In my search for a Quantum Logic I've started looking at formalisations of logic for classical mechanics. This seems like a reasonable place to start.
Of course some of you know that you can easily get an intuisionistic logic from spatial operations where where meet and join are specified by intersection and union (almost, we have to be careful about boundaries). For more on how this is done and it's connection with modal logic, look at thatlogicblog.
This is nearly enough to start reasoning about classical mechanics since we can view space as 4 dimensionally static. I haven't worked through it yet since I've been a bit busy. I'll update you later.
[Update: See The Logic of Space Part II ]