\pushoverloadmode

    \immutable\Umathdictdef\vdash 1 \mathbinarylogicaldictionary  "22A2 \mathrelationcode 0 "22A2
    \immutable\Umathdictdef\leq   1 \mathbinaryrelationdictionary "2264 \mathrelationcode 0 "2264
    \immutable\Umathdictdef\geq   1 \mathbinaryrelationdictionary "2265 \mathrelationcode 0 "2265

    \startluacode
        mathematics.dictionaries.registercharacter("binary logical", 0x22A2,"implies")
        mathematics.dictionaries.registercharacter("binary relation",0x2264,"less or equal")
        mathematics.dictionaries.registercharacter("binary relation",0x2265,"greater or equal")
    \stopluacode

    \immutable\Umathdictdef\ndivides 1 \mathbinaryarithmicdictionary "2224 \mathbinarycode   0 "2224
    \immutable\Umathdictdef\nmid     1 \mathbinaryrelationdictionary "2224 \mathrelationcode 0 "2224

    \startluacode
        mathematics.dictionaries.registercharacter("binary arithmic",0x2224,"don't divide")
        mathematics.dictionaries.registercharacter("binary relation",0x2224,"undivided")
    \stopluacode

\popoverloadmode


%definecolor[dictionary:default]
\definecolor[dictionary:binary arithmic]       [r=.5]
%definecolor[dictionary:binary linear algebra]
\definecolor[dictionary:binary logical]        [r=.5,b=.5]
\definecolor[dictionary:binary relation]       [g=.5]
%\definecolor[dictionary:binary set]
%definecolor[dictionary:constant arithmic]
\definecolor[dictionary:constant set]          [s=.5]
%definecolor[dictionary:differential]
%definecolor[dictionary:integral]
%definecolor[dictionary:interval]
%definecolor[dictionary:lambda]
%definecolor[dictionary:limit]
\definecolor[dictionary:nary arithmic]         [r=.5,g=.5]
%definecolor[dictionary:nary constructor]
%definecolor[dictionary:nary functional]
%definecolor[dictionary:nary linear algebra]
%definecolor[dictionary:nary logical]
%definecolor[dictionary:nary minmax]
\definecolor[dictionary:nary relation]         [b=.5]
%definecolor[dictionary:nary set list]
%definecolor[dictionary:nary set relation]
%definecolor[dictionary:nary set]
%definecolor[dictionary:nary statistics]
%definecolor[dictionary:partial]
%definecolor[dictionary:product]
%definecolor[dictionary:quantifier]
%definecolor[dictionary:unary arithmic]
%definecolor[dictionary:unary elementary]
%definecolor[dictionary:unary functional]
%definecolor[dictionary:unary linear algebra]
%definecolor[dictionary:unary logical]
%definecolor[dictionary:unary set]
%definecolor[dictionary:unary vector]

%mathdictproperties \plusone
\mathdictgroup      \mathdefaultdictionary

\enabletrackers[math.dictionaries]

\starttext

\definemathgroupset[demoa][binary arithmic,nary relation]
\definemathgroupset[demob][binary relation,nary relation]

% \tracingmath2 \tracingonline2 \showmakeup[mathglue]

\startbuffer[a]
$ a \leq b \geq c < d > e = \naturalnumbers = ℕ$
\stopbuffer

\getbuffer[a] \blank

\startbuffer[b]
$ a \ndivides b \nmid c ^ {a \ndivides b \nmid c} + d ∤ e \times f > g × h - i $
\stopbuffer

{\setmathgroupset[binary arithmic]\getbuffer[b]} \blank
{\setmathgroupset[binary relation]\getbuffer[b]} \blank

{\setmathgroupset[demoa]\getbuffer[b]} \blank
{\setmathgroupset[demob]\getbuffer[b]} \blank

{\setmathgroupset[demoa]\getbuffer[a]} \blank
{\setmathgroupset[demob]\getbuffer[a]} \blank

\stoptext