{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,13]],"date-time":"2025-12-13T23:08:58Z","timestamp":1765667338229,"version":"3.37.3"},"reference-count":18,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2021,4,5]],"date-time":"2021-04-05T00:00:00Z","timestamp":1617580800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["075-15-2019-1614"],"award-info":[{"award-number":["075-15-2019-1614"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,7,23]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The idea of treating negation as a modality manifests itself in various logical systems, especially in Do\u0161en\u2019s propositional logic $\\textsf {N}$, whose negation is weaker than that of Johansson\u2019s minimal logic. Among the interesting extensions of $\\textsf {N}$ are the propositional logics $\\textsf {N}^{\\ast }$ and $\\textsf {Hype}$; the former was proposed in Cabalar et al. (2006, Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning, 25\u201336), while the latter has recently been advocated in Leitgeb (2019, J. Philos. Logic, 48, 305\u2013405), but was first introduced in Moisil (1942, Disquisitiones Math. et Phys., 2, 3\u201398). I shall develop predicate versions of $\\textsf {N}$ and $\\textsf {N}^{\\ast }$ and provide a simple Routley-style semantics for the predicate version of $\\textsf {Hype}$. The corresponding strong completeness results will be proved by means of a useful general technique. It should be remarked that this work can also be seen as a starting point for the investigation of intuitionistic predicate modal logics.<\/jats:p>","DOI":"10.1093\/logcom\/exab025","type":"journal-article","created":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T20:13:15Z","timestamp":1615839195000},"page":"1330-1355","source":"Crossref","is-referenced-by-count":6,"title":["Negation as a modality in a quantified setting"],"prefix":"10.1093","volume":"31","author":[{"given":"Stanislav O","family":"Speranski","sequence":"first","affiliation":[{"name":"Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, 119991, Russia"}]}],"member":"286","published-online":{"date-parts":[[2021,4,5]]},"reference":[{"key":"2021080400162643100_ref1","first-page":"25","article-title":"Logical foundations of well-founded semantics","volume-title":"Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning (KR 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