{"type":"ScholarlyArticle","title":"Forgetting Auxiliary Atoms in Forks (Extended Abstract)","authors":[{"name":"Felicidad Aguado","slug":"felicidad-aguado","given":"Felicidad","family":"Aguado","affiliation":"University of Corunna , Spain"},{"name":"Pedro Cabalar","slug":"pedro-cabalar","given":"Pedro","family":"Cabalar","affiliation":"University of Corunna , Spain"},{"name":"Jorge Fandinno","slug":"jorge-fandinno","given":"Jorge","family":"Fandinno","affiliation":"University of Potsdam , Germany"},{"name":"David Pearce","slug":"david-pearce","given":"David","family":"Pearce","affiliation":"Universidad Politécnica de Madrid , Spain"},{"name":"Gilberto Pérez","slug":"gilberto-perez","given":"Gilberto","family":"Pérez","affiliation":"University of Corunna , Spain"},{"name":"Concepción Vidal","slug":"concepcion-vidal","given":"Concepción","family":"Vidal","affiliation":"University of Corunna , Spain"}],"abstract":"This work tackles 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.","doi":"10.24963/ijcai.2020/696","url":"https://ijcai.org/proceedings/2020/696","pdf":"https://ijcai.org/proceedings/2020/0696.pdf","markdown":"https://ijcai.org/proceedings/2020/696.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/696","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Journal track","track":"Journal track","number":696,"pages":{"first":5005,"last":5009},"keywords":["Knowledge Representation and Reasoning: Non-monotonic Reasoning, Common-Sense Reasoning","Knowledge Representation and Reasoning: Logics for Knowledge Representation","Knowledge Representation and Reasoning: Knowledge Representation Languages"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/24858/file_24858.m3u8","length_sec":284,"provider":"hls"}],"references":[{"position":1,"raw":"[Aguado et al., 2015] Felicidad Aguado, Pedro Cabalar, David Pearce, Gilberto Pérez, and Concepción Vidal. 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