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{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T10:29:12Z","timestamp":1690453752024},"reference-count":40,"publisher":"Oxford University Press (OUP)","issue":"8","license":[{"start":{"date-parts":[[2021,2,24]],"date-time":"2021-02-24T00:00:00Z","timestamp":1614124800000},"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":[[2021,12,22]]},"abstract":"Abstract<\/jats:title>In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models evidence by a semiring. Hence justification terms can be interpreted as polynomial functions on that semiring. This provides an adequate semantics for evidence terms and clarifies the role of variables in justification logic. Moreover, the algebraic structure makes it possible to compute with evidence. Depending on the chosen semiring this can be used to model trust, probabilities, cost, etc. Last but not least the semiring approach seems promising for obtaining a realization procedure for modal fixed point logics.<\/jats:p>","DOI":"10.1093\/logcom\/exab007","type":"journal-article","created":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T15:49:27Z","timestamp":1612540167000},"page":"2084-2106","source":"Crossref","is-referenced-by-count":1,"title":["Semirings of Evidence"],"prefix":"10.1093","volume":"31","author":[{"given":"Michael","family":"Baur","sequence":"first","affiliation":[{"name":"Institute of Computer Science, University of Bern, 3012 Bern, Switzerland"}]},{"given":"Thomas","family":"Studer","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, University of Bern, 3012 Bern, Switzerland"}]}],"member":"286","published-online":{"date-parts":[[2021,2,24]]},"reference":[{"key":"2021121717353055800_ref1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/LICS.2017.8005088","article-title":"Cut-free completeness for modal mu-calculus","volume-title":"2017 32nd Annual ACM\/IEEE Symposium on Logic in Computer Science (LICS)","author":"Afshari","year":"2017"},{"key":"2021121717353055800_ref2","first-page":"22","article-title":"Reflective $\\lambda $-calculus","volume-title":"Proof Theory in Computer Science, International Seminar, PTCS 2001","author":"Alt","year":"2001"},{"key":"2021121717353055800_ref3","doi-asserted-by":"crossref","first-page":"346","DOI":"10.14778\/2095686.2095693","article-title":"Putting lipstick on pig: enabling database-style workflow provenance","volume":"5","author":"Amsterdamer","year":"2011","journal-title":"Proceedings of the VLDB Endowment"},{"key":"2021121717353055800_ref4","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1145\/1989284.1989302","article-title":"Provenance for aggregate queries","volume-title":"Proceedings of the Thirtieth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems","author":"Amsterdamer","year":"2011"},{"key":"2021121717353055800_ref5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/2687821","article-title":"Explicit provability and constructive semantics","volume":"7","author":"Artemov","year":"2001","journal-title":"Bulletin of Symbolic Logic"},{"key":"2021121717353055800_ref6","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/j.tcs.2006.03.009","article-title":"Justified common knowledge","volume":"357","author":"Artemov","year":"2006","journal-title":"Theoretical Computer Science"},{"key":"2021121717353055800_ref7","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1017\/S1755020308090060","article-title":"The logic of justification","volume":"1","author":"Artemov","year":"2008","journal-title":"The Review of Symbolic Logic"},{"key":"2021121717353055800_ref8","first-page":"61","article-title":"Tracking evidence","volume-title":"Logic and Computation, LNCS","author":"Artemov","year":"2010"},{"key":"2021121717353055800_ref9","first-page":"27","article-title":"On aggregating probabilistic evidence","volume-title":"LFCS 2016. 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