Answer Set Programming is a well-established paradigm of declarative programming in close relationship with other declarative formalisms such as SAT Modulo Theories, Constraint Handling Rules, PDDL and many others. Since its first informal editions, ASP systems are compared in the nowadays customary ASP Competition. The fourth ASP Competition, held in 2012/2013, is the sequel to previous editions and it was jointly organized by University of Calabria (Italy) and the Vienna University of Technology (Austria). Participants competed on a selected collection of benchmark problems, taken from a variety of research areas and real world applications. The Competition featured two tracks: the Model& Solve Track, held on an open problem encoding, on an open language basis, and open to any kind of system based on a declarative specification paradigm; and the System Track, held on the basis of fixed, public problem encodings, written in a standard ASP language.