A1 is not a conservative extension of S4 but of S5 (Q1123182)

A1 and A2 are logics of knowledge of the a priori. They are formed by adding to the alethic modal logic T, operators Ḵp and \b{A}p - read: it is known that p, and it is a priori that p - and approriate axiom schemata to govern them. A2 includes A1. \textit{D. W. Hart} and \textit{C. Mcginn}, who had introduced these systems, had shown that A2 is a conservative extension of S5. Here it is proved that A1 is likewise a conservative extension of S5, and not of S4 as had been conjectured.