{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T07:49:32Z","timestamp":1782460172764,"version":"3.54.5"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2022,2,16]],"date-time":"2022-02-16T00:00:00Z","timestamp":1644969600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,2,16]],"date-time":"2022-02-16T00:00:00Z","timestamp":1644969600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Log. Univers."],"published-print":{"date-parts":[[2022,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In the paper, we examine tableau systems for R. Epstein\u2019s logics of content relationship: <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathbf {D}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>D<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> (Dependence Logic), <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathbf {DD}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>DD<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> (Dual Dependence Logic), <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathbf {Eq}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>Eq<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> (Logic of Equality of Content), <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathbf {S}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>S<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> (Symmetric Relatedness Logic) and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathbf {R}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>R<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> (Nonsymmetric Relatedness Logic) (Epstein in The semantic foundations of Logic, Springer Science + Business Media, Dordrecht, (1990), cf. Epstein in Philos Stud 36:137\u2013173, 1979, Epstein in Rep. Math. Logic 21:19\u201334, 1987, Klonowski in Logic Log Philos, accepted for publication, Krajewski in J Non Class Logic 8:7\u201333, 1991). The first tableau systems for those logics were defined by Carnielli (Rep Math Logic 21:35\u201346, 1987). However, his approach has some limitations, for example, it requires a proof of functional completeness and axiomatization. Notwithstanding the first two constraints, it does not include all Epstein logics, e.g., logic <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathbf {Eq}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>Eq<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Unlike Carnielli\u2019s approach, here we use set-assignment semantics to determine those logics. Since syntax and semantics of a given logic usually determine a minimal syntax and structure of a tableau system for the logic along with other properties, we propose a uniform tableau framework for the logics determined by set-assignment semantics. What distinguishes our tableau systems is that they combine the features of tableaux for propositional logics and syllogistic logics when the problem of content of propositions is analysed in tableau proofs. To denote the content of propositions in the proofs, we use generalised labels (explored in the syllogistic context in Jarmu\u017cek and Gor\u00e9 (In: Fitting (ed.) Landscapes in Logic, College Publications, London, accepted)).<\/jats:p>","DOI":"10.1007\/s11787-022-00293-w","type":"journal-article","created":{"date-parts":[[2022,2,16]],"date-time":"2022-02-16T12:16:33Z","timestamp":1645013793000},"page":"195-219","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Tableaux for Logics of Content Relationship and Set-Assignment Semantics"],"prefix":"10.1007","volume":"16","author":[{"given":"Tomasz","family":"Jarmu\u017cek","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mateusz","family":"Klonowski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,2,16]]},"reference":[{"key":"293_CR1","first-page":"35","volume":"21","author":"WA Carnielli","year":"1987","unstructured":"Carnielli, W.A.: Methods of proofs of relatedness and dependence logic. 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