Re: Promotion of bare decorations & comparisons
Nate
Am 03.01.2013 15:15, schrieb Nathan T. Hayes:
Jurgen,
Motion 42 requires bare decorations dac, def and trv must promote to
decorated intervals Entire_dac, Entire_def and Entire_trv, respectively.
This gives two implications:
-- decoration emp is mostly superfluous, because only Empty can have
this decoration (except for ill decoration, which IMO still needs to be
dropped)
This makes the handling of empty sets easy.
-- certain comparison relations on bare decorations such as [1,2]
\subseteq def will always be true, and this seems very dangerous to me
bare decorations are dangerous, (hence they are optional)
the interpretation of DEF as an arbitrary nonempty interval is more
natural IMO than as Empty. "there is ab interval X so that [1,2]
\subseteq X"
In the decoration system with EIN, the decorated intervals Empty_EIN,
Empty_DAC, Empty_DEF and Empty_GAP are not contradictions. This means a bare
decoration can be defined as a compressed decorated empty set. This gives
the implications:
-- decoration NDF is not superfluous, because Empty can have any
decoration
-- all comparison relations on bare decorations are the same as the
equivalent comparison relations on Empty (since all bare decorations can be
viewed as compressed decorated empty sets), e. g., [1,2] \subseteq DEF is
false
I disagree in both cases
Juergen
Nate
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