# 4(e)

Posted by slow_eddy
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 4(e) May 28, 2011 11:55PM Registered: 10 years ago Posts: 3,496 Rating: 1
1. assumption-box-1... p ....
2. ... assumption-box-2.... box ~p (as per hint)
3. ... ~p ........... T, 2.
4. ... "bottom" ............ ~e 1,3. .... end of assumption-box-2
5. ~ box ~p ..... ~i 2-4
6. box ~ box ~p ...... 5 , 5.
7. box diamond p ......... Def. diamond. ..... end of assumtion-box-1
8. p -> box diamond p .................... ->i 1-7

How do we introduce the "definition of diamond" construct? For now this looks an adequate way to justify it, but maybe there's some special notation in the book. Anyone know?
 Re: 4(e) May 30, 2011 10:38AM Registered: 8 years ago Posts: 363 Rating: 0
I got pretty much the same answer except I redefined the question, without the box and I stated that diamond is equivalent to ~box~ and I left the end of the answer as is simply because all statements were done b4 the answer was attempted.
 Re: 4(e) May 30, 2011 12:21PM Registered: 10 years ago Posts: 3,496 Rating: 1
Yes, that sounds good. Give the def for diamond before doing anything, and then work purely in terms of box. No real need to give the answer in terms of diamond at the end, then... but if diamond is what's specified, it's probably safer and "more complete" to do so? It's no extra work, really.
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