Logic for the Sea-Battle - possible moves

 

In this article I explore the possibility of restating - for better comparison - some of the most important formal approaches to the sea-battle problem (as first stated in Aristotle's On interpretation 9) in terms of combined temporal and modal logic (CTML).

I compare the outlines of two two-valued versions of CTML (one with a strong and one with a weak future operator) and a three-valued version.

I argue that the standard objection against so-called "actualism", i.e. that it involves the presupposition of an actual future as different from possible futures, is not true and that therefore "actualism" is a misnomer.

The relation between different future operators and different truth concepts is discussed, and a suggestion is made how to make systematic sense of the traditionally obscure notions of "definitely / indefinitely true / false".

I conclude that, from a systematical point of view, a two-valued logic containing a weak future operator is to be favoured.

 

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