Unary Interpretability Logics for Sublogics of the Interpretability Logic IL
De Rijke introduced a unary interpretability logic il , and proved that il is the unary counterpart of the binary interpretability logic IL . In this paper, we find the unary counterparts of the sublogics of IL .
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| Published in | Studia logica Vol. 112; no. 3; pp. 693 - 721 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
2024
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| Online Access | Get full text |
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| Abstract | De Rijke introduced a unary interpretability logic
il
, and proved that
il
is the unary counterpart of the binary interpretability logic
IL
. In this paper, we find the unary counterparts of the sublogics of
IL
. |
|---|---|
| AbstractList | De Rijke introduced a unary interpretability logic
il
, and proved that
il
is the unary counterpart of the binary interpretability logic
IL
. In this paper, we find the unary counterparts of the sublogics of
IL
. |
| Author | Okawa, Yuya |
| Author_xml | – sequence: 1 givenname: Yuya surname: Okawa fullname: Okawa, Yuya email: ahga4770@chiba-u.jp organization: Graduate School of Science, Chiba University |
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| Copyright | Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| Copyright_xml | – notice: Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| DOI | 10.1007/s11225-023-10068-z |
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| Keywords | Interpretability logic Unary interpretability logic |
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| References | FefermanSArithmetization of metmathematics in a general settingFundamenta Mathematicae196049359210.4064/fm-49-1-35-92 Ignatiev, K.N., Partial conservativity and modal logics, Technical Report ITLI Publication Series X-91-04, University of Amsterdam, 1991. JaparidzeGde JonghDBussSRThe logic of provabilityHandbook of Proof Theory1998AmsterdamNorth-Holland47554610.1016/S0049-237X(98)80022-0 Ignatiev, K.N., Failure of interpolation for ILM, unpublished. VisserAPreliminary notes on interpretability logic, Technical Report 291988Department of PhilosophyUtrecht University GuaspariDPartially conservative extensions of arithmeticTransactions of the American Mathematical Society1979254476810.1090/S0002-9947-1979-0539907-7 Iwata, S., T. Kurahashi, and Y. Okawa, The fixed point and the Craig interpolation properties for sublogics ofIL, in press. de JonghDVeltmanFPetkovPPProvability logics for relative interpretabilityMathematical Logic1990New YorkPlenum Press314210.1007/978-1-4613-0609-2_3 de RijkeMUnary interpretability logicNotre Dame Journal of Formal Logic199233224927210.1305/ndjfl/1093636104 Lindström, P., Some results on interpretability, in F.V. Jensen, B.H. Mayoh, and K.K. Møller, (eds.), Proceedings of the 5th Scandinavian Logic Symposium, Aalborg University Press, Aalborg, 1979, pp. 329–361. Lindström, P., Aspects of Incompleteness, 2nd edn., vol. 10 of Lecture Notes in Logic, A K Peters, 2003. VukovićMSome correspondences of principles of interpretability logicGlasnik Matematiçki1996312193200 Areces, C., E. Hoogland, and D. de Jongh, Interpolation, definability and fixed points in interpretability logics, in M. Zakharyaschev, K. Segerberg, M. de Rijke, and H. Wansing, (eds.), Advances in Modal Logic, Vol. 2, vol. 119 of CSLI Lecture Notes, CSLI Publication, Stanford, CA, 2001, pp. 35–58. KurahashiTOkawaYModal completeness of sublogics of the interpretability logic IL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textbf{IL} $$\end{document}Mathematical Logic Quarterly202167216418510.1002/malq.202000037 SmoryńskiCCalculating self-referential statementsFundamenta Mathematicae1980109318921010.4064/fm-109-3-189-210 Verbrugge, R., Generalized Veltman frames and models, unpublished manuscript, Amsterdam, 1992. De JonghDVisserAExplicit fixed points in interpretability logicStudia Logica1991501394910.1007/BF00370386 HäjekPPudlákPMetamathematics of First-Order Arithmetic1993Springer, BerlinPerspectives in Mathematical Logic10.1007/978-3-662-22156-3 LindströmPProvability logic–a short introductionTheoria1996621–2196110.1111/j.1755-2567.1996.tb00529.x HájekPMontagnaFThe logic of Π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi $$\end{document}_1 conservativityArchive for Mathematical Logic199030211312310.1007/BF01634981 Joosten, J.J., Towards the interpretability logic of all reasonable arithmetical theories, Master’s thesis, University of Amsterdam, 1998. |
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| Snippet | De Rijke introduced a unary interpretability logic
il
, and proved that
il
is the unary counterpart of the binary interpretability logic
IL
. In this paper, we... |
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| SubjectTerms | Computational Linguistics Education Logic Mathematical Logic and Foundations Philosophy |
| Title | Unary Interpretability Logics for Sublogics of the Interpretability Logic IL |
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