A1 is not a conservative extension of s4 but of S

Journal of Philosophical Logic 18 (3):321 - 323 (1989)
Abstract
In [1], D. W. Hart and C. Mcginn considered two logics Al and A2. These logics embody part of a tradition about a priori knowledge and necessity. They proved that A2 is a conservative extension of a well-known modal logic S5 but left the problem whether Al is a conservative extension of S4 open. In this note, we shall show that Al is not a conservative extension of S4 but of S5, and also correct an inadequate proof
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