By restricting the common replacement axiom schema of ZF to ∑~M-formulae,Professor Zhang Jinwen constructed a series of subsystems of Zennelo-Frankel set theory ZF and he called them ZF^M.Zhao Xi shun show that the c...By restricting the common replacement axiom schema of ZF to ∑~M-formulae,Professor Zhang Jinwen constructed a series of subsystems of Zennelo-Frankel set theory ZF and he called them ZF^M.Zhao Xi shun show that the consistency of ZF^M can be deducted from ZF.Professor Zhang Jinwen raised the question whether the consistency of ZF^M can be deducted from ZF^(M+m(M)) for some m(n)≥1.In this paper,we get a positive solution to Professor Zhang's problem.Moreover,we show that the consistency of ZF^M can be deducted from ZF^(M+3).展开更多
Vagueness of language has long been explored in the fields of philosophy and logic. Although Zadeh put forward fuzzy sets theory which was considered to be a decent quantitative instrument for the study of language va...Vagueness of language has long been explored in the fields of philosophy and logic. Although Zadeh put forward fuzzy sets theory which was considered to be a decent quantitative instrument for the study of language vagueness, the source of vagueness still remains a disputed issue. As the study of vagueness goes further, researchers attached more and more attention to the relation between language-cognition- reality, especially in the cognitive field. Thus we found that it would be more satisfied with the issue to construct a relation-model between five factors： reality, concept, human, language, and context. This model, which is different from the semantic triangle in explicating the factors, human and context, may help to explain the nature of vagueness and reclassify the language vagueness.展开更多
文摘By restricting the common replacement axiom schema of ZF to ∑~M-formulae,Professor Zhang Jinwen constructed a series of subsystems of Zennelo-Frankel set theory ZF and he called them ZF^M.Zhao Xi shun show that the consistency of ZF^M can be deducted from ZF.Professor Zhang Jinwen raised the question whether the consistency of ZF^M can be deducted from ZF^(M+m(M)) for some m(n)≥1.In this paper,we get a positive solution to Professor Zhang's problem.Moreover,we show that the consistency of ZF^M can be deducted from ZF^(M+3).
文摘Vagueness of language has long been explored in the fields of philosophy and logic. Although Zadeh put forward fuzzy sets theory which was considered to be a decent quantitative instrument for the study of language vagueness, the source of vagueness still remains a disputed issue. As the study of vagueness goes further, researchers attached more and more attention to the relation between language-cognition- reality, especially in the cognitive field. Thus we found that it would be more satisfied with the issue to construct a relation-model between five factors： reality, concept, human, language, and context. This model, which is different from the semantic triangle in explicating the factors, human and context, may help to explain the nature of vagueness and reclassify the language vagueness.
