{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:02Z","timestamp":1753894382924,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2021,12,2]],"date-time":"2021-12-02T00:00:00Z","timestamp":1638403200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We introduce PHFL, a probabilistic extension of higher-order fixpoint logic,\nwhich can also be regarded as a higher-order extension of probabilistic\ntemporal logics such as PCTL and the $\\mu^p$-calculus. We show that PHFL is\nstrictly more expressive than the $\\mu^p$-calculus, and that the PHFL\nmodel-checking problem for finite Markov chains is undecidable even for the\n$\\mu$-only, order-1 fragment of PHFL. Furthermore the full PHFL is far more\nexpressive: we give a translation from Lubarsky's $\\mu$-arithmetic to PHFL,\nwhich implies that PHFL model checking is $\\Pi^1_1$-hard and $\\Sigma^1_1$-hard.\nAs a positive result, we characterize a decidable fragment of the PHFL\nmodel-checking problems using a novel type system.<\/jats:p>","DOI":"10.46298\/lmcs-17(4:15)2021","type":"journal-article","created":{"date-parts":[[2021,12,9]],"date-time":"2021-12-09T07:50:12Z","timestamp":1639036212000},"source":"Crossref","is-referenced-by-count":0,"title":["A Probabilistic Higher-order Fixpoint Logic"],"prefix":"10.46298","volume":"Volume 17, Issue 4","author":[{"given":"Yo","family":"Mitani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naoki","family":"Kobayashi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takeshi","family":"Tsukada","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2021,12,2]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/8790\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/8790\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:18:39Z","timestamp":1687292319000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/6939"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,2]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-17(4:15)2021","relation":{"has-preprint":[{"id-type":"arxiv","id":"2011.14303v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2011.14303v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2011.14303","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2011.14303","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2021,12,2]]},"article-number":"6939"}}