模态逻辑系统S4中的度量结构

Metric structure in modal logic system S4

在模态逻辑S4中通过有限模型建立了模态公式的(n)真度理论,研究了模态逻辑S4中命题的(n)真度的性质。提出了模态公式间的(n)相似度理论,并由此在全体公式集中,建立了(n)伪距离,得出了(n)模态逻辑S4的度量空间,该空间以经典逻辑度量空间为子空间,提出了一种模态逻辑S4中近似推理的框架。

The theory of（ n） truth degrees of formulas is proposed in modal logic system S4. Some properties of（ n）truth are investigated in modal logic system S4. The theory of（ n） similarity degrees among modal formulas is proposed and a pseudo-metric is defined thereform on the set of all formulas. 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 system S4.