In Christianity,the passion and resurrection of Jesus Christ are a fact of history.If his resurrection is a miracle to be accepted by faith,no rational demonstration of it is needed,although the Apostle Paul argues by...In Christianity,the passion and resurrection of Jesus Christ are a fact of history.If his resurrection is a miracle to be accepted by faith,no rational demonstration of it is needed,although the Apostle Paul argues by analogy for the resurrection in 1 Corinthians.Being a realist and using Latin,Aquinas holds that human reason can contribute to an understanding of faith;he has no strict distinction between hades and hell.He uses logos to emphasize reason and instrumental causality in explaining the relationship between humanity and divinity for Jesus.Arguing for the resurrection of Jesus,Aquinas should be consistent with his principle of the individualization of a soul through a body,and a separate soul being a substance,but he is inconsistent.Considering Jesus’soul before his resurrection,Aquinas supports the Apostles’Creed,but he develops the notion of purgatory,where departed souls sojourn temporarily.This paper argues that Aquinas,in discussing the passion and resurrection of Jesus Christ,obscures the distinction he draws between faith and reason.展开更多
The cross-modal person re-identification task aims to match visible and infrared images of the same individual.The main challenges in this field arise from significant modality differences between individuals and the ...The cross-modal person re-identification task aims to match visible and infrared images of the same individual.The main challenges in this field arise from significant modality differences between individuals and the lack of high-quality cross-modal correspondence methods.Existing approaches often attempt to establish modality correspondence by extracting shared features across different modalities.However,these methods tend to focus on local information extraction and fail to fully leverage the global identity information in the cross-modal features,resulting in limited correspondence accuracy and suboptimal matching performance.To address this issue,we propose a quadratic graph matching method designed to overcome the challenges posed by modality differences through precise cross-modal relationship alignment.This method transforms the cross-modal correspondence problem into a graph matching task and minimizes the matching cost using a center search mechanism.Building on this approach,we further design a block reasoning module to uncover latent relationships between person identities and optimize the modality correspondence results.The block strategy not only improves the efficiency of updating gallery images but also enhances matching accuracy while reducing computational load.Experimental results demonstrate that our proposed method outperforms the state-of-the-art methods on the SYSU-MM01,RegDB,and RGBNT201 datasets,achieving excellent matching accuracy and robustness,thereby validating its effectiveness in cross-modal person re-identification.展开更多
The evidential reasoning(ER)rule framework has been widely applied in multi-attribute decision analysis and system assessment to manage uncertainty.However,traditional ER implementations rely on two critical limitatio...The evidential reasoning(ER)rule framework has been widely applied in multi-attribute decision analysis and system assessment to manage uncertainty.However,traditional ER implementations rely on two critical limitations:1)unrealistic assumptions of complete evidence independence,and 2)a lack of mechanisms to differentiate causal relationships from spurious correlations.Existing similarity-based approaches often misinterpret interdependent evidence,leading to unreliable decision outcomes.To address these gaps,this study proposes a causality-enhanced ER rule(CER-e)framework with three key methodological innovations:1)a multidimensional causal representation of evidence to capture dependency structures;2)probabilistic quantification of causal strength using transfer entropy,a model-free information-theoretic measure;3)systematic integration of causal parameters into the ER inference process while maintaining evidential objectivity.The PC algorithm is employed during causal discovery to eliminate spurious correlations,ensuring robust causal inference.Case studies in two types of domains—telecommunications network security assessment and structural risk evaluation—validate CER-e’s effectiveness in real-world scenarios.Under simulated incomplete information conditions,the framework demonstrates superior algorithmic robustness compared to traditional ER.Comparative analyses show that CER-e significantly improves both the interpretability of causal relationships and the reliability of assessment results,establishing a novel paradigm for integrating causal inference with evidential reasoning in complex system evaluation.展开更多
