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On Combining Intuitionistic and S4 Modal Logic

dc.contributor.authorRasga, João
dc.contributor.authorSernadas, Cristina
dc.date.accessioned2024-09-30T13:40:19Z
dc.date.available2024-09-30T13:40:19Z
dc.date.issued2024-06-05
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/53271
dc.description.abstractWe address the problem of combining intuitionistic and S4 modal logic in a non-collapsing way inspired by the recent works in combining intuitionistic and classical logic. The combined language includes the shared constructors of both logics namely conjunction, disjunction and falsum as well as the intuitionistic implication, the classical implication and the necessity modality. We present a Gentzen calculus for the combined logic defined over a Gentzen calculus for the host S4 modal logic. The semantics is provided by Kripke structures. The calculus is proved to be sound and complete with respect to this semantics. We also show that the combined logic is a conservative extension of each component. Finally we establish that the Gentzen calculus for the combined logic enjoys cut elimination.en
dc.language.isoen
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl
dc.relation.ispartofseriesBulletin of the Section of Logic;3en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0
dc.subjectcombination of logicsen
dc.subjectintuitionistic logicen
dc.subjectmodal logicen
dc.subjectcut eliminationen
dc.titleOn Combining Intuitionistic and S4 Modal Logicen
dc.typeArticle
dc.page.number321-344
dc.contributor.authorAffiliationRasga, João - Instituto de Telecomunicações, Basic Sciences and Enabling Technologies Campus Universitário de Santiago; Universidade de Lisboa, Instituto Superior Técnico, Dep. Matemáticaen
dc.contributor.authorAffiliationSernadas, Cristina - Instituto de Telecomunicações, Basic Sciences and Enabling Technologies Campus Universitário de Santiago; Universidade de Lisboa, Instituto Superior Técnico, Dep. Matemáticaen
dc.identifier.eissn2449-836X
dc.referencesL. F. del Cerro, A. Herzig, Combining classical and intuitionistic logic, [in:] F. Baader, K. U. Schulz (eds.), Frontiers of Combining Systems, Springer (1996), pp. 93–102, DOI: https://doi.org/10.1007/978-94-009-0349-4_4en
dc.referencesG. Dowek, On the definition of the classical connectives and quantifiers, [in:] Why is this a Proof? Festschrift for Luiz Carlos Pereira, College Publications (2015), pp. 228–238.en
dc.referencesD. Gabbay, Fibred semantics and the weaving of logics: Modal and intuitionistic logics, The Journal of Symbolic Logic, vol. 61(4) (1996), pp. 1057–1120, DOI: https://doi.org/10.2307/2275807en
dc.referencesD. Gabbay, Fibring Logics, Oxford University Press, Oxford (1999), DOI: https://doi.org/10.1093/oso/9780198503811.001.0001en
dc.referencesJ.-Y. Girard, On the unity of logic, Annals of Pure and Applied Logic, vol. 59(3) (1993), pp. 201–217, DOI: https://doi.org/10.1016/0168-0072(93)90093-Sen
dc.referencesK. Gödel, Collected Works. Vol. I, Oxford University Press (1986).en
dc.referencesS. Marin, L. C. Pereira, E. Pimentel, E. Sales, A pure view of ecumenical modalities, [in:] Logic, Language, Information, and Computation, vol. 13038 of Lecture Notes in Computer Science, Springer (2021), pp. 388– 407, DOI: https://doi.org/10.1007/978-3-030-88853-4_24en
dc.referencesJ. C. C. McKinsey, A. Tarski, Some theorems about the sentential calculi of Lewis and Heyting, The Journal of Symbolic Logic, vol. 13 (1948), pp. 1–15, DOI: https://doi.org/10.2307/2268135en
dc.referencesS. Negri, J. von Plato, Structural Proof Theory, Cambridge University Press, Cambridge (2001), DOI: https://doi.org/10.1017/CBO9780511527340en
dc.referencesL. C. Pereira, R. O. Rodriguez, Normalization, Soundness and Completeness for the Propositional Fragment of Prawitz’ Ecumenical System, Revista Portuguesa de Filosofia, vol. 73(3/4) (2017), pp. 1153–1168, DOI: https://doi.org/10.17990/RPF/2017_73_3_1153en
dc.referencesE. Pimentel, L. C. Pereira, V. de Paiva, An ecumenical notion of entailment, Synthese, vol. 198(suppl. 22) (2021), pp. S5391–S5413, DOI: https://doi.org/10.1007/s11229-019-02226-5en
dc.referencesD. Prawitz, Classical versus intuitionistic logic, [in:] Why is this a Proof? Festschrift for Luiz Carlos Pereira, College Publications (2015), pp. 15–32.en
dc.referencesD. Prawitz, P.-E. Malmn¨as, A survey of some connections between classical, intuitionistic and minimal logic, [in:] Contributions to Mathematical Logic Colloquium, North-Holland, Amsterdam (1968), pp. 215–229, DOI: https://doi.org/10.1016/S0049-237X(08)70527-5en
dc.referencesJ. Rasga, C. Sernadas, Decidability of Logical Theories and their Combination, Birkh¨auser, Basel (2020), DOI: https://doi.org/10.1007/978-3-030-56554-1en
dc.referencesV. Rybakov, Admissibility of Logical Inference Rules, North-Holland, Amsterdam (1997), URL: https://www.sciencedirect.com/bookseries/studies-in-logic-and-the-foundations-of-mathematics/vol/136/suppl/Cen
dc.referencesC. Sernadas, J. Rasga, W. A. Carnielli, Modulated fibring and the collapsing problem, The Journal of Symbolic Logic, vol. 67(4) (2002), pp. 1541–1569, DOI: https://doi.org/10.2178/jsl/1190150298en
dc.referencesA. S. Troelstra, H. Schwichtenberg, Basic Proof Theory, Cambridge University Press, Cambridge (2000), DOI: https://doi.org/10.1017/CBO9781139168717en
dc.contributor.authorEmailRasga, João - joao.rasga@tecnico.ulisboa.pt
dc.contributor.authorEmailSernadas, Cristina - cristina.sernadas@tecnico.ulisboa.pt
dc.identifier.doi10.18778/0138-0680.2024.11
dc.relation.volume53


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