Top.Mail.Ru
? ?
Notes from a Medium-Sized Island [entries|archive|friends|userinfo]
Jason

[ website | My Website ]
[ userinfo | livejournal userinfo ]
[ archive | journal archive ]

[Apr. 4th, 2013|06:08 pm]
Jason
[Tags|, , ]

Talked some more with Rowan today in which I discovered the fascinating fact that the modal Diamond in "Pfenning-Davies K" according to the recent "Weather Report" draft is not quite what I would have predicted from the modal encoding I worked out with Sean last summer. A shibboleth proposition is:

<><>0 |- <>0

which my system (given a krikpe relation with no particular properties) will nonetheless prove, and which Pfenning-Davies K does not.

This is because their <>L rule is like

A |- C
----------------
G, <>A |- C poss

and mine turns out to be something way weirder, which is close to being like

A |- poss
----------------
G, <>A |- C poss

with some sort of abomination where the conclusion is poss (thus permitting further <>L decompositions) but there's nothing there, so my system still does refuse to prove

<><>A |- <>A

in general, just like you'd expect from K.
LinkReply