Unicode cannot be the arbiter of mathematical (or other) notation, but,
within limits, you could ask for some annotations if this would help
ensure that there's some uniformity in how people pick symbols for
certain purposes.
Why not contact the relevant publishers and find out what they are using?
A./
On 7/19/2013 12:43 AM, Stephan Stiller wrote:
What is wrong with using DIAMOND OPERATOR?
"wrong" is strong wording and goes beyond what I suggested or implied,
but it's not clear to a user of Unicode that it's the right fit
either. There are a couple of indicators factoring in:
* The charts mention modal logic in conjunction with ◻ (U+25FB) and
⟠ (U+27E0) but not with ⋄ (U+22C4).
* The glyph in the code charts is tiny (and that of Cambria Math is
tiny as well). Typographically you see various things (a lozenge,
fallback to letter-M) in esp older books, but it feels like it's
meant to be an orthogonal diamond of perhaps slightly less area
than the box but descending a little above and below the box,
which is somewhat taller than x-height. The book by {Blackburn, de
Rijke, Venema} has glyphs that look right. This is more than a
guess: it makes sense if they have similar visual weight, as they
are – literally – defined to be duals of one another; but whether
you can make them geometrically congruent symbols of equal area I
haven't tested (this might have the diamond ascend too far).
* The vague notion of "operator" (a word with different meanings in
math, from /logical relation/ to /[non-logical/non-relational]
mapping of type A×A→A or perhaps A×A→B/ to /(linear) map (between
say vector spaces) in linear algebra/) in this context (in the
code charts) seems to refer to something like my middle meaning,
which is likely to use a smaller symbol around x-height in
placement and dimensions.
* The glyph of ⬦ (U+2B26) seems to have a more appropriate name, but
in the charts I like ◇ U+25C7. The differently sized square-like
symbols are hard to semantically tell apart in/from the charts anyway.
* These symbols are the first two visually distinct ones you define
in modal logic, so they're well-known and standardized in meaning
for anyone who had had contact with the field. It's surprising
they're not explicitly named in the charts. (There's stuff like
the outdated horseshoe for logical implication popping up in the
relevant books, but that is a leftover or outdated logic notation
in general.) So for box and diamond it's quite reasonable to be
expecting a standard math font to provide them just right out of
the box; for whatever commonly used box-like symbols in math there
are, one would assume that there are corresponding codepoints;
otherwise you'd have to choose a different font.
Stephan
