On 7/31/2011 12:50 PM, Avril Styrman wrote:
> what is the practical difference in applying Dunn's approach vs.
> applying Kripke's approach? Suppose that you are implementing a chess
> program. You have a repository where are all the possible games, all the
> possible sequences of the discrete steps that can be taken in chess.
> Now, how do I apply D here, and how do I apply K here? What's the
> difference? (01)
The simple answer is that *every* application uses Dunn's method. (02)
Nobody can observe possible worlds or derive any information from them.
Every statement that anybody makes about possible worlds is derived
from some specification -- formal, informal, or just imagined in
somebody's head. (03)
That specification generates the laws of each world, the facts of
each world, and Kripke's accessibility relation between worlds. (04)
For your example of chess, the laws are the rules of the game, as
specified by FIDE, and all implications derivable from those rules. (05)
The set of possible worlds consists of all games generated from
the starting position by making legal moves that terminate in
a win by white, a win by black, or a draw. (06)
All worlds have the same laws. The facts of each world (game)
consist of the set of all FOL statements that are true of that game. (07)
From any possible world (game), Kripke's accessibility relation
determines the games that can be reached from that game by changing
one move in the play. (08)
One correction: I don't think you mean a repository "of all the
possible games". That is far too huge to store. But there are
many repositories of actual games that have been played. Those
repositories contain a tiny subset of all possible games. (09)
John (010)
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