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A Proof-Theoretic Interpolation Theorem for Inquisitive Propositional Logic

dc.contributor.authorFjellstad, Andreas
dc.date.accessioned2026-04-30T10:13:13Z
dc.date.available2026-04-30T10:13:13Z
dc.date.issued2026-04-24
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/58260
dc.description.abstractThis paper presents a sequent calculus for Inquisitive Propositional Logic obtained by expanding the sequent calculus g3ip for intuitionistic propositional logic with suitable rules for double negation elimination for atoms and the Split Property. A suitable rule for the Split Property is obtained by taking advantage of the connection between the truth-conditional fragment in Inquisitive Logic and Harrop formulas. The paper proves admissibility of cut for the sequent calculus and uses the sequent calculus to prove interpolation for Inquisitive Propositional Logic. Interpolation is obtained using Maehara’s lemma.en
dc.language.isoen
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl
dc.relation.ispartofseriesBulletin of the Section of Logic;1en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0
dc.subjectInquisitive Logicen
dc.subjectHarrop formulasen
dc.subjectinterpolationen
dc.subjectMaehara's lemmaen
dc.subjectintermediate logicsen
dc.titleA Proof-Theoretic Interpolation Theorem for Inquisitive Propositional Logicen
dc.typeOther
dc.page.number49-71
dc.contributor.authorAffiliationUniversity of Padova, FISPPA, Padova, Italyen
dc.identifier.eissn2449-836X
dc.referencesA. Anttila, Not Nothing: Nonemptiness in Team Semantics, Ph.D. thesis, Universiteit van Amsterdam (2025).en
dc.referencesJ. Chen, M. Ma, Labelled Sequent Calculus for Inquisitive Logic, [in:]Logic, Rationality, and Interaction (2017), pp. 526–540, DOI: https://doi.org/10.1007/978-3-662-55665-8_36.en
dc.referencesI. Ciardelli, Inquisitive Logic: Consequences and Inference in the Realm of Questions, Springer, Cham (2022), DOI: https://doi.org/10.1007/978-3-031-09706-5.en
dc.referencesI. Ciardelli, J. Groenendijk, F. Roelofsen, Inquisitive Semantics, Oxford University Press, Oxford, England (2018), DOI: https://doi.org/10.1093/oso/9780198814788.001.0001.en
dc.referencesI. Ciardelli, R. Iemhoff, F. Yang, Questions and Dependency in Intuitionistic Logic, Notre Dame Journal of Formal Logic, vol. 61(1) (2020), pp. 75–115, DOI: https://doi.org/10.1215/00294527-2019-0033.en
dc.referencesI. Ciardelli, F. Roelofsen, Inquisitive Logic, Journal of Philosophical Logic, vol. 40(1) (2011), pp. 55–94, DOI: https://doi.org/10.1007/s10992-010-9142-6.en
dc.referencesR. Harrop, Concerning Formulas of the Types A→B∨C , A→(Ex)B(x),Journal of Symbolic Logic, vol. 25(1) (1960), pp. 27–32, DOI: https://doi.org/10.2307/2964334.en
dc.referencesL. L. Maksimova, Craig’s theorem in superintuitionistic logics and amalgamable varieties of pseudo-boolean algebras, Algebra and Logic, vol. 16 (1977), p. 427–455, DOI: https://doi.org/10.1007/BF01670006.en
dc.referencesV. Müller, On the Proof Theory of Inquisitive Logic, Master’s thesis, Universiteit van Amsterdam (2023).en
dc.referencesS. Negri, J. von Plato, Structural Proof Theory, Cambridge University Press, New York (2001).en
dc.referencesI. Pezlar, Constructive Validity of a Generalized Kreisel–Putnam Rule,Studia Logica, vol. 113 (2025), p. 1367–1399, DOI: https://doi.org/10.1007/s11225-024-10129-x.en
dc.referencesV. Punčochár, A Generalization of Inquisitive Semantics, Journal of Philosophical Logic, vol. 45(4) (2016), pp. 399–428, DOI: https://doi.org/10.1007/s10992-015-9379-1.en
dc.referencesA. S. Troelstra, H. Schwichtenberg, Basic Proof Theory, Cambridge University Press, New York (2000), DOI: https://doi.org/10.1017/CBO9781139168717.en
dc.referencesJ. von Plato, A Proof of Gentzen’s Hauptsatz Without Multicut, Archive for Mathematical Logic, vol. 40(1) (2001), pp. 9–18, DOI: https://doi.org/10.1007/s001530050170.en
dc.contributor.authorEmailafjellstad@gmail.com
dc.identifier.doi10.18778/0138-0680.2026.02
dc.relation.volume55


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