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#conditional-doxastic-models #doxastic-logic #logic-of-conditional-beliefs #private-announcements #public-announcements #serious-possibility-paradox-project

So we formulate our revised multi-agent (epistemic) AGM pos tulates, by giving, for every agent a ∈ A: a family T a ⊆ P(BKL) of sets of sentences in the language BKL, called a-theories, and a belief revision operator ∗ a : T a × BKL → T a , taking pairs of a-theories and BKL-sentences into new a-theories; and requiring them to satisfy the following conditions: (T1) ⊥ ∈ T a (where ⊥ := BKL is the inconsistent theory, containing all the sentences in BKL); (T2) every T ∈ T a is deductively closed, w.r.t. the complete proof system of BKL; (T3) for every ϕ ∈ BKL and every T ∈ T a , we have either K a ϕ ∈ T or (¬K a ϕ) ∈ T ; (T4) all the above postulates of epistemic AGM, in which we label with agent names both the knowledge K a and the revision ∗ a operators. Observe that it is not necessary to require an introspective condition corresponding to (T3) for belief, since this follows from the above conditions, given the axioms of BKL. Indeed, one can easily prove that for every ϕ ∈ BKL and every T ∈ T a , we have either B a ϕ ∈ T or (¬B a ϕ) ∈ T

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owner: rappatoni - (no access) - Baltag and Smets - conditional doxastic models a qualiltative approach to odynamic belief revision.pdf, p6

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