Introspective forgetting (Q1036061)

The starting point for this investigation is a paper of \textit{J. Lang, P. Liberatore} and \textit{P. Marquis} [``Propositional independence: formula-variable independence and forgetting'', J. Artif. Intell. Res. (JAIR) 18, 391--443 (2003; Zbl 1056.68112)]. There, the notion of `forgetting' an elementary letter in a formula of classical propositional logic was given three different definitions, which were shown to be equivalent. The paper under review explores ways of extending those definitions to languages that are modalized to express belief. It begins by considering standard modal logics with belief as a box operator determined by a Kripke structure, only to conclude that in this context all three kinds of definition lead to counter-intuitive results. The authors then turn to modeling the notion as an event in dynamic epistemic logic. For simplicity, this is done for the case of a single elementary letter forgotten by a single agent, although a generalization to the multi-agent case is sketched and the multi-letter extension is said to be straightforward. Semantics and axiomatics are given in this framework for `introspective forgetting', with soundness and completeness theorems established and the relation to `unawareness forgetting' discussed.