The main results of this note are an extension of (1)Definition. Let S be a set of lock clauses, D a linear deduction about empty clause □ from S. Its side clauses are B0, B1,..., Bn-1 and center clauses are C0, C1, ...The main results of this note are an extension of (1)Definition. Let S be a set of lock clauses, D a linear deduction about empty clause □ from S. Its side clauses are B0, B1,..., Bn-1 and center clauses are C0, C1, ...,展开更多
In Ref. [1], a conclusion was reached that input paramodulation refutation and unit paramodulation refutation are equivalent for a set of unit clauses, and a supposition was made that the converse of Theorem 8.4 is al...In Ref. [1], a conclusion was reached that input paramodulation refutation and unit paramodulation refutation are equivalent for a set of unit clauses, and a supposition was made that the converse of Theorem 8.4 is also true. In this note, we shall prove that both the conclusion and the supposition are wrong.展开更多
Refutation methods based on the resolution principle are generally applied to a (finite) set of sentences, which must have a series of pre-transformations (prenex normalization, Skolemization and conjunction normaliza...Refutation methods based on the resolution principle are generally applied to a (finite) set of sentences, which must have a series of pre-transformations (prenex normalization, Skolemization and conjunction normalization) before starting the refutation. In this paper, the authors first generalize the concept of abatract consistency class to the most general form-universal abstract consistency class, and prove its universal unifying principle. Then, based on the R-refutation, a universal refutation method is proposed and its soundness and completeness are proved by means of the universal unifying principle. This method can be applied directly to any finite set of wffs without preprocessing the wffs at all so that the refutation procedure is more natural.展开更多
By manually collecting data on Internet-based rumors concerning COVID-19,we investigate the market reactions to the spread of such rumors and the government’s refutation of them.We find that frightening(reassuring)ru...By manually collecting data on Internet-based rumors concerning COVID-19,we investigate the market reactions to the spread of such rumors and the government’s refutation of them.We find that frightening(reassuring)rumors have a negative(positive)impact on investors.The refutation of frightening rumors triggers a positive market response,whereas the refutation of reassuring rumors does not cause a significant market reaction.Further analysis shows that there is a stock price drift when frightening rumors are refuted by governments.Our conclusions remain robust after considering endogeneity.Our findings support the notion that epidemic-related rumors affect investors’decisions,which add to literatures of the market responses of companies in the context of the COVID-19 pandemic and provide incremental evidence for the“the spiral of silence”theory.展开更多
The Internet era has brought great convenience to our life and communication.Meanwhile,it also makes a bunch of rumors propagate faster and causes even more harm to human life.Therefore,it is necessary to perform effe...The Internet era has brought great convenience to our life and communication.Meanwhile,it also makes a bunch of rumors propagate faster and causes even more harm to human life.Therefore,it is necessary to perform effective control mechanisms to minimize the negative social impact from rumors.Thereout,firstly,we formulate a rumor spreading model considering psychological factors and thinking time,then,we add white noise(i.e.,stochastic interference)and two pulse control strategies which denote education mechanism and refutation mechanism into the model.Secondly,we obtain the global positive solutions and demonstrate the global exponential stability of the unique positive periodic rumor-free solution.Thirdly,we discuss the extinction and persistence of rumor.Moreover,we use Pontriagin’s minimum principle to explore the optimal impulse control.Finally,several numerical simulations are carried out to verify the effectiveness and availability of the theoretical analysis.We conclude that the pulse control strategies have a great influence on controlling rumor spreading,and different control strategies should be adopted under different transmission scenarios.展开更多
The culture of every nation is bound to develop and make progress along with social development and progress. This is true, too, of Tibetan culture. As China furthers the cause of building socialism with Chinese chara...The culture of every nation is bound to develop and make progress along with social development and progress. This is true, too, of Tibetan culture. As China furthers the cause of building socialism with Chinese characteristics, a new progressive culture will keep replacing an old and backward culture. Any attempt to impede and reverse such progress constitutes real destruction of a culture. Such an attempt can never succeed. Nor will the attempt of the Dalai Lama.展开更多
文摘The main results of this note are an extension of (1)Definition. Let S be a set of lock clauses, D a linear deduction about empty clause □ from S. Its side clauses are B0, B1,..., Bn-1 and center clauses are C0, C1, ...,
基金Project supported by the National Natural Science Foundation of China
文摘In Ref. [1], a conclusion was reached that input paramodulation refutation and unit paramodulation refutation are equivalent for a set of unit clauses, and a supposition was made that the converse of Theorem 8.4 is also true. In this note, we shall prove that both the conclusion and the supposition are wrong.
