Syntactic ASP forgetting with forks

Answer Set Programming (ASP) constitutes nowadays one of the most successful paradigms for practical Knowledge Representation and declarative problem solving. The formal analysis of ASP programs is essential for a rigorous treatment of specifications, the correct construction of solvers and the extension with other representational features. In this paper, we present a syntactic transformation, called the unfolding operator, that allows forgetting an atom in a logic program (under ASP semantics). The main advantage of unfolding is that, unlike other syntactic operators, it is always applicable and guarantees strong persistence, that is, the result preserves the same stable models with respect to any context where the forgotten atom does not occur. The price for its completeness is that the result is an expression that may contain the fork operator. Yet, we illustrate how, in some cases, the application of fork properties may allow us to reduce the fork to a logic program.