Four-valued logic using two lines and its application to modal logic

The author discusses a four-valued logic using two lines each of which consists of two-valued logical elements. It is obtained by adding a few monomial operators to the operators of the four-valued logic reported by T. Chen et al. (1983). Functional completeness, duality, canonical form, simplification and other theorems are discussed. It is concluded that the functional space of four-valued logic is equivalent to that of two-valued logic. It is also found that variables and operators of modal logic correspond to those of four-valued logic using two lines.<>