BACKGROUND Patients with major depression(MD)exhibit conditional reasoning dysfunction;however,no studies on the event-related potential(ERP)characteristics of conditional reasoning in MD have been reported.AIM To inv...BACKGROUND Patients with major depression(MD)exhibit conditional reasoning dysfunction;however,no studies on the event-related potential(ERP)characteristics of conditional reasoning in MD have been reported.AIM To investigate the ERP characteristics of conditional reasoning in MD patients and explore the neural mechanism of cognitive processing.METHODS Thirty-four patients with MD and 34 healthy controls(HCs)completed ERP measurements while performing the Wason selection task(WST).The clusterbased permutation test in FieldTrip was used to compare the differences in the mean amplitudes between the patients with MD and HCs on the ERP components under different experimental conditions.Behavioral data[accuracy(ACC)and reaction times(RTs)],the ERP P100 and late positive potentials(LPPs)were analyzed.RESULTS Although the mean ACC was greater and the mean of RTs was shorter in HCs than in MD patients,the differences were not statistically significant.However,across both groups,the ACC in the precautionary WST was greater than that in the other tasks,and the RTs in the abstract task were greater than those in the other tasks.Importantly,compared with that of HCs,the P100 of the left centroparietal sites was significantly increased,and the early LPP was attenuated at parietal sites and increased at left frontocentral sites;the medium LPP and late LPP were increased at the left frontocentral sites.CONCLUSION Patients with MD have conditional reasoning dysfunction and exhibit abnormal ERP characteristics evoked by the WST,which suggests neural correlates of abnormalities in conditional reasoning function in MD patients.展开更多
In this paper,a robust and consistent COVID-19 emergency decision-making approach is proposed based on q-rung linear diophantine fuzzy set(q-RLDFS),differential evolutionary(DE)optimization principles,and evidential r...In this paper,a robust and consistent COVID-19 emergency decision-making approach is proposed based on q-rung linear diophantine fuzzy set(q-RLDFS),differential evolutionary(DE)optimization principles,and evidential reasoning(ER)methodology.The proposed approach uses q-RLDFS in order to represent the evaluating values of the alternatives corresponding to the attributes.DE optimization is used to obtain the optimal weights of the attributes,and ER methodology is used to compute the aggregated q-rung linear diophantine fuzzy values(q-RLDFVs)of each alternative.Then the score values of alternatives are computed based on the aggregated q-RLDFVs.An alternative with the maximum score value is selected as a better one.The applicability of the proposed approach has been illustrated in COVID-19 emergency decision-making system and sustainable energy planning management.Moreover,we have validated the proposed approach with a numerical example.Finally,a comparative study is provided with the existing models,where the proposed approach is found to be robust to perform better and consistent in uncertain environments.展开更多
This paper proposed a new systematic approach-functional evidential reasoning model(FERM) for exploring hazardous chemical operational accidents under uncertainty. First, FERM was introduced to identify various causal...This paper proposed a new systematic approach-functional evidential reasoning model(FERM) for exploring hazardous chemical operational accidents under uncertainty. First, FERM was introduced to identify various causal factors and their performance changes in hazardous chemical operational accidents, along with determining the functional failure link relationships. Subsequently, FERM was employed to elucidate both qualitative and quantitative operational accident information within a unified framework, which could be regarded as the input of information fusion to obtain the fuzzy belief distribution of each cause factor. Finally, the derived risk values of the causal factors were ranked while constructing multi-level accident causation chains to unveil the weak links in system functionality and the primary roots of operational accidents. Using the specific case of the “1·15” major explosion and fire accident at Liaoning Panjin Haoye Chemical Co., Ltd., seven causal factors and their corresponding performance changes were identified. Additionally, five accident causation chains were uncovered based on the fuzzy joint distribution of the functional assessment level(FAL) and reliability distribution(RD),revealing an overall increase in risk along the accident evolution path. The research findings demonstrated that FERM enabled the effective characterization, rational quantification and accurate analysis of the inherent uncertainties in hazardous chemical operational accident risks from a systemic perspective.展开更多
Extrapolation on Temporal Knowledge Graphs(TKGs)aims to predict future knowledge from a set of historical Knowledge Graphs in chronological order.The temporally adjacent facts in TKGs naturally form event sequences,ca...Extrapolation on Temporal Knowledge Graphs(TKGs)aims to predict future knowledge from a set of historical Knowledge Graphs in chronological order.The temporally adjacent facts in TKGs naturally form event sequences,called event evolution patterns,implying informative temporal dependencies between events.Recently,many extrapolation works on TKGs have been devoted to modelling these evolutional patterns,but the task is still far from resolved because most existing works simply rely on encoding these patterns into entity representations while overlooking the significant information implied by relations of evolutional patterns.However,the authors realise that the temporal dependencies inherent in the relations of these event evolution patterns may guide the follow-up event prediction to some extent.To this end,a Temporal Relational Context-based Temporal Dependencies Learning Network(TRenD)is proposed to explore the temporal context of relations for more comprehensive learning of event evolution patterns,especially those temporal dependencies caused by interactive patterns of relations.Trend incorporates a semantic context unit to capture semantic correlations between relations,and a structural context unit to learn the interaction pattern of relations.By learning the temporal contexts of relations semantically and structurally,the authors gain insights into the underlying event evolution patterns,enabling to extract comprehensive historical information for future prediction better.Experimental results on benchmark datasets demonstrate the superiority of the model.展开更多
