一元子结构谓词逻辑中相似的代数语义

王军涛; 王梅; 折延宏

doi:10.12263/DZXB.20210267

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一元子结构谓词逻辑中相似的代数语义

学术论文 | 更新时间：2025-12-08

- 一元子结构谓词逻辑中相似的代数语义
- Algebraic Semantics of Similarity in Monadic Substructural Predicate Logics
- 电子学报 2023年51卷第4期页码：956-964
- 作者机构：
  
  1.西安石油大学理学院，陕西西安 710065
  2.陕西科技大学电气与控制工程学院，陕西西安 710021
- 作者简介：
  
  [ "王军涛男，1987年12月生，陕西咸阳人，2018年7月获西北大学理学博士学位.现为西安石油大学理学院副教授、硕士生导师.主要研究方向为序代数、模糊逻辑及不确定性推理." ]
  [ "王梅女，1992年3月生，山西长治人.现为陕西科技大学电气与控制工程学院博士研究生.主要研究方向为序代数及不确定性推理." ]
  [ "折延宏（通讯作者）男，1983 年 5 月生，陕西延安人 . 2010 年 7 月获陕西师范大学理学博士学位. 现为西安石油大学理学院教授、硕士生导师. 主要研究方向为多粒度数据分析、模糊逻辑及不确定性推理. Email: yanhongshe@xsyu.edu.cn" ]
- 基金信息：
  
  国家自然科学基金(12001423;61976244;12171294);陕西省自然科学基础研究计划(2020JQ-762;2021JQ-580);陕西省教育厅自然科学研究专项计划(20JK0626)
- DOI：10.12263/DZXB.20210267
  中图分类号： O155;
- 收稿：2021-02-22，
  
  修回：2021-12-06，
  
  纸质出版：2023-04-25
- 稿件说明：
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王军涛,王梅,折延宏.一元子结构谓词逻辑中相似的代数语义[J].电子学报,2023,51(04):956-964.

WANG Jun-tao,WANG Mei,SHE Yan-hong.Algebraic Semantics of Similarity in Monadic Substructural Predicate Logics[J].ACTA ELECTRONICA SINICA,2023,51(04):956-964.
王军涛,王梅,折延宏.一元子结构谓词逻辑中相似的代数语义[J].电子学报,2023,51(04):956-964. DOI： 10.12263/DZXB.20210267.

WANG Jun-tao,WANG Mei,SHE Yan-hong.Algebraic Semantics of Similarity in Monadic Substructural Predicate Logics[J].ACTA ELECTRONICA SINICA,2023,51(04):956-964. DOI： 10.12263/DZXB.20210267.

摘要

借助一元模糊谓词逻辑与S5型模糊模态逻辑的等价性，建立了一元子结构谓词逻辑中相似联结词的代数语义，引入了相似一元剩余格，并研究了其基本的代数性质.其次，研究了相似一元剩余格上的相似滤子，刻画了可表示的相似一元剩余格. 最后，引入了相似一元剩余格对应的逻辑系统，证明了其完备性定理，并解决了其最小半线性扩张问题.

Abstract

Using the equivalence between monadic fuzzy predicate logics and S5 type fuzzy modal logic

the algebraic semantics of similarity in monadic substructural predicate logics are introduced

the resulting class of algebras called similarity monadic residuated lattices

and their basic algebraic properties are studied. Secondly

the similarity filters of similarity monadic residuated lattices are introduced

and representable similarity monadic residuated lattices are characterized by using them. Finally

the logic system corresponding to similarity monadic residuated lattices is established

and its minimum semilinear extension and completeness are studied.

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Keywords

references

ZADEH L A . Fuzzy sets [J ] . Information and Control , 1965 , 8 ( 3 ): 338 - 353 .

王军涛 , 折延宏 . 不确定性推理的代数理论 [M ] . 北京 : 电子工业出版社 , 2020 .

WANG J T , SHE Y H . Algebraic Theory of Uncertain Reasoning [M ] . Beijing : Electronic Industry Press , 2020 . (in Chinese)

辛小龙 , 王军涛 , 杨将 . 逻辑代数上的非可换测度 [M ] . 北京 : 科学出版社 , 2019 .

