dc.contributor.author Maffezioli, Paolo dc.contributor.author Orlandelli, Eugenio dc.date.accessioned 2019-10-13T10:26:05Z dc.date.available 2019-10-13T10:26:05Z dc.date.issued 2019 dc.identifier.issn 0138-0680 dc.identifier.uri http://hdl.handle.net/11089/30602 dc.description.abstract In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that interpolation fails for the implication-free fragment. In this paper an equivalent calculus is introduced that satisfies full cut elimination and allows a direct proof of interpolation via Maehara's lemma. In this way, it is possible to obtain much simpler interpolants and to better understand and (partly) overcome the failure of interpolation for the implication-free fragment. en_GB dc.language.iso en en_GB dc.publisher Wydawnictwo Uniwersytetu Łódzkiego en_GB dc.relation.ispartofseries Bulletin of the Section of Logic; 2 dc.rights This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. en_GB dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0 en_GB dc.subject intuitionistic logic en_GB dc.subject existence predicate en_GB dc.subject sequent calculi en_GB dc.subject cut elimination en_GB dc.subject interpolation en_GB dc.subject Maehara's lemma en_GB dc.title Full Cut Elimination and Interpolation for Intuitionistic Logic with Existence Predicate en_GB dc.type Article en_GB dc.page.number 137-158 dc.contributor.authorAffiliation Departamet de Filosofia, Universitat de Barcelona, Barcelona, Spain dc.contributor.authorAffiliation Dipartimento di Filosofia e Comunicazione, Universitá di Bologna, Bologna, Italy dc.identifier.eissn 2449-836X dc.references M. Baaz and R. Iemhoff. On interpolation in existence logics, Logic for Programming, Articial Intelligence, and Reasoning ed. by G. Sutcliffe and A. Voronkov, vol. 3835 of Lecture Notes in Computer Science. Springer, 2005, pp. 697–711. https://doi.org/10.1007/11591191_48 en_GB dc.references M. Baaz and R. Iemhoff, Gentzen calculi for the existence predicate, Studia Logica, vol. 82, no. 1 (2006), pp. 7–23. https://doi.org/10.1007/s11225-006-6603-6 en_GB dc.references M. Beeson, Foundations of Constructive Mathematics. Springer, 1985. https://doi.org/10.1007/978-3-642-68952-9 en_GB dc.references G. Gherardi, P. Maffezioli, and E. Orlandelli, Interpolation in extensions of first-order logic, Studia Logica (2019), pp. 1–30. (published online). https://doi.org/10.1007/s11225-019-09867-0 en_GB dc.references S. Maehara, On the interpolation theorem of Craig. Suugaku, vol. 12 (1960), pp. 235–237. (in Japanese). en_GB dc.references S. Negri, Contraction-free sequent calculi for geometric theories with an application to Barr's theorem, Archive for Mathematical Logic, vol. 42, no. 4 (2003), pp. 389–401. https://doi.org/10.1007/s001530100124 en_GB dc.references S. Negri, Proof analysis in modal logic, Journal of Philosophical Logic, vol. 34, no. (5-6) (2005), pp. 507–544. https://doi.org/10.1007/s10992-005-2267-3 en_GB dc.references S. Negri and J. von Plato, Structural Proof Theory. Cambridge University Press, 2001. https://doi.org/10.1017/CBO9780511527340 en_GB dc.references D. Scott, Identity and existence in intuitionistic logic. In M. Fourman, C. Mulvey, and D. Scott, editors, Application of Shaves. Springer, 1979, pp. 660–696. https://doi.org/10.1007/BFb0061839 en_GB dc.references A.S. Troelstra and H. Schwichtenberg, Basic Proof Theory. Cambridge University Press, 2nd edition, 2000. https://doi.org/10.1017/CBO9781139168717 en_GB dc.contributor.authorEmail paolo.maffezioli@ub.edu dc.contributor.authorEmail eugenio.orlandelli@unibo.it dc.identifier.doi 10.18778/0138-0680.48.2.04 dc.relation.volume 48 en_GB dc.subject.jel logic en_GB
﻿