This study investigated the relationship between parental cognitive ability and child logical reasoning ability,and the role of academic expectation and family environment in that relationship.Based on the 2020 China ...This study investigated the relationship between parental cognitive ability and child logical reasoning ability,and the role of academic expectation and family environment in that relationship.Based on the 2020 China Family Panel Studies(CFPS)data,1491 children(girls ratio=53.78%;average grade=6.023 years,school grade standard deviation=1.825 years).Results following multiple regression model(OLS)show that the higher the parental cognitive ability,the higher the children’s logical reasoning ability.Secondly,parental academic expectation serves as a mediator between their cognitive ability and children’s logical reasoning ability for higher logical reasoning by children.Third,a possible family environment acts as a mediator in the relationship between parents’cognitive ability and children’s logical reasoning ability to be higher.We conclude from thesefindings that parents with high cognitive abilities can enhance their children’s logical reasoning skills not only by setting higher academic expectations,but also by cultivating a supportive family environment.Thesefindings imply a need for intervention to improve family quality of life to enhance children’s thinking abilities to optimize their academic learning.展开更多
Large language models(LLMs)have demonstrated remarkable generalization abilities across multiple tasks in natural language processing(NLP).For multi-step reasoning tasks,chain-of-thought(CoT)prompting facilitates step...Large language models(LLMs)have demonstrated remarkable generalization abilities across multiple tasks in natural language processing(NLP).For multi-step reasoning tasks,chain-of-thought(CoT)prompting facilitates step-by-step thinking,leading to improved performance.However,despite significant advancements in LLMs,current CoT prompting performs suboptimally on smaller-scale models that have fewer parameters.Additionally,the common paradigm of few-shot CoT prompting relies on a set of manual demonstrations,with performance contingent on the quality of these annotations and varying with task-specific requirements.To address these limitations,we propose a select-and-answer prompting method(SAP)to enhance language model performance on reasoning tasks without the need for manual demonstrations.This method comprises two primary steps:guiding the model to conduct preliminary analysis and generate several candidate answers based on the prompting;allowing the model to provide final answers derived from these candidate answers.The proposed prompting strategy is evaluated across two language models of varying sizes and six datasets.On ChatGLM-6B,SAP consistently outperforms few-shot CoT across all datasets.For GPT-3.5,SAP achieves comparable performance to few-shot CoT and outperforms zero-shot CoT in most cases.These experimental results indicate that SAP can significantly improve the accuracy of language models in reasoning tasks.展开更多
0 INTRODUCTION Due to the rapid population growth and the accelerated urbanization process,the contradiction between the demand for expanding ground space and the limited available land scale is becoming increasingly ...0 INTRODUCTION Due to the rapid population growth and the accelerated urbanization process,the contradiction between the demand for expanding ground space and the limited available land scale is becoming increasingly prominent.China has implemented and completed several largescale land infilling and excavation projects(Figure 1),which have become the main way to increase land resources and expand construction land.展开更多
The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensiona...The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensional space and one-dimensional time.With broad applications spanning fluid dynamics,shallow water waves,plasma physics,and condensed matter physics,the investigation of its solutions holds significant importance.Traditional analytical methods face limitations due to their dependence on bilinear forms.To overcome this constraint,this letter proposes a novel multi-modal neurosymbolic reasoning intelligent algorithm(MMNRIA)that achieves 100%accurate solutions for nonlinear partial differential equations without requiring bilinear transformations.By synergistically integrating neural networks with symbolic computation,this approach establishes a new paradigm for universal analytical solutions of nonlinear partial differential equations.As a practical demonstration,we successfully derive several exact analytical solutions for the(3+1)-dimensional BLMP equation using MMNRIA.These solutions provide a powerful theoretical framework for studying intricate wave phenomena governed by nonlinearity and dispersion effects in three-dimensional physical space.展开更多
presented The conceptions of abstract default reasoning frameworks （ADRFs） and D-consequence relations are Based on representation properties of D-consequence relations, it proves that any cumulative nonmonotonic co...presented The conceptions of abstract default reasoning frameworks （ADRFs） and D-consequence relations are Based on representation properties of D-consequence relations, it proves that any cumulative nonmonotonic consequence relation with the connective-free form can be represented by ADRFs.展开更多
基金The Study of the Separation of Judaism and Early Christianity on the Texts,Ideas,and Community(犹太教和早期基督教“文本、思想和社群”的分离研究),awarded by the Ministry of Education of the People’s Republic of China,Number:22JJD73001.
