若干命题联结词集合的完备性和不完备性证明

Adequacy or Inadequacy Proof of Several Propositional Connection Sets

命题联结词集合的完备性和不完备性是命题逻辑中一种有趣的现象,证明了联结词集合{∨,∧,→,}和{～,}的不完备性,并在表明联结词集合{～,∧},{～,∨}和{～,→}是完备的基础上证明了两个单元集{↓}和{|}是完备的。

Adequacy or inadequacy of propositional connective sets is an interesting phenomenon in propositional logic. This essay proves the inadequacy of the connective sets{∨,∧,←→,→} and {～,←→}. The adequacy of the singleton sets { ↓}and {｜} is also proved.