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.
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.
基金
Supported by the National Natural Science Foundation of China (Grant Nos. 10331010 and 10771129)
the Foundation of 211 Constructionof Shaanxi Normal University
