You don't seem understand assignment.
Assignment has nothing to do with the relationship between relations
and logic or the relational model per se. The semantics of assignment
in a dbms language is exactly the same as it is in every programming
language.
You evaluate expressions using the current values of variables. You
can assign the value of an expression to a variable. This gives a new
overall state. The relationship between the values of one or more
variables in the post-(multiple-)assignment state and the expressions
that were used to express those values in the pre-assignment state
is simply (and tautologically) that the values of the assigned
expressions evaluated using the pre-assignment variable values are
the same as the values of the expressions consisting of just the
variable names evaluated using the post-assignment variable values
(ie the post-assignment values of the variables).
It doesn't matter what the types of variables are.
If a language allows assignment to an expression then the language
designer has to say what that means. Presumably the
post-assignment values of the variables in the assigned-to expressions
must be such that when they are evaluated in the post-assignment
state then their values are the same as the values of the assignedfrom
expressions evaluated in the pre-assignment state. If the language
processor cannot determine a single choice for the post-assignment
values of variables then the language designer has to give some sort
of
policy. But again, the particular assigned-from expressions have no
other relationship with the new state than that when evaluated in the
old state they give the values of the variables in the new state. The
particular assigned-from expressions don't matter, just their values.
