A computer architecture can be seen as a turing machine. But how to express interrupt in turing machine?
I think that we can see interrupt a the flowing condition statement. This statement get executed whenever a instruction is executed.
if (condition_1)
condition_1 interrupt service routine
else if (condition_2)
condition_2 interrupt service routine
....
else if (condition_n)
condition_n interrupt service routine
else
do the normal computation. For example, execute the current instruction.
What I say is a only my rough thinking. It is by no means technically correct.