[om] Bug in definition of `strict_order'

[Scott L. Burson]

Hi,

I just now learned about OpenMath as I was using Google to look for some
definitions.

I seem to have found a bug in the definition of `strict_order', or more
precisely, in that of `antireflexive' on which it depends.  A strict order
is irreflexive, meaning `forall(x) ~R(x, x)'.  The current definition of
`antireflexive', however, says

   forall(x, y) R(x, y) -> R(y, x) -> x = y

But this definition does not work as part of the definition of
`strict_order', because by irreflexivity and transitivity, there are no x, y
such that `R(x, y) & R(y, x)'.  It could be written instead as something
like

   forall(x, y) (R(x, y) = R(y, x)) -> x = y

and then it would work for both reflexive and irreflexive relations.

Please CC: me in replies as I am not on the mailing list.

-- Scott
--
om at openmath.org  -  general discussion on OpenMath
Post public announcements to om-announce at openmath.org
Automatic list maintenance software at majordomo at openmath.org
Mail om-owner at openmath.org for assistance with any problems