Abstract A new semantic forgetting for answer set programs (ASP), called SM-forgetting, is proposed in the paper. It distinguishes itself from the others in that it preserves not only skeptical and credulous consequences on unforgotten variables, but also strong equivalence – forgetting same variables in strongly equivalent logic programs has strongly equivalent results. The forgetting presents a positive answer to Gabbay, Pearce and Valverde’s open question – if ASP has uniform interpolation property. We also investigate some properties, algorithm and computational complexities for the forgetting. It shows that computing the forgetting result is generally intractable even for Horn logic programs.