Articles

1. Refinements of provability and consistency principles for the second incompleteness theorem
   Taishi Kurahashi, in preparation.
   ResearchGate
   arXiv:2507.00955
2. Hierarchical formula classes with respect to semi-classical prenex normalization
   Makoto Fujiwara and Taishi Kurahashi, submitted.
   ResearchGate
   arXiv.2506.22348
3. Extensional independence
   Taishi Kurahashi and Albert Visser, in preparation.
   ResearchGate
   arXiv:2506.13524
4. Doubly partially conservative sentences
   Haruka Kogure and Taishi Kurahashi, submitted.
   ResearchGate
   arXiv:2503.12373
5. A variety of partially conservative sentences
   Haruka Kogure and Taishi Kurahashi, submitted.
   ResearchGate
   arXiv:2412.08208
6. Visser frames for sublogics of \(\mathbf{IL}\)
   Yuya Okawa and Taishi Kurahashi, submitted.
   ResearchGate
   arXiv:2211.15919
7. The modal logic of provability and forcing
   Taishi Kurahashi and Rihito Takase, submitted.
   ResearchGate
   arXiv:2311.00581
8. Lyndon interpolation property for extensions of \(\mathbf{S4}\) and intermediate propositional logics
   Taishi Kurahashi, The Journal of Symbolic Logic, accepted.
   ResearchGate
   arXiv:2407.00505
9. Cut-free sequent calculi for the provability logic D
   Ryo Kashima, Taishi Kurahashi, Sohei Iwata and So Morioka, The Review of Symbolic Logic, accepted.
   doi: 10.1017/S1755020325000036
   ResearchGate
   arXiv:2310.16369
10. Interpolation properties for the bimodal provability logic \(\mathbf{GR}\)
    Haruka Kogure and Taishi Kurahashi, Studia Logica, accepted.
    doi: 10.1007/s11225-024-10167-5
    ResearchGate
    arXiv:2311.10583
11. Certified \(\Sigma_1\)-sentences
    Taishi Kurahashi and Albert Visser, The Journal of Symbolic Logic, accepted.
    doi: 10.1017/jsl.2024.84
    ResearchGate
    arXiv:2306.13049
12. The finite frame property of some extensions of the pure logic of necessitation
    Taishi Kurahashi and Yuta Sato, Studia Logica, accepted.
    doi: 10.1007/s11225-024-10154-w
    ResearchGate
    arXiv:2305.14762
13. Smullyan's truth and provability
    Taishi Kurahashi and Kohei Tominaga, Journal of Logic and Computation, vol.35, no.5, exaf001, 2025.
    doi: 10.1093/logcom/exaf001
    ResearchGate
    arXiv:2410.17895
14. Mathematical developments of the incompleteness theorems
    Taishi Kurahashi, Sugaku Expositions, vol.38, no.1, pp. 1--32, 2025.
    doi: 10.1090/suga/487
    This is an English translation of an article published in Sugaku.
15. On the conservation results for local reflection principles
    Haruka Kogure and Taishi Kurahashi, Journal of Logic and Computation, vol.35, no.2, exad076, 2025.
    doi: 10.1093/logcom/exad076
    ResearchGate
    arXiv.2306.07243
16. Pour-El's landscape
    Taishi Kurahashi and Albert Visser, The Bulletin of Symbolic Logic, vol.30, no.3, pp. 362--397, 2024.
    doi: 10.1017/bsl.2024.26
    ResearchGate
    arXiv:2310.04814
17. On collection schemes and Gaifman's splitting theorem
    Taishi Kurahashi and Yoshiaki Minami, Mathematical Logic Quarterly, vol.70, no.4, pp. 398--413, 2024.
    doi: 10.1002/malq.202400021
    ResearchGate
    arXiv:2402.09255
18. The provability logic of all provability predicates
    Taishi Kurahashi, Journal of Logic and Computation, vol.34, no.6, pp. 1108--1135, 2024.
    doi: 10.1093/logcom/exad060
    ResearchGate
    arXiv:2208.03553
19. The persistence principle over weak interpretability logic
    Sohei Iwata, Taishi Kurahashi and Yuya Okawa, Mathematical Logic Quarterly, vol.70, no.1, pp. 37--63, 2024.
    doi: 10.1002/malq.202200020
    ResearchGate
    arXiv:2203.02183
20. Prenex normalization and the hierarchical classification of formulas
    Makoto Fujiwara and Taishi Kurahashi, Archive for Mathematical Logic, vol.63, no.3-4, pp. 391--403, 2024.
    doi: 10.1007/s00153-023-00899-x
    ResearchGate
    arXiv:2302.11808
21. Disjunction and existence properties in modal arithmetic
    Taishi Kurahashi and Motoki Okuda, The Review of Symbolic Logic, vol.17, no.1, pp. 178--205, 2024.
    doi: 10.1017/S1755020322000363
    ResearchGate
    arXiv:2110.02576
    Erratum
22. The fixed point and the Craig interpolation properties for sublogics of \(\mathbf{IL}\)
    Sohei Iwata, Taishi Kurahashi and Yuya Okawa, Archive for Mathematical Logic, vol.63, no.1-2, pp. 1--37, 2024.
    doi: 10.1007/s00153-023-00882-6
    ResearchGate
    arXiv:2007.05427
23. Conservation theorems on semi-classical arithmetic
    Makoto Fujiwara and Taishi Kurahashi, The Journal of Symbolic Logic, vol.88, no.4, pp.1469--1496, 2023.
    doi: 10.1017/jsl.2022.25
    ResearchGate
    arXiv:2107.11356
24. Some observations on the FGH theorem
    Taishi Kurahashi, Studia Logica, vol.111, no.5, pp.749--778, 2023.
    doi: 10.1007/s11225-023-10045-6
    ResearchGate
    arXiv:2110.14872
25. Arithmetical completeness theorems for monotonic modal logics
    Haruka Kogure and Taishi Kurahashi, Annals of Pure and Applied Logic, vol.174, no.7, 103271, 2023.
    doi: 10.1016/j.apal.2023.103271
    ResearchGate
    arXiv:2208.03555
26. Refining the arithmetical hierarchy of classical principles
    Makoto Fujiwara and Taishi Kurahashi, Mathematical Logic Quarterly, vol.68, no.3, pp.318--345, 2022.
    doi: 10.1002/malq.202000077
    ResearchGate
    arXiv:2010.11527
27. Effectively constructible fixed points in Sacchetti's modal logics of provability
    Taishi Kurahashi and Yuya Okawa, Notre Dame Journal of Formal Logic, vol.63, no.1, pp.35--49, 2022.
    doi: 10.1215/00294527-2022-0003
    ResearchGate
    arXiv:1811.12827
28. On inclusions between quantified provability logics
    Taishi Kurahashi, Studia Logica, vol.110, no.1, pp.165--188, 2022.
    doi: 10.1007/s11225-021-09957-y
    ResearchGate
    arXiv:2101.03384
29. On Guaspari's problem about partially conservative sentences
    Taishi Kurahashi, Yuya Okawa, V. Yu. Shavrukov and Albert Visser, Annals of Pure and Applied Logic, vol.173, no.5, 103087, 2022.
    doi: 10.1016/j.apal.2022.103087
    ResearchGate
    arXiv:1909.02761
30. Rosser provability and the second incompleteness theorem
    Taishi Kurahashi, In: Arai T., Kikuchi M., Kuroda S., Okada M., Yorioka T. (eds) Advances in Mathematical Logic. SAML 2018, Springer Proceedings in Mathematics & Statistics, vol.369, Springer, Singapore, pp.77--97, 2021.
    doi: 10.1007/978-981-16-4173-2_4
    ResearchGate
    arXiv:1902.06863
31. Prenex normal form theorems in semi-classical arithmetic
    Makoto Fujiwara and Taishi Kurahashi, The Journal of Symbolic Logic, vol.86, no.3, pp.1124--1153, 2021.
    doi: 10.1017/jsl.2021.47
    ResearchGate
    arXiv:2009.03485
32. Topological semantics of conservativity and interpretability logics
    Sohei Iwata and Taishi Kurahashi, Journal of Logic and Computation, vol.31, no.7, pp.1716--1739, 2021.
    doi: 10.1093/logcom/exab046
    ResearchGate
    arXiv:2102.02483
33. Modal completeness of sublogics of the interpretability logic \(\mathbf{IL}\)
    Taishi Kurahashi and Yuya Okawa, Mathematical Logic Quarterly, vol.67, no.2, pp.164--185, 2021.
    doi: 10.1002/malq.202000037
    ResearchGate
    arXiv:2004.03813
34. Mathematical developments of the incompleteness theorems (in Japanese)
    Taishi Kurahashi, Sugaku, vol.73, no.1, pp.60--87, 2021.
    
