, and Counterfactuals.' 展开更多
关键词 counterfactualS CONTEXT B. Brogaard J. Salerno R. Stalnaker J. Ichikawa
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Unveiling the impact and mechanism of digital technology on agricultural economic resilience 被引量:4
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作者 Tianshu Quan Hui Zhang +1 位作者 Tianli Quan Yi Yu 《Chinese Journal of Population,Resources and Environment》 2024年第2期136-145,共10页
Enhancing the economic resilience of agriculture is essential for promoting sustainable and high-quality agricultural development.The emergence of digital technology has created new opportunities in this field.However... Enhancing the economic resilience of agriculture is essential for promoting sustainable and high-quality agricultural development.The emergence of digital technology has created new opportunities in this field.However,existing research predominantly focuses on traditional agricultural factors and technologies.Therefore,the impact of digital technology on agricultural economic resilience within the broader context of the“production-operation-industry”system in agriculture has not been comprehensively explored.To bridge this gap,this study analyzes panel data from 30 Chinese provinces from 2011 to 2020.It employs the static Van Dorn’s law and a dynamic spatial panel model to examine how digital technology empowers agricultural resilience.The findings indicate a continuous strengthening of digital technology development in China,albeit with significant polarization and spatial imbalances.Moreover,the resilience of the agricultural economy undergoes notable fluctuations,initially narrowing and subsequently displaying an upward trend.Digital technology clearly plays a pivotal role in empowering resilience through agricultural scale operation,industrial transformation,and technological progress.Its impact,particularly on the promotion of resilience in the eastern region and non-grain-producing areas and on high-level agricultural economies,also shows regional and technological variations. 展开更多
关键词 Digital technology Agricultural economic resilience counterfactual method Dynamic spatial panel model Agricultural scale
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