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Unlike first-order temporal logics for hyperproperties, such as HyperLTL, Hyper<jats:sup>2<\/jats:sup>LTL can express complex epistemic properties like common knowledge, Mazurkiewicz trace theory, and asynchronous hyperproperties. The model checking problem of Hyper<jats:sup>2<\/jats:sup>LTL is, in general, undecidable. For the expressive fragment where second-order quantification is restricted to smallest and largest sets, we present an approximate model-checking algorithm that computes increasingly precise under- and overapproximations of the quantified sets, based on fixpoint iteration and automata learning. We report on encouraging experimental results with our model-checking algorithm, which we implemented in the tool\u00a0.<\/jats:p>","DOI":"10.1007\/978-3-031-37703-7_15","type":"book-chapter","created":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T17:02:15Z","timestamp":1689613335000},"page":"309-332","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Second-Order Hyperproperties"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6234-5651","authenticated-orcid":false,"given":"Raven","family":"Beutner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4280-8441","authenticated-orcid":false,"given":"Bernd","family":"Finkbeiner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3566-0338","authenticated-orcid":false,"given":"Hadar","family":"Frenkel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3184-6335","authenticated-orcid":false,"given":"Niklas","family":"Metzger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,7,18]]},"reference":[{"key":"15_CR1","doi-asserted-by":"publisher","unstructured":"Alur, R., Henzinger, T.A.: A really temporal logic. 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