Delay Circuit after Logic Gate
A 555 would certainly be a viable component to realize this!
However, it would also be a bit of a complex solution, if your accuracy requirements are low.
Assuming the circuit you want to trigger is also a logic gate with a well-defined low-high threshold that you can rely on, it would be much easier to charge a capacitor with your AND's output slowly (when high) and discharge it quickly (when low). Something like:
                D        Some other circuit's input
   -----   ----|&lt;----
--|     \  |        |     |\
  | AND |--·-====---·-----| &gt;
--|     /      R    |     |/ 
   -----            = C
                    |
                    V GND

What happens here is that the output of your AND gate charges the (let's assume) previously uncharged C through R. R limits the current very much, and thus takes time; assuming R is high enough (e.g. 100kΩ) to never &quot;significantly&quot; load the AND gate's output, we can model the gate output as a constant voltage source, and that means the voltage across C follows an \$U(t)=U_{max}·(1-e^{\tau t})\$ function, ie. it's nice and monotonously growing. You can control \$\tau\$ through choice of R and C.
At some point, the threshold voltage of your &quot;other triggered circuitry&quot; is reached. If you tuned this correctly, that's after 0.5s (do use an adjustable resistor - it makes fine-tuning easy).
This charging happens for as long as the output voltage of your AND is higher than the voltage over C.
If, however, the AND toggles its output and  becomes lower than the voltage over C, then D is not in reverse bias anymore - it starts conducting, and quickly so, thus discharging C relatively rapidly. (Hence, use a large R and a low C value, if possible, as that discharge current could else fry your AND gate. Also, use a Schottky diode as D - they have low forward voltage.)