The original purpose of the PLC ladder logic programming method was to allow the then existing power electrical engineers and technicians to program a PLC application with just the knowledge and experience they used in designing and building power and control relay cabinets. These first came out in the mid to late 1970s. It made heavy use of a primitive CRT based GUI format where they defined 'coils' output and 'contacts' inputs coorosponding to real digital inputs and outputs, and could if required 'wire' them to internal function blocks like counters, shift registers, timers, etc.
Today there is little reason to limit ones self to just creating such ladder logic applications, and most modern PLC offer an alternate 'higher level' programming language to support user created programs. The biggest advantage to using PLCs are there very rugged and reliable construction rather then their ability of being able to be programmed in 'ladder logic'. If one was going to emulate a PLC system with an arduino board it would be pretty dumb in my opinion to not just program the application directly in the arduino C/C++ sketch language, rather then trying to implement a ladder logic interrupter 'programmer'/runtime emulator. Lots of work to do that with little payback benefits, just learn to program in C/C++. 
Lefty