PLC's are a software mode of replacement for machine logic control that was originally done with relays.
They take the system inputs and after processing the internal logic, the result placed on physical outputs.
The Boolean type logic is often programmed using either Ladder or Mnemonic format.
If you do a Google of PLC, Boolean or Ladder program, you should find more information.
Al.
CNC, Mechatronics Integration and Custom Machine Design
“Logic will get you from A to B. Imagination will take you everywhere.”
Albert E.