{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:48:04Z","timestamp":1760240884578,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,10,17]],"date-time":"2019-10-17T00:00:00Z","timestamp":1571270400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004281","name":"Narodowe Centrum Nauki","doi-asserted-by":"publisher","award":["2017\/25\/B\/HS1\/00503"],"award-info":[{"award-number":["2017\/25\/B\/HS1\/00503"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We study deduction systems for the weakest, extensional and two-valued non-Fregean propositional logic    SCI   . The language of    SCI    is obtained by expanding the language of classical propositional logic with a new binary connective \u2261 that expresses the identity of two statements; that is, it connects two statements and forms a new one, which is true whenever the semantic correlates of the arguments are the same. On the formal side,    SCI    is an extension of classical propositional logic with axioms characterizing the identity connective, postulating that identity must be an equivalence and obey an extensionality principle. First, we present and discuss two types of systems for    SCI    known from the literature, namely sequent calculus and a dual tableau-like system. Then, we present a new dual tableau system for    SCI    and prove its soundness and completeness. Finally, we discuss and compare the systems presented in the paper.<\/jats:p>","DOI":"10.3390\/axioms8040115","type":"journal-article","created":{"date-parts":[[2019,10,17]],"date-time":"2019-10-17T11:07:59Z","timestamp":1571310479000},"page":"115","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Deduction in Non-Fregean Propositional Logic SCI"],"prefix":"10.3390","volume":"8","author":[{"given":"Joanna","family":"Goli\u0144ska-Pilarek","sequence":"first","affiliation":[{"name":"Institute of Philosophy, University of Warsaw, 00\u2013927 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4886-5607","authenticated-orcid":false,"given":"Magdalena","family":"Welle","sequence":"additional","affiliation":[{"name":"Institute of Philosophy, University of Warsaw, 00\u2013927 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,17]]},"reference":[{"key":"ref_1","first-page":"105","article-title":"Non-Fregean logic and theories","volume":"11","author":"Suszko","year":"1968","journal-title":"Analele Univ. 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Math."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/8\/4\/115\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:27:08Z","timestamp":1760189228000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/8\/4\/115"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,17]]},"references-count":17,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,12]]}},"alternative-id":["axioms8040115"],"URL":"https:\/\/doi.org\/10.3390\/axioms8040115","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2019,10,17]]}}}