  The present paper investigates a natural generalization of the duality
between Riemannian symmetric pairs of compact type and those of non-compact
type \`a la \'E. Cartan. The main result of this paper is to construct an
explicit description of a one-to-one correspondence between non-compact
pseudo-Riemannian semisimple symmetric pairs and commutative compact semisimple
symmetric triads, which is called the duality theorem. Further, we develop a
general theory of the duality theorem.