XIN X L , WANG J T , YANG J . Non Probabilistic Measures on Logical Algebras [M ] . Beijing : The Science Publishing Company , 2019 . (in Chinese)

WARD M , DILWORTH P R . Residuated lattice [J ] . Transactions of the American Mathematical Society , 1939 , 45 ( 3 ): 335 - 354 .

左卫兵 . 基于剩余格语义的格值逻辑系统的程度化方法 [J ] . 电子学报 , 2017 , 45 ( 8 ): 1842 - 1848 .

ZUO W B . Graded method of lattice-valued logic system based on residuated lattice semantics [J ] . Acta Electronica Sinca , 2017 , 45 ( 8 ): 1842 - 1848 . (in Chinese)

吴洪博 , 王娜 . BR 0 -代数中MT理想的扩展及素MT理想的存在性 [J ] . 电子学报 , 2015 , 43 ( 6 ): 1137 - 1143 .

WU H B , WANG N . The extension of MT ideals and the existence of prime MT ideal in BR 0 -algebras [J ] . Acta Electronica Sinca , 2015 , 43 ( 6 ): 1137 - 1143 . (in Chinese)

左卫兵 . MTL-代数语义上逻辑公式的概率真度 [J ] . 电子学报 , 2015 , 43 ( 2 ): 293 - 298 .

ZUO W B . Probability truth degrees of formulas in MTL-algebras semantics [J ] . Acta Electronica Sinca , 2015 , 43 ( 2 ): 293 - 298 . (in Chinese)

左卫兵 . 基于MV-代数语义的格值逻辑的程度化方法 [J ] . 电子学报 , 2013 , 41 ( 10 ): 2035 - 2040 .

ZUO W B . Graded method of lattice-valued logic system based on MV-algebras semantics [J ] . Acta Electronica Sinca , 2013 , 41 ( 10 ): 2035 - 2040 . (in Chinese)

吴洪博 , 汪宁 . 基于正则FI-代数的MT理想及其应用 [J ] . 电子学报 , 2013 , 41 ( 7 ): 1389 - 1394 .

WU H B , WANG N . MT ideals of regular FI-algebras with their applications [J ] . Acta Electronica Sinca , 2013 , 41 ( 7 ): 1389 - 1394 . (in Chinese)

吴洪博 , 张琼 . NML系统的有限强完备性 [J ] . 电子学报 , 2010 , 38 ( 6 ): 1414 - 1418 .

WU H B , ZHANG Q . On the finite strong completeness of NML [J ] . Acta Electronica Sinca , 2010 , 38 ( 6 ): 1414 - 1418 . (in Chinese)

吴洪博 , 石慧君 . Heyting 系统及其H-空间化表示形式 [J ] . 电子学报 , 2012 , 40 ( 5 ): 995 - 999 .

WU H B , SHI H J . Heyting system and its representation by H-spatilization [J ] . Acta Electronica Sinca , 2012 , 40 ( 5 ): 995 - 999 . (in Chinese)

ZHU Y Q , XU Y . On filter theory of residuated lattices [J ] . Information Sciences , 2010 , 180 ( 19 ): 3614 - 3632 .

ZADEH L A . Similarity relations and fuzzy orderings [J ] . Information Sciences , 1971 , 3 ( 2 ): 177 - 200 .

井美 , 惠小静 , 王蓉 . 基于相似度的直觉模糊推理反向三I算法的鲁棒性 [J ] . 电子学报 , 2020 , 48 ( 2 ): 265 - 271 .

JING M , HUI X J , WANG R . Robustness of intuitionistic fuzzy inference reverse triple I methods based on similarity [J ] . Acta Electronica Sinca , 2020 , 48 ( 2 ): 265 - 271 . (in Chinese)

高峰 , 赵竹新 , 文攻坚 , 等 . 基于Vague集的特征不确定性建模及相似度求解 [J ] . 电子学报 , 2011 , 39 ( 11 ): 2622 - 2626 .

GAO F , ZHAO Z X , WEN G J , et al . Modeling of the uncertain of image features and their simiularity computing based on vague sets [J ] . Acta Electronica Sinca , 2011 , 39 ( 11 ): 2622 - 2626 . (in Chinese)

罗敏霞 , 姚宁 . L系统中公式的语构程度化方法 [J ] . 电子学报 , 2011 , 39 ( 2 ): 424 - 428 .

