A Dynamic Solution to the Puzzle of Sea Battle

11/08/2017

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by   Fengkui Ju, et al.

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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.