word - Monoalphabetic Equation

A set of letters has been replaced by $a$, $b$, $c$, and $d$.
Following are some of the words that consist of those letters, and their meaning:

$abc = a\ title\ (n.)$

$abcd = a\ title\ > abc\ (n.),\ give\ cbad\ to\ (v.)$

$Dcba ⊂ (a\ title\ > abcd)\ (n.)$

$Dcba = Represents\ what\ often\ comes\ before\ or\ after\ bcd\ (n.)$

$bcd = ARGHH!\ (n.)$

$cbad = move\ abc\ to\ abcd\ (v.),\ \land (v.)$

What are the letters that $a$, $b$, $c$, and $d$ replace, respectively?

Answer

a, b, c, d are

s, i, r, e

"sir" = a title (given to a man)
"sire" = a title greater than "sir" (given to a king), or to give "rise" to
"Eris" = Name (names are titles) of someone greater than a "sire" (specifically, a greek goddess, see below)
"Eris" = Greek goddess of strife (strife can lead to or cause "ire", coming before or after it)
"ire" = anger

"rise" = move from "sir" to "sire", or to go up

etc.