文摘In Christianity,the passion and resurrection of Jesus Christ are a fact of history.If his resurrection is a miracle to be accepted by faith,no rational demonstration of it is needed,although the Apostle Paul argues by analogy for the resurrection in 1 Corinthians.Being a realist and using Latin,Aquinas holds that human reason can contribute to an understanding of faith;he has no strict distinction between hades and hell.He uses logos to emphasize reason and instrumental causality in explaining the relationship between humanity and divinity for Jesus.Arguing for the resurrection of Jesus,Aquinas should be consistent with his principle of the individualization of a soul through a body,and a separate soul being a substance,but he is inconsistent.Considering Jesus’soul before his resurrection,Aquinas supports the Apostles’Creed,but he develops the notion of purgatory,where departed souls sojourn temporarily.This paper argues that Aquinas,in discussing the passion and resurrection of Jesus Christ,obscures the distinction he draws between faith and reason.
文摘The cross-modal person re-identification task aims to match visible and infrared images of the same individual.The main challenges in this field arise from significant modality differences between individuals and the lack of high-quality cross-modal correspondence methods.Existing approaches often attempt to establish modality correspondence by extracting shared features across different modalities.However,these methods tend to focus on local information extraction and fail to fully leverage the global identity information in the cross-modal features,resulting in limited correspondence accuracy and suboptimal matching performance.To address this issue,we propose a quadratic graph matching method designed to overcome the challenges posed by modality differences through precise cross-modal relationship alignment.This method transforms the cross-modal correspondence problem into a graph matching task and minimizes the matching cost using a center search mechanism.Building on this approach,we further design a block reasoning module to uncover latent relationships between person identities and optimize the modality correspondence results.The block strategy not only improves the efficiency of updating gallery images but also enhances matching accuracy while reducing computational load.Experimental results demonstrate that our proposed method outperforms the state-of-the-art methods on the SYSU-MM01,RegDB,and RGBNT201 datasets,achieving excellent matching accuracy and robustness,thereby validating its effectiveness in cross-modal person re-identification.
基金supported by the Natural Science Foundation of China(Nos.U22A2099,62273113,62203461,62203365)the Innovation Project of Guangxi Graduate Education under Grant YCBZ2023130by the Guangxi Higher Education Undergraduate Teaching Reform Project Key Project,grant number 2022JGZ130.
文摘The evidential reasoning(ER)rule framework has been widely applied in multi-attribute decision analysis and system assessment to manage uncertainty.However,traditional ER implementations rely on two critical limitations:1)unrealistic assumptions of complete evidence independence,and 2)a lack of mechanisms to differentiate causal relationships from spurious correlations.Existing similarity-based approaches often misinterpret interdependent evidence,leading to unreliable decision outcomes.To address these gaps,this study proposes a causality-enhanced ER rule(CER-e)framework with three key methodological innovations:1)a multidimensional causal representation of evidence to capture dependency structures;2)probabilistic quantification of causal strength using transfer entropy,a model-free information-theoretic measure;3)systematic integration of causal parameters into the ER inference process while maintaining evidential objectivity.The PC algorithm is employed during causal discovery to eliminate spurious correlations,ensuring robust causal inference.Case studies in two types of domains—telecommunications network security assessment and structural risk evaluation—validate CER-e’s effectiveness in real-world scenarios.Under simulated incomplete information conditions,the framework demonstrates superior algorithmic robustness compared to traditional ER.Comparative analyses show that CER-e significantly improves both the interpretability of causal relationships and the reliability of assessment results,establishing a novel paradigm for integrating causal inference with evidential reasoning in complex system evaluation.
基金Supported by Wuxi Taihu Talent Project,No.WXTTP 2021the General Scientific Research Program of Wuxi Municipal Health Commission,No.M202447.
