Aguado, FelicidadCabalar, PedroFandiño, JorgePearce, DavidPérez, GilbertoVidal, Concepción2023-12-262023-12-262019F. Aguado, P. Cabalar, J. Fandinno, D. Pearce, G. Pérez, and, C. Vidal, "Forgetting Auxiliary Atoms in Forks", Artificial Intelligence, Vol. 275, pp. 575-601, Oct. 2019, doi: 10.1016/j.artint.2019.07.005http://hdl.handle.net/2183/34642©2019 Elsevier B.V. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/bync-nd/4.0/. This version of the article has been accepted for publication in Artificial Intelligence. The Version of Record is available online at https://doi.org/10.1016/j.artint.2019.07.005Versión final aceptada de: F. Aguado, P. Cabalar, J. Fandinno, D. Pearce, G. Pérez, and, C. Vidal, "Forgetting Auxiliary Atoms in Forks", Artificial Intelligence, Vol. 275, pp. 575-601, Oct. 2019, doi: 10.1016/j.artint.2019.07.005[Abstract]: In this work we tackle the problem of checking strong equivalence of logic programs that may contain local auxiliary atoms, to be removed from their stable models and to be forbidden in any external context. We call this property projective strong equivalence (PSE). It has been recently proved that not any logic program containing auxiliary atoms can be reformulated, under PSE, as another logic program or formula without them – this is known as strongly persistent forgetting. In this paper, we introduce a conservative extension of Equilibrium Logic and its monotonic basis, the logic of Here-and-There, in which we deal with a new connective ‘|’ we call fork. We provide a semantic characterisation of PSE for forks and use it to show that, in this extension, it is always possible to forget auxiliary atoms under strong persistence. We further define when the obtained fork is representable as a regular formula.engAtribución-NoComercial-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nc-nd/3.0/es/Answer set programmingNon-monotonic reasoningEquilibrium logicDenotational semanticsForgettingStrong equivalencejournal articleopen access10.1016/j.artint.2019.07.005