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The puzzle of sea battle involves an argument that is an instantiation ofreasoning by cases. Its premises include the conditionals "if there is a/no seabattle tomorrow, it is necessarily so". It has a fatalistic conclusion. Tworeadings 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 thatconsists of possible futures. As a consequence, the argument is not sound. Wepresent a dynamic temporal logic to formalize this idea. The base of this logicis CTL* without the operator until. The logic has a dynamic operator thatshrinks models. The completeness of the logic is shown by reducing the dynamicoperator.

A Dynamic Solution to the Puzzle of Sea Battle