文摘BACKGROUND Patients with major depression(MD)exhibit conditional reasoning dysfunction;however,no studies on the event-related potential(ERP)characteristics of conditional reasoning in MD have been reported.AIM To investigate the ERP characteristics of conditional reasoning in MD patients and explore the neural mechanism of cognitive processing.METHODS Thirty-four patients with MD and 34 healthy controls(HCs)completed ERP measurements while performing the Wason selection task(WST).The clusterbased permutation test in FieldTrip was used to compare the differences in the mean amplitudes between the patients with MD and HCs on the ERP components under different experimental conditions.Behavioral data[accuracy(ACC)and reaction times(RTs)],the ERP P100 and late positive potentials(LPPs)were analyzed.RESULTS Although the mean ACC was greater and the mean of RTs was shorter in HCs than in MD patients,the differences were not statistically significant.However,across both groups,the ACC in the precautionary WST was greater than that in the other tasks,and the RTs in the abstract task were greater than those in the other tasks.Importantly,compared with that of HCs,the P100 of the left centroparietal sites was significantly increased,and the early LPP was attenuated at parietal sites and increased at left frontocentral sites;the medium LPP and late LPP were increased at the left frontocentral sites.CONCLUSION Patients with MD have conditional reasoning dysfunction and exhibit abnormal ERP characteristics evoked by the WST,which suggests neural correlates of abnormalities in conditional reasoning function in MD patients.
文摘In this paper,a robust and consistent COVID-19 emergency decision-making approach is proposed based on q-rung linear diophantine fuzzy set(q-RLDFS),differential evolutionary(DE)optimization principles,and evidential reasoning(ER)methodology.The proposed approach uses q-RLDFS in order to represent the evaluating values of the alternatives corresponding to the attributes.DE optimization is used to obtain the optimal weights of the attributes,and ER methodology is used to compute the aggregated q-rung linear diophantine fuzzy values(q-RLDFVs)of each alternative.Then the score values of alternatives are computed based on the aggregated q-RLDFVs.An alternative with the maximum score value is selected as a better one.The applicability of the proposed approach has been illustrated in COVID-19 emergency decision-making system and sustainable energy planning management.Moreover,we have validated the proposed approach with a numerical example.Finally,a comparative study is provided with the existing models,where the proposed approach is found to be robust to perform better and consistent in uncertain environments.
基金supported by the National Key Research&Development Program of China(2021YFB3301100)the National Natural Science Foundation of China(52004014)the Fundamental Research Funds for the Central Universities(ZY2406).
文摘This paper proposed a new systematic approach-functional evidential reasoning model(FERM) for exploring hazardous chemical operational accidents under uncertainty. First, FERM was introduced to identify various causal factors and their performance changes in hazardous chemical operational accidents, along with determining the functional failure link relationships. Subsequently, FERM was employed to elucidate both qualitative and quantitative operational accident information within a unified framework, which could be regarded as the input of information fusion to obtain the fuzzy belief distribution of each cause factor. Finally, the derived risk values of the causal factors were ranked while constructing multi-level accident causation chains to unveil the weak links in system functionality and the primary roots of operational accidents. Using the specific case of the “1·15” major explosion and fire accident at Liaoning Panjin Haoye Chemical Co., Ltd., seven causal factors and their corresponding performance changes were identified. Additionally, five accident causation chains were uncovered based on the fuzzy joint distribution of the functional assessment level(FAL) and reliability distribution(RD),revealing an overall increase in risk along the accident evolution path. The research findings demonstrated that FERM enabled the effective characterization, rational quantification and accurate analysis of the inherent uncertainties in hazardous chemical operational accident risks from a systemic perspective.
基金supported in part by the National Natural Science Foundation of China(No.62302507)and the funding of Harbin Institute of Technology(Shenzhen)(No.20210035).
文摘Extrapolation on Temporal Knowledge Graphs(TKGs)aims to predict future knowledge from a set of historical Knowledge Graphs in chronological order.The temporally adjacent facts in TKGs naturally form event sequences,called event evolution patterns,implying informative temporal dependencies between events.Recently,many extrapolation works on TKGs have been devoted to modelling these evolutional patterns,but the task is still far from resolved because most existing works simply rely on encoding these patterns into entity representations while overlooking the significant information implied by relations of evolutional patterns.However,the authors realise that the temporal dependencies inherent in the relations of these event evolution patterns may guide the follow-up event prediction to some extent.To this end,a Temporal Relational Context-based Temporal Dependencies Learning Network(TRenD)is proposed to explore the temporal context of relations for more comprehensive learning of event evolution patterns,especially those temporal dependencies caused by interactive patterns of relations.Trend incorporates a semantic context unit to capture semantic correlations between relations,and a structural context unit to learn the interaction pattern of relations.By learning the temporal contexts of relations semantically and structurally,the authors gain insights into the underlying event evolution patterns,enabling to extract comprehensive historical information for future prediction better.Experimental results on benchmark datasets demonstrate the superiority of the model.
