BL命题逻辑系统的强同余关系及演绎系统
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摘要
通过在BL命题逻辑系统的公式集F(S)中提出演绎系统的概念,并引入强同余关系,讨论BL系统中演绎系统和强同余关系之间的联系,给出二者之间相互转换的方法,并得到了二者之间相互转换的还原性.
The concept of deductive system was proposed on formula set F(S)of BL propositional logic system,and the strong congruence relation was introduced.We discussed the connection between deductive systems and strong congruence relations in BL system,gave the method of interconversion between them,and obtained the reducibility of interconversion between them.
The concept of deductive system was proposed on formula set F(S)of BL propositional logic system,and the strong congruence relation was introduced.We discussed the connection between deductive systems and strong congruence relations in BL system,gave the method of interconversion between them,and obtained the reducibility of interconversion between them.
引文
[1]Chang C C.Algebraic Analysis of Many Valued Logic[J].Trans Amer Math Soc,1958,88(2):467-490.
[2]Hajek P.Metamathematics of Fuzzy Logic[M].Dordrecht,Netherlands:Kluwer Academic Publishers,1998.
[3]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.
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[8]张小红.模糊逻辑及其代数分析[M].北京:科学出版社,2008.(ZHANG Xiaohong.Fuzzy Logic and Its Algebraic Analysis[M].Beijing:Science Press,2008.)
[9]周建仁,吴洪博.R0-蕴涵算子所导出的逻辑函数的特征[J].数学学报(中文版),2014,57(2):235-248.(ZHOU Jianren,WU Hongbo.The Characteristics of Logic Functions Determined by R0-Implication Operator[J].Acta Mathematica Sinica(Chinese Series),2014,57(2):235-248.)
[10]吴洪博,石慧君.Heyting系统及其H-Locale化形式[J].数学学报(中文版),2012,55(6):1119-1130.(WU Hongbo,SHI Huijun.Heyting System and Its H-Localification[J].Acta Mathematica Sinica(Chinese Series),2012,55(6):1119-1130.)
[11]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 Hongbo,WANG Ning.MT Ideals of Regular FI Algebras with Their Applications[J].Acta Electronica Sinica,2013,41(7):1389-1394.)
[12]周建仁,谢晶晶,吴洪博.基于剩余格的一类度量空间及性质[J].吉林大学学报(理学版),2012,50(5):897-901.(ZHOU Jianren,XIE Jingjing,WU Hongbo.A Metric Structure and Its Properties Based on Metric Residual Lattice[J].Journal of Jilin University(Science Edition),2012,50(5):897-901.)
[13]周建仁,吴洪博.BL代数的一种弱化形式[J].吉林大学学报(理学版),2014,52(2):231-236.(ZHOU Jianren,WU Hongbo.A Weakened Form of BL-Aigebra[J].Journal of Jilin University(Science Edition),2014,52(2):231-236.)
[14]刘春辉.有界Heyting代数的模糊LI-理想[J].工程数学学报,2016,33(4):391-401.(LIU Chunhui.Fuzzy LI-Ideals in Bounded Heyting Algebras[J].Chinese Journal of Engineering Mathematics,2016,33(4):391-401.)
[15]刘慧敏,吴洪博.DFI代数的距离函数及其性质[J].吉林大学学报(理学版),2016,54(2):207-214.(LIU Huimin,WU Hongbo.Distance Function of DFI-Algebras and Its Properties[J].Journal of Jilin University(Science Edition),2016,54(2):207-214.)
[16]汪宁,吴洪博.SWBR0代数的蕴涵理想及其诱导的商代数[J].吉林大学学报(理学版),2013,51(1):21-26.(WANG Ning,WU Hongbo.Implication Ideal with Derived Quotient Algebra of SWBR0-Algebra[J].Journal of Jilin University(Science Edition),2013,51(1):21-26.)
[17]吴洪博.ukasiewicz命题逻辑中公式的Γ-真度理论和极限定理[J].中国科学(信息科学),2014,44(12):1542-1559.(WU Hongbo.The Theory ofΓ-Truth Degrees of Formulas and Limit Theorem inukasiewicz Propositional Logic[J].Scientia Sinica(Informationis),2014,44(12):1542-1559.)
[18]吴洪博.推理闭包算子及其诱导的空间[J].西北大学学报(自然科学版),2008,38(1):9-14.(WU Hongbo.The Reasoning Closure Operator with Its Induced Space[J].Journal of Northwest University(Natural Science Edition),2008,38(1):9-14.)
[19]王国俊,折延宏.二值命题逻辑中理论的发散性、相容性及其拓扑刻画[J].数学学报,2007,50(4):841-850.(WANG Guojun,ZHE Yanhong.Topological Description of Divergency and Consistency of Two-Valued Propositional Theories[J].Acta Mathematica Sinica,2007,50(4):841-850.)
[20]折延宏,王国俊.三值命题逻辑系统*3中逻辑理论性态的拓扑刻画[J].数学学报,2009,52(6):1225-1234.(ZHE Yanhong,WANG Guojun.Topological Characterizations of Properties of Logic Theories in Three-Valued Propositional Logic System*3[J].Acta Mathematica Sinica,2009,52(6):1225-1234.)
