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 (There's stuff like the outdated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but that is a leftover or outdated logic notation in general.)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
