 General frames for CCL are required to satisfy condition CA □→ A in order to make sure that Boethius’ theses are indeed validated. In Unterhuber and Wansing 2019 sound and complete tableau calculi are presented for CCL and the weaker system cCL that validates Aristotle’s theses but not Boethius’ theses and that is obtained by giving up CA □→ A. In Wansing and Unterhuber 2019 these results are then extended to systems that are obtained by adding a constructive implication to the language of cCL and CCL.