[2]Hajek P.Metamathematics of Fuzzy Logic[M].Dordrecht,Netherlands:Kluwer Academic Publishers,1998.
[3]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.
[4]裴道武,王国俊.形式系统L*的完备性及其应用[J].中国科学(技术科学),2002,32(1):56-64.(PEI Daowu,WANG Guojun.The Completeness and Application of Form SystemL*[J].Scientia Sinica(Technologica),2002,32(1):56-64.)
[5]吴洪博.基础R0-代数与基础L*系统[J].数学进展,2003,32(5):565-576.(WU Hongbo.Basis R0-Algebra and Basis L*System[J].Advances in Mathematics,2003,32(5):565-576.)
[6]吴望名.Fuzzy蕴涵代数[J].模糊系统与数学,1990,4(1):56-64.(WU Wangming.Fuzzy Implication Algebras[J].Fuzzy Systems and Mathematics,1990,4(1):56-64.)
[7]徐扬.格蕴涵代数[J].西南交通大学学报,1993,28(1):20-27.(XU Yang.Lattice Implication Algebras[J].Journal of Southwest Jiaotong University,1993,28(1):20-27.)
[8]张小红.模糊逻辑及其代数分析[M].北京:科学出版社,2008.(ZHANG Xiaohong.Fuzzy Logic and Its Algebraic Analysis[M].Beijing:Science Press,2008.)
[9]周建仁,吴洪博.R0-蕴涵算子所导出的逻辑函数的特征[J].数学学报(中文版),2014,57(2):235-248.(ZHOU Jianren,WU Hongbo.The Characteristics of Logic Functions Determined by R0-Implication Operator[J].Acta Mathematica Sinica(Chinese Series),2014,57(2):235-248.)
[10]吴洪博,石慧君.Heyting系统及其H-Locale化形式[J].数学学报(中文版),2012,55(6):1119-1130.(WU Hongbo,SHI Huijun.Heyting System and Its H-Localification[J].Acta Mathematica Sinica(Chinese Series),2012,55(6):1119-1130.)
[11]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 Hongbo,WANG Ning.MT Ideals of Regular FI Algebras with Their Applications[J].Acta Electronica Sinica,2013,41(7):1389-1394.)
[12]周建仁,谢晶晶,吴洪博.基于剩余格的一类度量空间及性质[J].吉林大学学报(理学版),2012,50(5):897-901.(ZHOU Jianren,XIE Jingjing,WU Hongbo.A Metric Structure and Its Properties Based on Metric Residual Lattice[J].Journal of Jilin University(Science Edition),2012,50(5):897-901.)
[13]周建仁,吴洪博.BL代数的一种弱化形式[J].吉林大学学报(理学版),2014,52(2):231-236.(ZHOU Jianren,WU Hongbo.A Weakened Form of BL-Aigebra[J].Journal of Jilin University(Science Edition),2014,52(2):231-236.)
[14]刘春辉.有界Heyting代数的模糊LI-理想[J].工程数学学报,2016,33(4):391-401.(LIU Chunhui.Fuzzy LI-Ideals in Bounded Heyting Algebras[J].Chinese Journal of Engineering Mathematics,2016,33(4):391-401.)
[15]刘慧敏,吴洪博.DFI代数的距离函数及其性质[J].吉林大学学报(理学版),2016,54(2):207-214.(LIU Huimin,WU Hongbo.Distance Function of DFI-Algebras and Its Properties[J].Journal of Jilin University(Science Edition),2016,54(2):207-214.)
[16]汪宁,吴洪博.SWBR0代数的蕴涵理想及其诱导的商代数[J].吉林大学学报(理学版),2013,51(1):21-26.(WANG Ning,WU Hongbo.Implication Ideal with Derived Quotient Algebra of SWBR0-Algebra[J].Journal of Jilin University(Science Edition),2013,51(1):21-26.)
[17]吴洪博.ukasiewicz命题逻辑中公式的Γ-真度理论和极限定理[J].中国科学(信息科学),2014,44(12):1542-1559.(WU Hongbo.The Theory ofΓ-Truth Degrees of Formulas and Limit Theorem inukasiewicz Propositional Logic[J].Scientia Sinica(Informationis),2014,44(12):1542-1559.)
[18]吴洪博.推理闭包算子及其诱导的空间[J].西北大学学报(自然科学版),2008,38(1):9-14.(WU Hongbo.The Reasoning Closure Operator with Its Induced Space[J].Journal of Northwest University(Natural Science Edition),2008,38(1):9-14.)
[19]王国俊,折延宏.二值命题逻辑中理论的发散性、相容性及其拓扑刻画[J].数学学报,2007,50(4):841-850.(WANG Guojun,ZHE Yanhong.Topological Description of Divergency and Consistency of Two-Valued Propositional Theories[J].Acta Mathematica Sinica,2007,50(4):841-850.)
[20]折延宏,王国俊.三值命题逻辑系统*3中逻辑理论性态的拓扑刻画[J].数学学报,2009,52(6):1225-1234.(ZHE Yanhong,WANG Guojun.Topological Characterizations of Properties of Logic Theories in Three-Valued Propositional Logic System*3[J].Acta Mathematica Sinica,2009,52(6):1225-1234.)