35. A note on derivability conditions
    Taishi Kurahashi, The Journal of Symbolic Logic, vol.85, no.3, pp.1224--1253, 2020.
    doi: 10.1017/jsl.2020.33
    ResearchGate
    arXiv:1902.00895
36. Uniform Lyndon interpolation property in propositional modal logics
    Taishi Kurahashi, Archive for Mathematical Logic, vol.59, no.5-6, pp.659--678, 2020.
    doi: 10.1007/s00153-020-00713-y
    ResearchGate
    arXiv:1809.00943
37. Fixed-point properties for predicate modal logics
    Sohei Iwata and Taishi Kurahashi, Annals of the Japan Association for Philosophy of Science, vol.29, pp.1--25, 2020.
    doi: 10.4288/jafpos.29.0_1
    ResearchGate
    arXiv:1907.00306
38. Rosser provability and normal modal logics
    Taishi Kurahashi, Studia Logica, vol.108, no.3, pp.597--617, 2020.
    doi: 10.1007/s11225-019-09865-2
    ResearchGate
    arXiv:1812.09735
39. On arithmetical completeness of the Logic of Proofs
    Sohei Iwata and Taishi Kurahashi, Annals of Pure and Applied Logic, vol.170, no.2, pp.163--179, 2019.
    doi: 10.1016/j.apal.2018.09.004
    ResearchGate
    
