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Theory of (n) truth degrees of formulas in modal logic and a consistency theorem
【摘要】 The theory of (n) truth degrees of formulas is proposed in modal logic for the first time. A consistency theorem is obtained which says that the (n) truth degree of a modality-free formula equals the truth degree of the formula in two-valued propositional logic. Variations of (n) truth degrees of formulas w.r.t. n in temporal logic is investigated. Moreover, the theory of (n) similarity degrees among modal formulas is proposed and the (n) modal logic metric space is derived therefrom which contains the classical logic metric space as a subspace. Finally, a kind of approximate reasoning theory is proposed in modal logic.
【Abstract】 The theory of (n) truth degrees of formulas is proposed in modal logic for the first time. A consistency theorem is obtained which says that the (n) truth degree of a modality-free formula equals the truth degree of the formula in two-valued propositional logic. Variations of (n) truth degrees of formulas w.r.t. n in temporal logic is investigated. Moreover, the theory of (n) similarity degrees among modal formulas is proposed and the (n) modal logic metric space is derived therefrom which contains the classical logic metric space as a subspace. Finally, a kind of approximate reasoning theory is proposed in modal logic.
【Key words】 modal logic； (n) truth degrees； consistency theorem； temporal logic； (n) modality similarity degrees； (n) modality logic metric space； approximate reasoning；
- 【文献出处】 Science in China(Series F:Information Sciences) ,中国科学(F辑:信息科学)(英文版) , 编辑部邮箱 ,2009年01期
- 【分类号】O141
- 【被引频次】15
- 【下载频次】62