A1 is not a conservative extension of S4 but of S5
Copyright policy )A1 is not a conservative extension of S4 but of S5
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.
- Josai University Japan
alethic modal logic, knowledge, a priori, Philosophical and critical aspects of logic and foundations, Modal logic (including the logic of norms), conservative extension
alethic modal logic, knowledge, a priori, Philosophical and critical aspects of logic and foundations, Modal logic (including the logic of norms), conservative extension
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