LUO M X , YAO N . Syntactic graded method of formulars in the system L [J ] . Acta Electronica Sinca , 2011 , 39 ( 2 ): 424 - 428 . (in Chinese)

HAJEK P . Metamathematics of Fuzzy Logic [M ] . Dordrecht : Kluwer Academic Publishers , 1998 .

BVELOHLAVEK R . Similarity relations in concept lattices [J ] . Journal of Logic and Computation , 2000 , 10 ( 6 ): 823 - 845 .

GEORGESCU G , POPESCU A . Concept lattices and similarity in non commutative fuzzy logic [J ] . Fundamenta Informaticae , 2002 , 53 ( 1 ): 23 - 54 .

TURUNEN E . A Lukasiewicz-style many-valued similarity reasoning review [C ] // Beyond Two: Theory and Applications of Multiple-Valued Logic . Heidelberg : Physica-Verlag , 2003 : 315 - 348 .

GERLA B , LEUCSTEAN I . Similarity MV-algebras [J ] . Fundamenta Informaticae , 2006 , 69 ( 3 ): 287 - 300 .

ALMINANA F G , PELAYSE M E . Similarity DH-algebras [J ] . Journal of Algebraic Structures and Their Applications , 2015 , 2 ( 1 ): 59 - 71 .

WANG J T , BORUMAND S A , HE P F . Similarity MTL-algebras and their corresponding logics [J ] . Journal of Multiple-Valued Logic and Soft Computing , 2019 , 32 ( 5-6 ): 607 - 628 .

王军涛 . 相似剩余格及其对应逻辑系统的完备性 [J ] . 高校应用数学学报 , 2021 , 36 ( 1 ): 111 - 126 .

WANG J T . Similarity residuated lattices and the completeness of their corresponding logics [J ] . Applied Mathematics-A Journal of Chinese Universities , 2021 , 36 ( 1 ): 111 - 126 . (in Chinese)

HAJEK P . Monadic fuzzy predicate logics [J ] . Studia Logica , 2002 , 71 : 165 - 175 .

RUTLEDGE J D . A Preliminary Investigation of the Intinitely Many-Valued Predicate Calculus [D ] . New York : Cornell University , 1959 .

WANG J T , XIN X L , HE P F . Monadic bounded hoops [J ] . Soft Computing , 2018 , 22 : 1749 - 1762 .

LIU H X . On categorical equivalences of equality algebras and monadic equality algebras [J ] . Logic Journal of the IGPL , 2019 , 27 ( 3 ): 267 - 280 .

CASTANO D , CIMADAMORE C R , DIAZ VARELA J P , et al . Monadic BL-algebras: The equivalent algebraic semantics of Hájek's monadic fuzzy logic [J ] . Fuzzy Sets and Systems , 2017 , 320 : 40 - 59 .

WANG J T , HE P F , SHE Y H . Monadic NM-algebras [J ] . Logic Journal of the IGPL , 2019 , 27 ( 6 ): 812 - 835 .

RACHUNEK J , SALOUNVA D . Monadic bounded residuated lattices [J ] . Order , 2013 , 30 : 195 - 210 .

NOGUERA C . Algebraic Study of Axiomatic Extensions of Triangular Norm Based Fuzzy Logics [D ] . Bellaterra : Artificial Intelligence Research Institute , 2006 .

BLOK W J , PIGOZZI D . Algebraizable logics [J ] . Memoirs of the American Mathematical Society , 1989 , 77 : 1 - 84 .

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 .

HAJEK P . On fuzzy modal logics S5(C) [J ] . Fuzzy Sets and Systems , 2010 , 161 : 2389 - 2396 .

CINTULA P , NOGUERA C . Implicational (semilinear) logics II: Additional connectives and characterizations of semilinearity [J ] . Archive for Mathematical Logic , 2016 , 55 : 353 - 372 .

张小红 , 折延宏 . 模糊量词及其积分语义 [M ] . 北京 : 科学出版社 , 2017 .

ZHANG X H , SHE Y H . Fuzzy Quantifier and Their Integral Semantics [M ] . Beijing : The Science Publishing Company , 2017 . (in Chinese)

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