Continua of Logics Related to Intuitionistic and Minimal Logics
| dc.contributor.author | Ichikura, Kaito | |
| dc.date.accessioned | 2025-12-12T15:22:22Z | |
| dc.date.available | 2025-12-12T15:22:22Z | |
| dc.date.issued | 2025-07-07 | |
| dc.identifier.issn | 0138-0680 | |
| dc.identifier.uri | http://hdl.handle.net/11089/56968 | |
| dc.description.abstract | We analyze the relationship between logics around intuitionistic logic and minimal logic. We characterize the intersection of minimal logic and co-minimal logic introduced by Vakarelov, and reformulate logics given in the previous studies by Vakarelov, Bezhanishvili, Colacito, de Jongh, Vargas, and Niki in a uniform language. We also compare the new logic with other known logics in terms of the cardinalities of logics between them. Specifically, we apply Wronski’s algebraic semantics, instead of neighborhood semantics used in the previous studies, to show the existence of continua of logics between known logics and the new logic. This result is an extension of the conventional results, and the proof is given in a simpler way. | en |
| dc.language.iso | en | |
| dc.publisher | Wydawnictwo Uniwersytetu Łódzkiego | pl |
| dc.relation.ispartofseries | Bulletin of the Section of Logic;2 | en |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0 | |
| dc.subject | intuitionistic logic | en |
| dc.subject | minimal logic | en |
| dc.subject | subminimal logic | en |
| dc.subject | co-minimal logic | en |
| dc.subject | Yankov formula | en |
| dc.title | Continua of Logics Related to Intuitionistic and Minimal Logics | en |
| dc.type | Article | |
| dc.page.number | 283-323 | |
| dc.contributor.authorAffiliation | Tohoku University, Graduate School of Information Sciences | en |
| dc.identifier.eissn | 2449-836X | |
| dc.references | N. Bezhanishvili, A. Colacito, D. de Jongh, A study of subminimal logics of negation and their modal companions, [in:] Language, Logic, and Computation 12th International Tbilisi Symposium, TbiLLC 2017, Lagodekhi, Georgia, September 18-22, 2017, Revised Selected Papers 12, Springer (2019), pp. 21–41, DOI: https://doi.org/10.1007/978-3-662-59565-7_2 | en |
| dc.references | A. Chagrov, M. Zakharyaschev, Modal logic, Oxford University Press (1997). | en |
| dc.references | A. Colacito, Minimal and Subminimal Logic of Negation, Master’s thesis, University of Amsterdam (2016), URL: https://eprints.illc.uva.nl/id/eprint/986 | en |
| dc.references | A. Colacito, D. de Jongh, A. L. Vargas, Subminimal negation, Soft Computing, vol. 21 (2017), pp. 165–174, DOI: https://doi.org/10.1007/s00500-016-2391-8 | en |
| dc.references | T. Hosoi, H. Ono, Intermediate propositional logics (a survey), Journal of Tsuda College, vol. 5 (1973), pp. 67–82. | en |
| dc.references | I. Johansson, Der Minimalkalkül, ein reduzierter intuitionistischer Formalismus, Compositio Mathematica, vol. 4 (1937), pp. 119–136, URL: http://eudml.org/doc/88648 | en |
| dc.references | S. Niki, Decidable variables for constructive logics, Mathematical Logic Quarterly, vol. 66(4) (2020), pp. 484–493, DOI: https://doi.org/10.1002/malq.202000022 | en |
| dc.references | S. Niki, Subminimal logics in light of Vakarelov’s logic, Studia Logica, vol. 108(5) (2020), pp. 967–987, DOI: https://doi.org/10.1007/s11225-019-09884-z | en |
| dc.references | H. Ono, On some intuitionistic modal logics, Publications of the Research Institute for Mathematical Sciences, vol. 13(3) (1977), pp. 687–722. | en |
| dc.references | N. Suzuki, The existence of 2ω logics lacking the weakening rule below the intuitionistic logic, Reports on Mathematical Logic, vol. 21 (1987), pp. 85–95. | en |
| dc.references | M. Takano, A Syntactical Study of the Subminimal Logic with Nelson Negation, Nihonkai Mathematical Journal, vol. 18(1–2) (2007), pp. 17–31, URL: https://projecteuclid.org/journals/nihonkai-mathematical-journal/volume-18/issue-1-2/A-Syntactical-Study-of-the-Subminimal-Logic-with-Nelson-Negation/nihmj/1273587757.full | en |
| dc.references | D. Vakarelov, Consistency, Completeness and Negation, [in:] G. Priest, R. Routley, J. Norman (eds.), Paraconsistent Logic: Essays on the inconsistent, Philosophia Verlag (1989), pp. 328–363. | en |
| dc.references | D. Vakarelov, Nelson’s negation on the base of weaker versions of intuitionistic negation, Studia Logica, vol. 80 (2005), pp. 393–430, DOI: https://doi.org/10.1007/s11225-005-8476-5 | en |
| dc.references | P. W. Woodruff, A note on JP, Theoria, vol. 36 (2008), pp. 183–184, URL: https://api.semanticscholar.org/CorpusID:145545536 | en |
| dc.references | A. Wroński, The degree of completeness of some fragments of the intuitionistic propositional logic, Reports on Mathematical Logic, vol. 2 (1974). | en |
| dc.references | V. Yankov, On the relation between deducibility in intuitionistic propositional calculus and finite implicative structures, Doklady Akademii Nauk SSSR, vol. 151(6) (1963), pp. 1293–1294. | en |
| dc.references | V. Yankov, The construction of a sequence of strongly independent superintuitionistic propositional calculi, Doklady Akademii Nauk SSSR, vol. 181 (1968), pp. 33–34. | en |
| dc.contributor.authorEmail | ichikura.kaito.t7@dc.tohoku.ac.jp | |
| dc.identifier.doi | 10.18778/0138-0680.2025.06 | |
| dc.relation.volume | 54 |
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