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Extending a logic to its non-Fregean version involves introducing a new connective \n \n $$\\equiv $$<\/jats:tex-math>\n \n \u2261<\/mml:mo>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> that allows to separate denotations of sentences from their logical values. Intuitively, \n \n $$\\equiv $$<\/jats:tex-math>\n \n \u2261<\/mml:mo>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> combines two sentences \n \n $$\\varphi $$<\/jats:tex-math>\n \n \u03c6<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> and \n \n $$\\psi $$<\/jats:tex-math>\n \n \u03c8<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> into a true one whenever \n \n $$\\varphi $$<\/jats:tex-math>\n \n \u03c6<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> and \n \n $$\\psi $$<\/jats:tex-math>\n \n \u03c8<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> have the same semantic correlates, describe the same situations, or have the same content or meaning. The paper aims to compare non-Fregean paraconsistent Grzegorczyk\u2019s logics (Logic of Descriptions \n \n $$\\textsf{LD}$$<\/jats:tex-math>\n \n LD<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, Logic of Descriptions with Suszko\u2019s Axioms \n \n $$\\textsf{LDS}$$<\/jats:tex-math>\n \n LDS<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, Logic of Equimeaning \n \n $$\\textsf{LDE}$$<\/jats:tex-math>\n \n LDE<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>) with non-Fregean versions of certain well-known paraconsistent logics (Ja\u015bkowski\u2019s Discussive Logic \n \n $$\\textsf{D}_2$$<\/jats:tex-math>\n \n \n D<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, Logic of Paradox \n \n $$\\textsf{LP}$$<\/jats:tex-math>\n \n LP<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, Logics of Formal Inconsistency \n \n $$\\textsf{LFI}{1}$$<\/jats:tex-math>\n \n \n LFI<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> and \n \n $$\\textsf{LFI}{2}$$<\/jats:tex-math>\n \n \n LFI<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>). We prove that Grzegorczyk\u2019s logics are either weaker than or incomparable to non-Fregean extensions of \n \n $$\\textsf{LP}$$<\/jats:tex-math>\n \n LP<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, \n \n $$\\textsf{LFI}{1}$$<\/jats:tex-math>\n \n \n LFI<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, \n \n $$\\textsf{LFI}{2}$$<\/jats:tex-math>\n \n \n LFI<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>. Furthermore, we show that non-Fregean extensions of \n \n $$\\textsf{LP}$$<\/jats:tex-math>\n \n LP<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, \n \n $$\\textsf{LFI}{1}$$<\/jats:tex-math>\n \n \n LFI<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, \n \n $$\\textsf{LFI}{2}$$<\/jats:tex-math>\n \n \n LFI<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, and \n \n $$\\textsf{D}_2$$<\/jats:tex-math>\n \n \n D<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> are more expressive than their original counterparts. Our results highlight that the non-Fregean connective \n \n $$\\equiv $$<\/jats:tex-math>\n \n \u2261<\/mml:mo>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> can serve as a tool for expressing various properties of the ontology underlying the logics under consideration.<\/jats:p>","DOI":"10.1007\/s11225-024-10114-4","type":"journal-article","created":{"date-parts":[[2024,5,3]],"date-time":"2024-05-03T05:02:00Z","timestamp":1714712520000},"page":"915-953","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Paraconsistency in Non-Fregean Framework"],"prefix":"10.1007","volume":"113","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8546-2615","authenticated-orcid":false,"given":"Joanna","family":"Goli\u0144ska-Pilarek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,3]]},"reference":[{"key":"10114_CR1","unstructured":"Anderson, A.R., and N.D. 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