Though relays and logic gates are different components, they work in a comparable way. In this article you can see how I converted a relay based schematic to a logic gates diagram.
About the relay logic circuit
It is supposed to operate a roll shutter motor and features two run buttons, two limit switches and a safety switch. When a button is pressed, even for a bit, the motor starts running; it will be stopped by the limit switch, or by pressing any button, so it works like a car window.
The double function of the buttons is due to the relays K1 and K2, that are both off at the start condition. When a button is pressed the relay K1 turns on. When it is released the relays are both on. By pressing a button again the relay K1 backs off, while the other one keeps on. By releasing the button the relays are both off. This circuit schematic has been tested with a PLC ladder logic simulator.
From relays to logic gates
Since they work in a similar way, I associated the logic gates to the relay logic connections. Parallel and series connections, respectively, correspond to AND/OR logic gates. Normally closed contacts are associated to NOT logic gates.