40. Provability logics relative to a fixed extension of Peano Arithmetic
    Taishi Kurahashi, The Journal of Symbolic Logic, vol.83, no.3, pp.1229--1246, 2018.
    doi: 10.1017/jsl.2018.27
    ResearchGate
    
41. Arithmetical soundness and completeness for \(\Sigma_2\) numerations
    Taishi Kurahashi, Studia Logica, vol.106, no.6, pp.1181--1196, 2018.
    doi: 10.1007/s11225-017-9782-4
    ResearchGate
    
42. On partial disjunction properties of theories containing Peano arithmetic
    Taishi Kurahashi, Archive for Mathematical Logic, vol.57, no.7-8, pp.953--980, 2018.
    doi: 10.1007/s00153-018-0618-3
    ResearchGate
    
43. Arithmetical completeness theorem for modal logic \(\mathsf{K}\)
    Taishi Kurahashi, Studia Logica, vol.106, no.2, pp.219--235, 2018.
    doi: 10.1007/s11225-017-9735-y
    ResearchGate
    
44. Generalizations of Gödel's incompleteness theorems for \(\Sigma_n\)-definable theories of arithmetic
    Makoto Kikuchi and Taishi Kurahashi, The Review of Symbolic Logic, vol.10, no.4, pp.603--616, 2017.
    doi: 10.1017/S1755020317000235
    ResearchGate
    
45. Universal Rosser predicates
    Makoto Kikuchi and Taishi Kurahashi, The Journal of Symbolic Logic, vol.82, no.1, pp.292--230, 2017.
    doi: 10.1017/jsl.2016.19
    ResearchGate
    
46. Illusory models of Peano arithmetic
    Makoto Kikuchi and Taishi Kurahashi, The Journal of Symbolic Logic, vol.81, no.3, pp.1163--1175, 2016.
    doi: 10.1017/jsl.2015.52
    ResearchGate
    
47. Liar-type paradoxes and the incompleteness phenomena
    Makoto Kikuchi and Taishi Kurahashi, Journal of Philosophical Logic, vol.45, no.4, pp.381--398, 2016.
    doi: 10.1007/s10992-015-9378-2
    ResearchGate
    
48. Henkin sentences and local reflection principles for Rosser provability
    Taishi Kurahashi, Annals of Pure and Applied Logic, vol.167, no.2, pp.73--94, 2016.
    doi: 10.1016/j.apal.2015.10.002
    ResearchGate
    
49. Rosser-type undecidable sentences based on Yablo's paradox
    Taishi Kurahashi, Journal of Philosophical Logic, vol.43, no.5, pp.999--1017, 2014.
    doi: 10.1016/j.apal.2015.10.002
    ResearchGate
    
50. On Rosser's provability predicates (in Japanese)
    Taishi Kurahashi, Journal of the Japan Association for Philosophy of Science, vol.41, no.2, pp.13--21, 2014.
    doi: 10.4288/kisoron.41.2_93
    pdf (J-STAGE)
    
51. On predicate provability logics and binumerations of fragments of Peano arithmetic
    Taishi Kurahashi, Archive for Mathematical Logic, vol.52, no.7, pp.871--880, 2013.
    doi: 10.1007/s00153-013-0349-4
    ResearchGate
    
52. Arithmetical interpretations and Kripke frames of predicate modal logic of provability
    Taishi Kurahashi, The Review of Symbolic Logic, vol.6, no.1, pp.129--146, 2013.
    doi: 10.1017/S1755020312000275
    ResearchGate
    
53. On proofs of the incompleteness theorems based on Berry's paradox by Vopěnka, Chaitin, and Boolos
    Makoto Kikuchi, Taishi Kurahashi and Hiroshi Sakai, Mathematical Logic Quarterly, vol.58, no.4-5, pp.307--316, 2012.
    doi: 10.1002/malq.201110067
    ResearchGate
    
54. Three short stories anound Gödel's incompleteness theorems (in Japanese)
    Makoto Kikuchi and Taishi Kurahashi, Journal of the Japan Association for Philosophy of Science, vol.38, no.2, pp.27--32, 2011.
    doi: 10.4288/kisoron.38.2_75
    pdf (J-STAGE)