Conditional Action
Krister Segerberg · 1995
Abstract Normally one would expect the As to be pairwise inconsistent and jointly exhaustive, but there is no need to require that this be the case. In a situation where several As obtain, the claim of (§) amounts to the claim that all the corresponding Bs hold. If none of the As obtains, then the claim is vacuous and hence considered to be trivially true. In a similar way there is a concept of action by cases in dynamic logic. The corresponding concept is a 2n-ary operator (operating on n programs and n propositions to form a new program):