, Precisely, the postcondition is either restricted to epistemic formulas or defined by mutual recursion with the truth conditions

M. , As usual, V , w 0 , the notation ||? || M stands for the set of possible worlds w ? W such that W, {R} i?I

, Otherwise the operation (.) E is undefined

, Precisely, updates are defined by mutual recursion with the truth conditions

, It is easy to see that it is equivalent to the axiomatisations one usually finds in papers about DELs, such as in Wang and Cao, 2013.

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