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

From: Stephan Stiller <stephan.stiller_at_gmail.com>
Date: Fri, 19 Jul 2013 00:43:53 -0700

> 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