Is the semantics of branching structures adequate for non-metric Ockhamist tense logics?

The main purpose of this paper is to show that the whole discussion of our previous paper (Nishimura, 1979) can be generalized to non-metric Ockhamist tense logics. Since the difficulty arises solely in our present version of Theorem 5, the rest of this paper is devoted to the proof that the semantics of branching structures formulated in full detail by Thomason (1970, Section 7) validates the formula