信念算子运算的语义解释研究
|
摘要
在基于知识的推理中,由于知识源的不完全可靠和来自不同的知识源的知识可能相互抵触等原因,我们不能把这些知识看成绝对真理,只能将它们作为信念,对信念的处理是人工智能研究中的一个关键问题。
汲取算子模糊逻辑的思想,本文将[0,1]区间上的实数作为信念算子,用以描述命题的可信程度,从而在命题逻辑的基础上建立了带有信念算子的命题逻辑,我们称其为信念算子命题逻辑。
本文用一个实系数多项式函数定义信念算子之间的运算,证明了这种定义方法在一些比较基本的假设之下的唯一性。这个运算具有良好的数学性质和直观背景。为了实现基于信念的推理,我们将布尔算子模糊逻辑中公式的恒真水平的概念引入到信念算子命题逻辑中,根据信念算子运算的特点,建立了信念算子命题逻辑中求任意给定公式的恒真水平的机械推导算法BMD。这种方法优于算子模糊逻辑中的λ—归结方法。
根据形式推导算法BMD,本文给出了求解任意给定公式恒真水平的实现系统。该系统主要包括规则库模块、函数模块、逻辑联结词化简模块、模糊原子计算模块以及回溯求解模块。运行时,系统接收一个公式作为输入,自动计算出该公式的恒真水平。
In the knowledge-based reasoning,because that knowledge sources are incompletely reliable and the knowledge from different knowledge sources may conflict with each other,and some other reasons,we can not take this knowledge as an absolute truth,only as a belief.The dealing with the belief is a key issue-in artificial intelligence research.
Learning from the idea of the Operator Fuzzy Logic,this article takes a real number on the interval of[0,1]as a belief operator,describing the credibility of a proposition,so on the basis of Proposition Logic builds a proposition logic with belief operator,we call it as belief operator proposition logic.
In this paper,we use a real coefficient multinomial function to define the-operation between belief operators,prove the uniqueness in some relative basal a ssumptions.This operation has a good mathematical nature and intuitive background. To implement the belief-based consequence,we introduce the concept of constant real level of the formula in Boolean Operator Fuzzy Logic into Belief-Operator Proposition Logic.According to the characters of the operation between belief operators,we establish a mechanical derivation algorithm named by BMD which computes any given formula's constant true level which in Belief Operator Proposition Logic.This method is superior thanλ-attributed method in Operator Fuzzy Logic.
According to the formal derivation algorithm BMD,this paper gives a system to actualize computing any given formula's constant true level.The system-mainly consists of rule storeroom module,function module,simplification of the logical conjunction module,numberation of fuzzy atoms module and backdated-computation module.In running time,the system accepts a formula as an input, and calculates the formula's constant true level automatically.
汲取算子模糊逻辑的思想,本文将[0,1]区间上的实数作为信念算子,用以描述命题的可信程度,从而在命题逻辑的基础上建立了带有信念算子的命题逻辑,我们称其为信念算子命题逻辑。
本文用一个实系数多项式函数定义信念算子之间的运算,证明了这种定义方法在一些比较基本的假设之下的唯一性。这个运算具有良好的数学性质和直观背景。为了实现基于信念的推理,我们将布尔算子模糊逻辑中公式的恒真水平的概念引入到信念算子命题逻辑中,根据信念算子运算的特点,建立了信念算子命题逻辑中求任意给定公式的恒真水平的机械推导算法BMD。这种方法优于算子模糊逻辑中的λ—归结方法。
根据形式推导算法BMD,本文给出了求解任意给定公式恒真水平的实现系统。该系统主要包括规则库模块、函数模块、逻辑联结词化简模块、模糊原子计算模块以及回溯求解模块。运行时,系统接收一个公式作为输入,自动计算出该公式的恒真水平。
In the knowledge-based reasoning,because that knowledge sources are incompletely reliable and the knowledge from different knowledge sources may conflict with each other,and some other reasons,we can not take this knowledge as an absolute truth,only as a belief.The dealing with the belief is a key issue-in artificial intelligence research.
Learning from the idea of the Operator Fuzzy Logic,this article takes a real number on the interval of[0,1]as a belief operator,describing the credibility of a proposition,so on the basis of Proposition Logic builds a proposition logic with belief operator,we call it as belief operator proposition logic.
