Re: symbols/codepoints for necessity and possibility in modal logic

Hi Jörg,

Thanks for the info!

> U+25C7 WHITE DIAMOND
> is the best choice
I'm with you in that for now I'll go with
     ⟨◻ (U+25FB), ◇ (U+25C7)⟩
as the pair of choice, pending further decisions; see also what I'm
writing further down. Or objections from experts stating that the symbol
properties are not suited for a unary mathematical prefix operator,
whatever an "operator" is ("unary operator" is (at least) programming
terminology, found when operator precedence is discussed, so it seems
appropriate).

> followed by
> U+27E1 WHITE CONCAVE-SIDED DIAMOND • never (modal operator)
I'm assuming the charts are reliable in that this in some community (eg:
temporal modal logic) denotes a "never" modality. If so, it definitely
can't be used in place of a (straight-shaped, ordinary, 90°/square)
diamond. The abstract shapes are just clearly different in this case. So
– I wouldn't pick this one. Again: to me, ⬦ (U+2B26) is the next
contender, but that's admittedly impressionistic.

Just because you're mentioning this:
> I couldn't locate WHITE DIAMOND WITH LEFTWARDS TICK in UNicode.
"WHITE DIAMOND WITH RIGHTWARDS TICK" isn't in Unicode either, but then I
don't know whether you'd need such a character.

> (U+2662 WHITE DIAMOND SUIT would also look OK
I thought so too at first, but you are right about this:
> but I think this is symbol abuse
and I also think the lozenge-shape works against this character.

> For the properties of mathematical symbols, see also
> http://www.unicode.org/reports/tr25/
> ---but I have to admit that the report does not answer the specific
> question posed here.
Table 2.5 there (pp. 19-21) is actually quite helpful. From it I would
judge that ◇/U+25C7 is the only sensible choice for the diamond.
Depending on whether you want to match area or height as closely as
possible, it also seems like you really want to pair it up with either
◻/U+25FB or □/U+25A1; it's not clear this is a precise match, but this
is probably the best reasoning. I'd go with the former [my email program
displays the latter as a smaller symbol, but the former is supposed to
be smaller than the latter].

But this one
> Maybe this mapping table is more useful (but harder to read):
> http://www.w3.org/Math/characters/unicode.xml
I don't find helpful in resolving this issue.

Now that I'm reading this
> I'd consider U+22C4 DIAMOND OPERATOR as wrong because it is used as a
> binary operator
I'm thinking that "binary infix symbol" and "unary prefix symbol" might
be appropriate terminology too.

> which has a very different spacing than the unary modal operator
> needed here
The idea that a math symbol has inherent spacing is popular in the LaTeX
community, though I don't know where else this view exists. There it's
the math character class that a symbol is assigned to (⋄/U+22C4 is a
"binary relation" symbol). Of course the math character class can be
modified ad-hoc very easily, eg you can change it from "binary relation"
to "relation symbol" by writing "\mathrel{/whatever/}". (Now if this
doesn't make for messed-up terminology. And the TeXbook seems to use
"binary operation", plus "operator" by itself has its own association in
the TeX world, namely with summation and product symbols and other such
quantifying prefix accumulators.) It's my opinion that it might not be
good to think of such TeX math character classes as fixed anyways.

Stephan
Received on Fri Jul 19 2013 - 06:04:07 CDT