文摘Refutation methods based on the resolution principle are generally applied to a (finite) set of sentences, which must have a series of pre-transformations (prenex normalization, Skolemization and conjunction normalization) before starting the refutation. In this paper, the authors first generalize the concept of abatract consistency class to the most general form-universal abstract consistency class, and prove its universal unifying principle. Then, based on the R-refutation, a universal refutation method is proposed and its soundness and completeness are proved by means of the universal unifying principle. This method can be applied directly to any finite set of wffs without preprocessing the wffs at all so that the refutation procedure is more natural.
基金funded by the National Natural Science Foundation of China(Grant No.71672208 and71902210)National Social Science Foundation(Grant No.21BGL095)+1 种基金Humanities and Social Sciences Foundation of Ministry of Education of China(No.19YJC630092)Program for Innovation Research in Central University of Finance and Economics
文摘By manually collecting data on Internet-based rumors concerning COVID-19,we investigate the market reactions to the spread of such rumors and the government’s refutation of them.We find that frightening(reassuring)rumors have a negative(positive)impact on investors.The refutation of frightening rumors triggers a positive market response,whereas the refutation of reassuring rumors does not cause a significant market reaction.Further analysis shows that there is a stock price drift when frightening rumors are refuted by governments.Our conclusions remain robust after considering endogeneity.Our findings support the notion that epidemic-related rumors affect investors’decisions,which add to literatures of the market responses of companies in the context of the COVID-19 pandemic and provide incremental evidence for the“the spiral of silence”theory.
基金partially supported by the Project for the National Natural Science Foundation of China(Grant Nos.72174121 and 71774111)the Program for Professor of Special Appointment(Eastern Scholar)at Shanghai Institutions of Higher Learning+1 种基金the Project for the Natural Science Foundation of Shanghai(Grant No.21ZR1444100)Project Soft Science Research of Shanghai(Grant No.22692112600)。
文摘The Internet era has brought great convenience to our life and communication.Meanwhile,it also makes a bunch of rumors propagate faster and causes even more harm to human life.Therefore,it is necessary to perform effective control mechanisms to minimize the negative social impact from rumors.Thereout,firstly,we formulate a rumor spreading model considering psychological factors and thinking time,then,we add white noise(i.e.,stochastic interference)and two pulse control strategies which denote education mechanism and refutation mechanism into the model.Secondly,we obtain the global positive solutions and demonstrate the global exponential stability of the unique positive periodic rumor-free solution.Thirdly,we discuss the extinction and persistence of rumor.Moreover,we use Pontriagin’s minimum principle to explore the optimal impulse control.Finally,several numerical simulations are carried out to verify the effectiveness and availability of the theoretical analysis.We conclude that the pulse control strategies have a great influence on controlling rumor spreading,and different control strategies should be adopted under different transmission scenarios.
文摘The culture of every nation is bound to develop and make progress along with social development and progress. This is true, too, of Tibetan culture. As China furthers the cause of building socialism with Chinese characteristics, a new progressive culture will keep replacing an old and backward culture. Any attempt to impede and reverse such progress constitutes real destruction of a culture. Such an attempt can never succeed. Nor will the attempt of the Dalai Lama.