In this paper,we use a real coefficient multinomial function to define the-operation between belief operators,prove the uniqueness in some relative basal a ssumptions.This operation has a good mathematical nature and intuitive background. To implement the belief-based consequence,we introduce the concept of constant real level of the formula in Boolean Operator Fuzzy Logic into Belief-Operator Proposition Logic.According to the characters of the operation between belief operators,we establish a mechanical derivation algorithm named by BMD which computes any given formula's constant true level which in Belief Operator Proposition Logic.This method is superior thanλ-attributed method in Operator Fuzzy Logic.
According to the formal derivation algorithm BMD,this paper gives a system to actualize computing any given formula's constant true level.The system-mainly consists of rule storeroom module,function module,simplification of the logical conjunction module,numberation of fuzzy atoms module and backdated-computation module.In running time,the system accepts a formula as an input, and calculates the formula's constant true level automatically.
引文
[1]刘瑞胜,孙吉贵,刘叙华.认识逻辑(1):关于知识和信念的逻辑框架.计算机学报,1998,21(7):627-637.
[2]曹子宁,董红斌,石纯一.多Agent信念逻辑及其在概率意义下的推广.软件学报,2001,12(9):1366-1374.
[3]Alexander Bochman.A foundational theory of belief and belief change.Artificial Intelligence,1999,108:309-352.
[4]张丽丽,邓安生.常识推理中一种分层隔离矛盾的修正策略.第十一届中国人工智能学术年会,武汉,2005:89-94.
[5]Marcelo A.Falappa,Gabriele Kern-Isberner,Guillermo R.Simari.Explanations,belief revision and defeasible reasoning.Artificial Intelligence,2002,141:1-28.
[6]A.Darwiche,J.Pearl.On the Logic of Iterated Belief Revision.Artificial Intelligence.1997,89:1-29.
[7]张丽丽.常识推理中不一致信念的两种修正策略研究:(硕士学位论文).厦门:厦门大学,2005.
[8]尚颖,邓安生,鞠晓东.不一致信念的定量非修正方法满足AGM公设的讨论.计算机工程与科学,2004,26(5):106-109.
[9]Lee,R.C.T.,Chang,C.L.,Some properties of fuzzy logic,Information and Control,1971,19(5):417.
[10]Lee,R.C.T.,Chang,C.L.,Fuzzy logic and the resolution principle,J.A ssoc.Comput.Mach.,1972,19(1):109.
[11]林作栓,李未.超协调逻辑(Ⅱ)—新超协调逻辑研究.计算机科学,1994,21(6):1-7.
[12]林作栓,李未.超协调逻辑(Ⅲ)—超协调性的逻辑基础.计算机科学,1995,22(1):1-4.
[13]林作栓.容错推理.计算机科学,1993,20(2):18-22.
[14]Charles B.Cross.Nonmonotonic inconsistency.Artificial Intelligence,2003,149:161-178.
[15]关伟洲,邓安生.常识推理中不一致信念的一种非修正处理方法.东北师大学报自然科学版,2000,32(3):112-114.
[16]张丽英,邓安生.基于非修正方法的认识进程及其极限.东北师大学报自然科学版,2000,32(3):108-111.
[17]刘叙华,安直.算子Fuzzy逻辑及其归结推理的改进.计算机学报,1990,12:890-899.
[18]程晓春,姜云飞,刘叙华.基于辩论语义的算子模糊逻辑.中国科学(E辑),1996,26(1):64-71.
[19]程晓春.基于算子模糊逻辑的不确定程度计算.软件学报,1997,8(7):525-534.
[20]刘叙华,程晓春.基于信度语义的算子模糊逻辑.计算机学报,1995,18(12):881-885.
[21]邓安生.布尔算子模糊逻辑及其推理理论研究:(博士学位论文).长春:吉林大学.1995.
[22]J.A.Goguen.The logic of inexact concepts.Synthese 19,1968,69:325-373.
[23]L.A.Zadeh.The Concept of a Linguistic Variable and its Application to Approximate Reasoning-Ⅰ.Information Sciences,1975(8):199-249.
[24]王万森,何华灿.基于范逻辑学的逻辑关系柔性化研究.软件学报,2005,16(5):754-760.
[25]何华灿等.泛逻辑学原理.北京:科学出版社,2001.
[26]刘叙华,肖红.算子Fuzzy逻辑和λ-归结方法.计算机学报,1989,2:81-91.
[27]程晓春,刘叙华,陆汝铃.基于证据语义的算子模糊逻辑.科学通报,1995,40(1):86-88.
[28]邓安生,张丽英.算子模糊逻辑定量模型的局限性.中国科学(E辑),1998,28(5):446-453.
