JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (12): 28-34.doi: 10.6040/j.issn.1671-9352.0.2014.458

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A schematic extension of IMTL logic system

ZHOU Jian-ren1, WU Hong-bo2   

  1. 1. College of Mathematics and Statistics, Hexi University, Zhangye 734000, Gansu, China;
    2. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, Shaanxi, China
  • Received:2014-10-20 Revised:2015-01-26 Online:2015-12-20 Published:2015-12-23

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Abstract: A new fuzzy logic system IMTL* logic is introduced. The feature of this logic system is only one logic connective concerned. It is proved that IMTL* logic is a schematic extension of IMTL logic and ?ukasiewicz logic and logic system ℵ* are both schematic extension of IMTL* Logic. Finally the pure implication representation of ?ukasiewicz logic and logic ℵ* are obtained. The fuzzy logic systems which is only one logic connective implication concerned will bring convenience to use of fuzzy logic.

Key words: IMTL logic, logic ℵ, IMTL* logic, ukasiewicz logic, ?, fuzzy logic, *, implication representation

CLC Number: 

  • O141.1
[1] 王国俊. 非经典数理逻辑与近似推理[M].3版.北京:科学出版社,2006. WANG Guojun. Non-classical mathematical logic and approximate reasoning[M]. 3rd ed. Beijing: Science Press, 2006.
[2] HÁJEK P. Metamathematics of fuzzy logic[M]. Dordrecht: Kluwer Academic Publishers, 1998.
[3] 王国俊. 数理逻辑引论与归结原理[M].北京:科学出版社,2006. WANG Guojun. Introduction to mathematical logic and resolution principle[M]. Beijing: Science Press, 2006.
[4] 吴洪博. 基础R0-代数与基础ℵ*-系统[J].数学进展,2003,32(5):565-576. WU Hongbo. Basis R0-algebra and basis ℵ*-system[J]. Advances in Mathematics, 2003, 32(5):565-576.
[5] 吴洪博,王昭海. BR0-代数的无序表示形式及WBR0-代数的性质[J].工程数学学报, 2009,26(3):456-460. WU Hongbo, WANG Zhaohai. The non-ordered form of BR0-algebra and properties of WBR0-algebra[J]. Chinese Journal of Engineering Mathematics, 2009, 26(3):456-460.
[6] 吴洪博. R0-代数在一般集合上的⊕,→表示形式[J]. 吉林大学学报:自然科学版,2009,47(4):661-666. WU Hongbo. A form of R0-algebras on a set with binary operators ,→[J].Journal of Jilin University: Science Edition, 2009, 47(4):661-666.
[7] 周建仁,吴洪博. 剩余偏序集及其与FI代数的关系[J].云南师范大学学报:自然科学版, 2012,32(3):1-6. ZHOU Jianren, WU Hongbo. Residuated poset and its relation with FI-algebra[J]. Journal of Yunnan Normal University: Natural Sciences Edition, 2012, 32(3):1-6.
[8] 周建仁,吴洪博. WBR0-代数的正则性及与其它逻辑代数的关系[J].山东大学学报:理学版, 2012,47(2):86-92. ZHOU Jianren, WU Hongbo. The regularness of WBR0-algebras and relations with other logic algebras[J]. Journal of Shandong University: Natural Science, 2012, 47(2):86-92.
[9] 李玲玲,吴洪博. BR0-分配性及其推广[J].山东大学学报:理学版, 2012,47(2):93-97. LI Lingling, WU Hongbo. BR0-distributivity and its generalization[J]. Journal of Shandong University: Natural Science, 2012, 47(2):93-97.
[10] ESTEVA F, GODO L. Monoidal t-norm-based logic: towards a logic for left-continuous t-norms[J]. Fuzzy Sets and Systems, 2001, 124(3):271-288.
[11] 周建仁,吴洪博. IMTL 逻辑代数的一种新强化形式[J].山东大学学报:理学版, 2014,49(4):84-89. ZHOU Jianren, WU Hongbo. A schematic extension of IMTL-logic algebras[J]. Journal of Shandong University: Natural Science, 2014, 49(4):84-89.
[12] WANG Sanmin, WANG Baoshu, WANG Xiangyun. A characterization of truth-functions in the nilpotent minimum logic[J]. Fuzzy Sets and Systems, 2004, 145(2):253-266.
[1] . Representative forms of commutative BR0-algebras on a set by implication operator [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 86-94.
[2] LIANG Ying, CUI Yan-li, WU Hong-bo. Properties of residuated lattice of deduction systems set algebra in BL system [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 65-70.
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[4] QIAO Xi-min, WU Hong-bo. 〈,(-overQ)〉-fuzzy filter and its characterization of the non-commutative residual lattices on the interval sets [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 102-107.
[5] KOU Hai-yan, WU Hong-bo. Wajsberg's form of MTL algebras with applications [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 75-82.
[6] LIU Chun-hui. Fuzzy ultra ⊙-ideals in regular residuated lattices [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(12): 87-94.
[7] YANG Gong-lin, JI Pei-sheng. Some properties of primitive ideal submodules in Hilbert C*-modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 50-55.
[8] LIU Chun-hui1,2. Prime fuzzy ⊙ideals and its topological properties of
regular residuated lattices [J]. J4, 2013, 48(12): 52-56.
[9] LIU Chun-hui1,2. Lattice of fuzzy filter in a Heyting algebra [J]. J4, 2013, 48(12): 57-60.
[10] LIU Chun-hui1,2. Theory of filters in Fuzzy implication algebras [J]. J4, 2013, 48(09): 73-77.
[11] ZHOU Jian-ren, WU Hong-bo*. The regularness of WBR0-algebras and relationship with other logic algebras [J]. J4, 2012, 47(2): 86-92.
[12] LI Ling-ling, WU Hong-bo*. BR0-distributivity and its generalization [J]. J4, 2012, 47(2): 93-97.
[13] QIN Xue-cheng, LIU Chun-hui*. The lattice of fuzzy ⊙-ideals in regular residuated lattices [J]. J4, 2011, 46(8): 73-76.
[14] QIAO Xi-min1,2, WU Hong-bo1*. The representation theorem of lattice BR0-algebraic structure [J]. J4, 2010, 45(9): 38-42.
[15] ZHANG Qiong, WU Hongbo*. The Δ-root of theory and generalized Δ-modus  ponens problem in BLΔ* [J]. J4, 2010, 45(4): 60-65.
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