A Dynamic Solution to the Puzzle of Sea Battle

The puzzle of sea battle involves an argument that is an instantiation of reasoning by cases. Its premises include the conditionals "if there is a/no sea battle tomorrow, it is necessarily so". It has a fatalistic conclusion. Two readings of necessity can be distinguished: absolute and relative necessity. The conditionals are valid for the latter reading. By the restrictor view of "if" in linguistics, the conditionals are not material implication. Instead, the if-clauses in them are devices for restricting the discourse domain that consists of possible futures. As a consequence, the argument is not sound. We present a dynamic temporal logic to formalize this idea. The base of this logic is CTL* without the operator until. The logic has a dynamic operator that shrinks models. The completeness of the logic is shown by reducing the dynamic operator.