【摘要】 证明了n元真值函数集L关于运算∨及其对偶运算∧、序结构≤作为一个布尔代数是一个F格半群:f∨g(x)=f(x)∨g(x),f∧g(x)=f(x)∧g(x),f≤g当且仅当f(x)≤g(x)( f,g∈L, x∈{0,1}n),并且确定了其分子结构.指出含n个变元的合式公式集关于合式公式等值关系 所构成的商结构L 与L同构,从而说明命题逻辑的基本框架实际上是一个特殊的双格半群,即F格半群.更多还原

【Abstract】 The thesis gives that n_dimensional truth_value functional set is a F_lattice semigroup concerning as follows the operation ∨ and the dual operation ∧,and the ordering relation ≤ constituting the boolean algebra:f∨g(x)=f(x)∨g(x),f∧g(x)=f(x)∧g(x) (f,g∈L,x∈｛0,1｝n),f≤g is and only is f(x)≤g(x)(f,g∈L,x∈｛0,1｝n). And its molecule structure make sured. The thesis point out to the quotient structure M/ and L are isomorphic,M means for proposition formulas to contain n proposition variable constituting the set and means the equal relation of proposition formulas,accordingly showed the cadre of the propositional logic is a special double lattice_ordered semigroup, i.e.F lattice_ordered semigroup. 更多还原