Jason (jcreed) wrote,

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.
Tags: logic, math, modal
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