A completeness proof in full DDL

Abstract

Dynamic doxastic logicians — not a large community — have trodden gingerly within the area of full DDL or, as with the present author, have not trodden at all. However, the latter, after having written up the final version of [6], realised that the proof given in that paper for two varieties of basic DDL can be extended to cover full DDL; in fact, the «full» proof is simpler than the «basic» one. The extended proof is outlined in Section 1–3. In Section 4, the relationship to AGM is considered. Section 5 puts the importance of the proof into perspective.

This note — an extended abstract rather than a full-fledged paper — should be read as an appendix to [6]. Although some definitions are repeated here, many are not. Readers who require more detail are referred to [6], a copy of which they should have on hand.