基金supported by scientific research fund of Jiangxi Provincial Social Sciences“14th Five-Year Plan”(No.23SH05).
文摘This study investigated the relationship between parental cognitive ability and child logical reasoning ability,and the role of academic expectation and family environment in that relationship.Based on the 2020 China Family Panel Studies(CFPS)data,1491 children(girls ratio=53.78%;average grade=6.023 years,school grade standard deviation=1.825 years).Results following multiple regression model(OLS)show that the higher the parental cognitive ability,the higher the children’s logical reasoning ability.Secondly,parental academic expectation serves as a mediator between their cognitive ability and children’s logical reasoning ability for higher logical reasoning by children.Third,a possible family environment acts as a mediator in the relationship between parents’cognitive ability and children’s logical reasoning ability to be higher.We conclude from thesefindings that parents with high cognitive abilities can enhance their children’s logical reasoning skills not only by setting higher academic expectations,but also by cultivating a supportive family environment.Thesefindings imply a need for intervention to improve family quality of life to enhance children’s thinking abilities to optimize their academic learning.
基金National Natural Science Foundation of China(No.62176052)。
文摘Large language models(LLMs)have demonstrated remarkable generalization abilities across multiple tasks in natural language processing(NLP).For multi-step reasoning tasks,chain-of-thought(CoT)prompting facilitates step-by-step thinking,leading to improved performance.However,despite significant advancements in LLMs,current CoT prompting performs suboptimally on smaller-scale models that have fewer parameters.Additionally,the common paradigm of few-shot CoT prompting relies on a set of manual demonstrations,with performance contingent on the quality of these annotations and varying with task-specific requirements.To address these limitations,we propose a select-and-answer prompting method(SAP)to enhance language model performance on reasoning tasks without the need for manual demonstrations.This method comprises two primary steps:guiding the model to conduct preliminary analysis and generate several candidate answers based on the prompting;allowing the model to provide final answers derived from these candidate answers.The proposed prompting strategy is evaluated across two language models of varying sizes and six datasets.On ChatGLM-6B,SAP consistently outperforms few-shot CoT across all datasets.For GPT-3.5,SAP achieves comparable performance to few-shot CoT and outperforms zero-shot CoT in most cases.These experimental results indicate that SAP can significantly improve the accuracy of language models in reasoning tasks.
基金funded by the Key Research and Development Program of Shaanxi Province(No.2024SFYBXM-669)the National Natural Science Foundation of China(No.42271078)。
文摘0 INTRODUCTION Due to the rapid population growth and the accelerated urbanization process,the contradiction between the demand for expanding ground space and the limited available land scale is becoming increasingly prominent.China has implemented and completed several largescale land infilling and excavation projects(Figure 1),which have become the main way to increase land resources and expand construction land.
基金supported by the National Natural Science Foundation of China(Grant No.62303289)Tianyuan Fund for Mathematics of the National Natural Science Foundation of China(Grant No.12426105)+3 种基金the Scientific and Technological Innovation Programs(STIP)of Higher Education Institutions in Shanxi(Grant No.2024L022)Fundamental Research Program of Shanxi Province(Grant Nos.202403021222001 and 202203021222003)the“Wen Ying Young Scholars”Talent Project of Shanxi University(Grant Nos.138541088,138541090,and 138541127)Funded by Open Foundation of Hubei Key Laboratory of Applied Mathematics(Hubei University)(Grant No.HBAM202401).
文摘The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensional space and one-dimensional time.With broad applications spanning fluid dynamics,shallow water waves,plasma physics,and condensed matter physics,the investigation of its solutions holds significant importance.Traditional analytical methods face limitations due to their dependence on bilinear forms.To overcome this constraint,this letter proposes a novel multi-modal neurosymbolic reasoning intelligent algorithm(MMNRIA)that achieves 100%accurate solutions for nonlinear partial differential equations without requiring bilinear transformations.By synergistically integrating neural networks with symbolic computation,this approach establishes a new paradigm for universal analytical solutions of nonlinear partial differential equations.As a practical demonstration,we successfully derive several exact analytical solutions for the(3+1)-dimensional BLMP equation using MMNRIA.These solutions provide a powerful theoretical framework for studying intricate wave phenomena governed by nonlinearity and dispersion effects in three-dimensional physical space.
文摘presented The conceptions of abstract default reasoning frameworks （ADRFs） and D-consequence relations are Based on representation properties of D-consequence relations, it proves that any cumulative nonmonotonic consequence relation with the connective-free form can be represented by ADRFs.