[29]邓安生,赵宏亮.多项式意义下模糊算子运算定义的唯一性.东北师大学报自然科学版,1998,3:1-3.
[30]萧瑶.信念修正逻辑初探(硕士学位论文).重庆:西南大学.2008.
[31]Jan Plaza.Logic of Public Communications.Synthese,2007,158:165-179.
[32]Frank Veltman.Defaults in Update Semantics.Journal of Philosophical Logic,1996,25:221-261.
[2]曹子宁,董红斌,石纯一.多Agent信念逻辑及其在概率意义下的推广.软件学报,2001,12(9):1366-1374.
[3]Alexander Bochman.A foundational theory of belief and belief change.Artificial Intelligence,1999,108:309-352.
[4]张丽丽,邓安生.常识推理中一种分层隔离矛盾的修正策略.第十一届中国人工智能学术年会,武汉,2005:89-94.
[5]Marcelo A.Falappa,Gabriele Kern-Isberner,Guillermo R.Simari.Explanations,belief revision and defeasible reasoning.Artificial Intelligence,2002,141:1-28.
[6]A.Darwiche,J.Pearl.On the Logic of Iterated Belief Revision.Artificial Intelligence.1997,89:1-29.
[7]张丽丽.常识推理中不一致信念的两种修正策略研究:(硕士学位论文).厦门:厦门大学,2005.
[8]尚颖,邓安生,鞠晓东.不一致信念的定量非修正方法满足AGM公设的讨论.计算机工程与科学,2004,26(5):106-109.
[9]Lee,R.C.T.,Chang,C.L.,Some properties of fuzzy logic,Information and Control,1971,19(5):417.
[10]Lee,R.C.T.,Chang,C.L.,Fuzzy logic and the resolution principle,J.A ssoc.Comput.Mach.,1972,19(1):109.
[11]林作栓,李未.超协调逻辑(Ⅱ)—新超协调逻辑研究.计算机科学,1994,21(6):1-7.
[12]林作栓,李未.超协调逻辑(Ⅲ)—超协调性的逻辑基础.计算机科学,1995,22(1):1-4.
[13]林作栓.容错推理.计算机科学,1993,20(2):18-22.
[14]Charles B.Cross.Nonmonotonic inconsistency.Artificial Intelligence,2003,149:161-178.
[15]关伟洲,邓安生.常识推理中不一致信念的一种非修正处理方法.东北师大学报自然科学版,2000,32(3):112-114.
[16]张丽英,邓安生.基于非修正方法的认识进程及其极限.东北师大学报自然科学版,2000,32(3):108-111.
[17]刘叙华,安直.算子Fuzzy逻辑及其归结推理的改进.计算机学报,1990,12:890-899.
[18]程晓春,姜云飞,刘叙华.基于辩论语义的算子模糊逻辑.中国科学(E辑),1996,26(1):64-71.
[19]程晓春.基于算子模糊逻辑的不确定程度计算.软件学报,1997,8(7):525-534.
[20]刘叙华,程晓春.基于信度语义的算子模糊逻辑.计算机学报,1995,18(12):881-885.
[21]邓安生.布尔算子模糊逻辑及其推理理论研究:(博士学位论文).长春:吉林大学.1995.
[22]J.A.Goguen.The logic of inexact concepts.Synthese 19,1968,69:325-373.
[23]L.A.Zadeh.The Concept of a Linguistic Variable and its Application to Approximate Reasoning-Ⅰ.Information Sciences,1975(8):199-249.
[24]王万森,何华灿.基于范逻辑学的逻辑关系柔性化研究.软件学报,2005,16(5):754-760.
[25]何华灿等.泛逻辑学原理.北京:科学出版社,2001.
[26]刘叙华,肖红.算子Fuzzy逻辑和λ-归结方法.计算机学报,1989,2:81-91.
[27]程晓春,刘叙华,陆汝铃.基于证据语义的算子模糊逻辑.科学通报,1995,40(1):86-88.
[28]邓安生,张丽英.算子模糊逻辑定量模型的局限性.中国科学(E辑),1998,28(5):446-453.
[29]邓安生,赵宏亮.多项式意义下模糊算子运算定义的唯一性.东北师大学报自然科学版,1998,3:1-3.
[30]萧瑶.信念修正逻辑初探(硕士学位论文).重庆:西南大学.2008.
[31]Jan Plaza.Logic of Public Communications.Synthese,2007,158:165-179.
[32]Frank Veltman.Defaults in Update Semantics.Journal of Philosophical Logic,1996,25:221-261.