Re: A Brief Note on Notation


adamgolding@xxxxxxxxx wrote:
> George Dance wrote:
> > IMO, when it comes to notation logic today is much like mathematics 500
> > years
> > ago. To me, that's a negative; I'd like to see a common notation, and
> > I think that one worthy goal of logic lists like this would be to agree
> >
> > on and work towards adoption of, a common notation.
>
>
> i agree. for starters let's rally against the 'horseshoe'
> operator--it's too easily confused with set inclusion--the single
> arrow, ->, is preferrable. accordingly we should use the <-> for
> material equivalence.

Agreed. Both also have the big advantage of being reproducible at the
keyboard (unlike the horseshoe, or the triple bar for equivalence). I
could go with > for conditional, but <> is confusing (I'd prefer that
as the sign for possibility) so one needs the tail there; in which case
it's consistent to add one to the conditional as well.

also, i would like to see more use of the
> reverse arrow, <- -- it often is disallowed entirely but to me allows
> for a greaty fluidity in constructing formulae


Well, OK - I don't see exactly how one would use it, but I see no
reason not to so long as it's strictly defined (I assume, as:
A <- B =df. B -> A).

> i'm also against the (x) for universal quantification--it doesn't mix
> well in mathematical contexts, so we should use \-/, since it works in
> all contexts.

I've always used (x) (because it's keyboard-friendly), but I'm starting
to come around to Ax and Ex - easier to type, less brackets to worry
about, stuff like that. I suppose that using those requires a
convention to *not* use A or E as predicates, as that would be
confusing as well.

> i like both ^ and * for and, but * makes complex formulas easier to
> read, IMO, although the ^ v symmetry is good for deMorgan's rule...

I like ^ and V for the same reason (and that symmetry would also be a
reason to use > for the conditional and < for your backwards
conditional, BTW); while I don't like * (for your reason, that's it
could easily be confused in some math contexts).

Thank you for your feedback.

.

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