{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T14:06:29Z","timestamp":1743084389044,"version":"3.40.3"},"publisher-location":"Cham","reference-count":25,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031384981"},{"type":"electronic","value":"9783031384998"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,9,2]],"date-time":"2023-09-02T00:00:00Z","timestamp":1693612800000},"content-version":"vor","delay-in-days":244,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Using Isabelle\/HOL, we verify the state-of-the-art decision procedure for multi-level syllogistic with singleton (<jats:bold>MLSS<\/jats:bold> for short), which is a quantifier-free fragment of set theory. We formalise its syntax and semantics as well as a sound and complete tableau calculus for it. We also provide an executable specification of a decision procedure that exhaustively applies the rules of the calculus and prove its termination. Furthermore, we extend the calculus with a lightweight type system that paves the way for an integration of the procedure into Isabelle\/HOL.<\/jats:p>","DOI":"10.1007\/978-3-031-38499-8_28","type":"book-chapter","created":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T23:03:25Z","timestamp":1693609405000},"page":"491-508","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Towards a\u00a0Verified Tableau Prover for\u00a0a\u00a0Quantifier-Free Fragment of\u00a0Set Theory"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0222-6858","authenticated-orcid":false,"given":"Lukas","family":"Stevens","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,9,2]]},"reference":[{"key":"28_CR1","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/3-540-69778-0_16","volume-title":"Automated Reasoning with Analytic Tableaux and Related Methods","author":"B Beckert","year":"1998","unstructured":"Beckert, B., Hartmer, U.: A tableau calculus for quantifier-free set theoretic formulae. 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