So, basically it's a chain reaction from the top down to SV1.
If BP1 and BP2 are pressed, CR3 energizes. On the second rung, if CR3 is energized, CR4 de-energizes (or, CR4 is energized as long as CR3 is not) but will also de-energize if BP3 is pressed (since it's a NC pushbutton). On the third rung, SV1 will energize as long as CR4 is de-energized.
So, to generate a truth table: (1 is electrical continuity, not whether the button is pressed)
BP1 | BP2 | BP3 | CR3 | CR4 | SV1
------------------------------------------
0 | 0 | 0 | 0 | 0 | 1
0 | 0 | 1 | 0 | 1 | 0
0 | 1 | 0 | 0 | 0 | 1
0 | 1 | 1 | 0 | 1 | 0
1 | 0 | 0 | 0 | 0 | 1
1 | 0 | 1 | 0 | 1 | 0
1 | 1 | 0 | 1 | 0 | 1
1 | 1 | 1 | 1 | 1 | 0
Now, you mentioned something about optimizing this logic. Are there any requirements? Do you have to keep CR3 and CR4? can you change the type of switch?