Search Advanced

AIMS Mathematics

2024, Volume 9, Issue 12: 36336-36350. doi: 10.3934/math.20241723
Previous Article Next Article
Research article Special Issues

An introduction to the theory of OBCI-algebras

  • 1.
    Department of Philosophy, Jeonbuk National University, Jeonju 54896, Korea
  • 2.
    Department of Mathematics Education, Chinju National University of Education, Jinju 52673, Korea
  • 3.
    Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
  • Received: 12 August 2024 Revised: 21 November 2024 Accepted: 18 December 2024 Published: 30 December 2024

  • MSC : 03B05, 03G25, 06F35

  • The purpose of this paper was to introduce the concept of "OBCI-algebras" as a partially ordered generalization of BCI-algebras. The notion of OBCI-algebras was introduced, and related properties were investigated. The notions of OBCI-subalgebras and (closed) OBCI-filters of OBCI-algebras were defined and the relationship between the OBCI-subalgebras and OBCI-filters was discussed. In addition, the direct product OBCI-algebra was discussed, and the OBCI-filter related to it was also addressed.

    Citation: Eunsuk Yang, Eun Hwan Roh, Young Bae Jun. An introduction to the theory of OBCI-algebras[J]. AIMS Mathematics, 2024, 9(12): 36336-36350. doi: 10.3934/math.20241723

    Related Papers:

  • The purpose of this paper was to introduce the concept of "OBCI-algebras" as a partially ordered generalization of BCI-algebras. The notion of OBCI-algebras was introduced, and related properties were investigated. The notions of OBCI-subalgebras and (closed) OBCI-filters of OBCI-algebras were defined and the relationship between the OBCI-subalgebras and OBCI-filters was discussed. In addition, the direct product OBCI-algebra was discussed, and the OBCI-filter related to it was also addressed.



    加载中


    [1] P. Cintula, Weakly Implicative (Fuzzy) Logics Ⅰ: Basic properties, Arch. Math. Logic, 45 (2006), 673–704. http://doi.org/10.1007/s00153-006-0011-5 doi: 10.1007/s00153-006-0011-5
    [2] P. Cintula, R. Horčík, C. Noguera, Non-associative substructural logics and their semilinear extensions: Axiomatization and completeness properties, Rev. Symbolic Logic, 6 (2013), 394–423. http://doi.org/10.1017/S1755020313000099 doi: 10.1017/S1755020313000099
    [3] P. Cintula, C. Noguera, Implicational (semilinear) logics Ⅰ: A new hierarchy, Arch. Math. Logic, 49 (2010), 417–446. http://doi.org/10.1007/s00153-010-0178-7 doi: 10.1007/s00153-010-0178-7
    [4] P. Cintula, C. Noguera, A general framework for mathematical fuzzy logic, In: Handbook of Mathematical Fuzzy Logic, London: College Publications, 2011,103–207.
    [5] P. Cintula, C. Noguera, Implicational (semilinear) logics Ⅲ: Completeness properties, Arch. Math. Logic, 57 (2018), 391–420. http://doi.org/10.1007/s00153-017-0577-0 doi: 10.1007/s00153-017-0577-0
    [6] J. M. Dunn, Partial gaggles applied to logics with restricted structural rules, Substructural Logics, 2 (1993), 63–108.
    [7] J. M. Dunn, G. Hardegree, Algebraic Methods in Philosophical Logic, Oxford: Oxford Univ Press, 2001.
    [8] G. Galatos, P. Jipsen, T. Kowalski, H. Ono, Residuated lattices: An algebraic glimpse at substructural logics, Amsterdam: Elsevier, 2007.
    [9] G. Galatos, H. Ono, Cut elimination and strong separation for substructural logics, Ann. Pure Appl. Logic, 161 (2010), 1097–1133. http://doi.org/10.1016/j.apal.2010.01.003 doi: 10.1016/j.apal.2010.01.003
    [10] Y. S. Huang, BCI-algebra, Beijing: Science Press, 2006.
    [11] P. M. Idziak, Lattice operations in BCK-algebras, PhD thesis, Jagiellonian University, 1984.
    [12] P. M. Idziak, Lattice operations in BCK-algebras, Math. Jpn., 29 (1984), 839–846.
    [13] Y. Imai, K. Iséki, On axiom systems of proposition calculi, Proc. Jpn. Acad., 42 (1966), 19–22. http://doi.org/10.3792/pja/1195522169 doi: 10.3792/pja/1195522169
    [14] K. Iséki, An algebra related with a propositional calculus, Proc. Jpn. Acad., 42 (1966), 26–29. http://doi.org/10.3792/pja/1195522171 doi: 10.3792/pja/1195522171
    [15] K. Iséki, On BCI-algebras, Math. Semin. Notes, 8 (1980), 125–130.
    [16] K. Iséki, S. Tanaka, An introduction to the theory of BCK-algebras, Math. Jpn., 23 (1978), 1–26.
    [17] G. Metcalfe, F. Montagna, Substructural Fuzzy Logics, J. Symbolic Logic, 72 (2007), 834–864. http://doi.org/10.2178/jsl/1191333844 doi: 10.2178/jsl/1191333844
    [18] A. N. Prior, Formal logic, 2 Eds., Oxford: Oxford University Press, 1962.
    [19] J. G. Raftery, Order algebraizable logics, Ann. Pure Appl. Logic, 164 (2013), 251–283. http://doi.org/10.1016/j.apal.2012.10.013 doi: 10.1016/j.apal.2012.10.013
    [20] E. Yang, J. M. Dunn, Implicational tonoid logics: Algebraic and relational semantics, Log. Universalis, 15 (2021), 435–456. http://doi.org/10.1007/s11787-021-00288-z doi: 10.1007/s11787-021-00288-z
    [21] E. Yang, J. M. Dunn, Implicational Partial Galois Logics: Relational semantics, Log. Universalis, 15 (2021), 457–476 (2021). http://doi.org/10.1007/s11787-021-00290-5 doi: 10.1007/s11787-021-00290-5
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(123) PDF downloads(38) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(8)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog