Forgetting in Answer Set Programming with Anonymous Cycles

It is now widely accepted that the operation of forgetting in the context of Answer Set Programming [10, 18] is best characterized by the so-called strong persistence, a property that requires that all existing relations between the atoms not to be forgotten be preserved. However, it has been shown that strong persistence cannot always be satisfied. What happens if we must nevertheless forget? One possibility that has been explored before is to consider weaker versions of strong persistence, although not without a cost: some relations between the atoms not to be forgotten are broken in the process. A different alternative is to enhance the logical language so that all such relations can be maintained after the forgetting operation. In this paper, we borrow from the recently introduced notion of fork [1] – a conservative extension of Equilibrium Logic and its monotonic basis, the logic of Here-and-There – which has been shown to be sufficient to overcome the problems related to satisfying strong persistence. We map this notion into the language of logic programs, enhancing it with so-called anonymous cycles, and we introduce a concrete syntactical forgetting operator over this enhanced language that we show to always obey strong persistence.