带Rough相等关系词的Rough逻辑系统及其推理

Rough Logic Systems with Rough Equality Relation and Its Reasoning

以公式的定义域集的下和上近似分别相等方法 ,定义了两个Rough逻辑公式Rough相等 ,并以此定义了Rough相等关系词“ =R” ,它不仅比等值词“ ”运算有更多的直观性 ,而且既考虑了可定义的公式 ,也包含了那些在边界线上不可定义或可能可定义的公式 .所以 ,经典逻辑中的隐含式 φ→ ψ被移至Rough逻辑中应当解释为R (d(φ) ) R (d(ψ) )∧R (d(φ) ) R (d(ψ) ) .经典逻辑中的等值式 φ ψ被移至Rough逻辑中应当解释为R (d(φ) ) =R (d(ψ) )∧R (d(φ) ) =R (d(ψ) ) ,其中d(F)是公式F的定义区域 ,它可能是可定义集 ,也可能是不可定义集或Rough集 .这是Rough逻辑与经典逻辑或其它非标准逻辑的重要区别之一 ,将这种Rough相等词“ =R”引入Rough逻辑中 ,因而得到了一些相关的性质和相关的推理规则 .文中建立了带Rough相等关系词“ =R”的Rough逻辑推理系统 。

By rough equality of lower and upper approximatins with respect to the domain of formulas, authors define the rough equality between two logical formulas, thus, defining rough equal relation '=R'. Hence, the operations of '=R' not only bring on more visual than the operations of equivalence '↔', but also include definable formulas in domain and indefinable or possible definable formulas in boundary. An important difference between rough logic and classical logic or other non-standard logic is given. The rough equal relation '=R' is quoted in the rough logic, to have some relative properties and inference rules. Authors establish a rough logical reasoning system with rough equality relation '=R' and prove a few real examples by deductive reasoning in the system.