{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T17:37:58Z","timestamp":1782927478232,"version":"3.54.5"},"reference-count":59,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T00:00:00Z","timestamp":1639353600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,1,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Novel three-valued non-deterministic level semantics for modal logics $\\textbf {T}$ and $\\textbf {S4}$ are presented. A criterion for partial level valuations is given, making it possible to create truth tables. Additionally, semantics and truth tables for $\\textbf {0}$ (defined as $\\textbf {PC}$ plus rule of necessitation) and $\\textbf {0T}$ with only two values are based on Ivlev\u2019s work. We need Kearns\u2019 notion of level valuations: a generalization of Dugundji\u2019s theorem shows that there is no non-deterministic semantics for modal logics up to $\\textbf {S5}$, containing the rule of necessitation.<\/jats:p>","DOI":"10.1093\/logcom\/exab068","type":"journal-article","created":{"date-parts":[[2021,10,20]],"date-time":"2021-10-20T01:10:40Z","timestamp":1634692240000},"page":"129-157","source":"Crossref","is-referenced-by-count":14,"title":["Truth tables for modal logics T and S4, by using three-valued non-deterministic level semantics"],"prefix":"10.1093","volume":"32","author":[{"given":"Lukas","family":"Gr\u00e4tz","sequence":"first","affiliation":[{"name":"Software Engineering Group, Department of Computer Science, Technische Universit\u00e4t Darmstadt, Darmstadt, 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