Abstract:

The equal weight property of Boolean functions in cryptology is introduced in two valued propositional logic and the corresponding definition of uniform logic formulas is proposed. It is proved that truth degrees of uniform logic formulas are less or equal to 1／2. The set consisting of truth degrees of all uniform logic formulas has exactly one limit point zero. Also, basic properties of uniform logic formulas are investigated, and a simple method for computing the truth degree of the disjunction of two uniform logic formulas with the same atoms, as well as the similarity degree of them are obtained。

Key words: equally weighted Boolean function; uniform logic formula; truth degree; quantitative logic; logic metric space; limit point