合并逻辑方法研究
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摘要
合并逻辑(Combining Logic),又称为逻辑的合并(Combination of Logics),是“当代逻辑的理论和应用研究中最令人感兴趣的题目之一。”以《哲学逻辑手册》的主编Dov.M.Gabby为首的众多学者对它进行了研究,并取得了重要的成果。它在哲学、逻辑学、语言学、人工智能与计算机科学等方面有着重要的理论和应用价值,并使逻辑成为一个更有力的工具。
最初,合并逻辑出现在模态逻辑的环境中。因此,许多方法被特别地创造出来一方面模型化(model)克瑞普克结构的合并,另一方面模型化公理系统的合并,尽管现在它们被应用于大量的模型论和证明论概念。
Marcelo Finger和Dov.M.Gabby 1992年发表“Adding a Temporal Dimension to a Logic System"一文,首次提出了时间化(Temporalization)方法；1996年二人又发表论文"Combining Temporal Logic Systems",论述了时间逻辑系统与时间逻辑系统的合并,即将两个一维时间逻辑系统合并从而得到一个二维的时间逻辑系统。后来,Marcelo Finger对这个问题进行了更深入地研究,于2002年发表"The Unrestricted Combining of Temporal Logic Systems"一文,把关于线性时间流逻辑系统的合并推广到任意时间流。时间化方法不是任意合并两种逻辑,而是把一逻辑系统镶嵌在时间逻辑系统之中,外在地为该逻辑系统增加时间特征,把它的不同状态与不同的时刻联系起来,从而刻画该系统中的理论和模型在时间上的发展变化。这种方法部分程度地满足两个不同逻辑系统的算子之间的交互作用。并且合并后的逻辑系统保留了原来时间逻辑的几个性质,比如可靠性、完全性、可判定性、守恒性和线性时间流上的分离性等。
1996年Dov.M.Gabby创立了纤维(Fibring)方法。使用这种方法可以将两个逻辑系统合并从而得到一个新的逻辑系统；在新逻辑系统中,不但可以将命题变项和联结词混合,而且可以将推理规则合并。由于这种方法允许不同的模态算子交互作用,克服了融合方法的局限,并且在证明——理论的层面上也极易被理解,因而,纤维被认为是合并逻辑中最有效的方法,在数理逻辑的理论和应用方面具有重要意义。
当使用纤维方法将经典命题逻辑与直觉主义命题逻辑合并时,所得到的逻辑坍塌为经典命题逻辑。为了解决这个“坍塌问题”3,Cristina Sernadas, Joao Rasga和Walter A.Carnielli三人于2002年提出了调制纤维(Modulated Fibring)方法。这种方法通过使用附加格结构之间的模型来解决坍塌问题。调制纤维逻辑保持了可靠性、完全性等性质。
在Cristina Sernadas, Joao Rasga和Walter A.Carnielli提出调制纤维方法之后,Carlos Caleiro和Jaime Ramos于2004年提出了另一种解决坍塌问题的方法——隐纤维(Cryptofibring)。这种方法比调制纤维方法的结构更简单。它采用一个普遍化的隐态射的纤维语义来解决语义坍塌问题。
当前,刻画认知逻辑的动态特征也是现代逻辑研究中的重要问题。在双主体认知逻辑中,关于知道、相信的逻辑系统被构造,它们为分析和推理在特定外界和系统中的知识、信任等提供了一个基础。双主体认知逻辑能够表达知识、信任的静态特征。但是,知识、信任是观察的结果,这导致知道、相信另一种行为在没有明确保证的情况下可以被知道、相信,以致能在特殊的环境中完成目标。所以,知识、信任作为一系列明确观察的结果,是在时间上发展变化的。一个主体由于某些原因,比如来自其它主体的建议,可能在时间的某个时刻失去它的知识、信任或者增加新的知识、信任。如果将时间引入到双主体认知逻辑中,就能表达双主体认知的动态特征和双主体知识的演进。
本文力图在充分考察合并逻辑主要方法的基础上,尝试运用时间化和纤维方法,建立两个双主体时间认知逻辑系统,从而刻画双主体认知的动态特征并模拟双主体认知理论的发展变化。概括说来,本文的工作包括以下三个方面：
第一,对国外有关合并逻辑发展的资料进行了梳理,限于篇幅,对时间化、纤维、调制纤维和隐纤维这四种主要的方法进行介绍。时间化、纤维这两种方法应用最多。尤其是纤维方法,是合并逻辑中最重要的机制。国外很多逻辑学者对Dov.M.Gabby创立的这种方法进行了探讨,并对这种方法中存在的问题提出了一些解决办法。调制纤维和隐纤维这两种方法就是为了解决纤维方法中的问题而创立的。
第二,采用纤维方法,将时间逻辑系统与极小双主体认知逻辑系统Bm合并,构造一个新的逻辑系统——纤维的双主体时间认知逻辑系统F(Bm),从而表达双主体认知的动态特征及其知识的演进。它允许我们说明认知的动态并且及时地修正基于认知变化的一给定系统的认知理论。
第三,采用时间化方法,将时间逻辑系统与极小双主体认知逻辑系统Bm合并,构造一新的逻辑系统——时间化的双主体时间认知逻辑系统T(Bm),从而能以一种自然的方式表达有关主体认知的依赖于时间的性质。
Among the contemporary research on theory and application of logic, the topic of the combining logics or Combination of Logics, is one of the most interesting. The editor of Handbook of Philosophical Logic, Dov.M. Gabby, and other researchers study it and obtain important results. It has important theoretical and applicable value in Philosophy, Logic, artificial intelligence and computer, linguistics etc; and makes logic a powerful tool.
At first,the combining of Logics arise the backgroud of Modal logic.Therefore, many ways that was created specially on the one hand modelled the Combination of Kripke structure,on the other hand,modelled the Fibring axiomatic system,although nowadays they are largely applied to Model theory and the concept of proof theory.
Dov.M.Gabby and Marcelo Finger in 1992 published "Adding a Temporal Dimension to a Logic System"and put forward Temporalization methods.They published "Combining Temporal Logic Systems" 1996 and discussed the combination between temporal logic system and temporal logic system,that is combining two one-Dimension temporal logic system to obtain a two-Dimension temporal logic system. Marcelo Finger later studied it deeply and published "The Unrestricted Combining of Temporal Logic Systems",generalisationthe combination of the linear time flow to any time flow.The way is not combing arbitraryly two logics,but embeding one logic in temporal logic system and extentlly add the time to it and describe the evolution in time of a theory in L and its models. This mothed can satisfy partly the mutual action between different system operators. And the combined logic system preserves some nature of original temporal logic system, such soundness, completeness and decidability.
1996 Dov.M.Gabby established "Fibring". Using the motheds can combin two logic systems and build one new logic. In the new logic not only constructors are mixed, but proof Methods are combined. For it allows the mutual action between different system operators and overcome the defail of fuison and is well understand in the proof and theory, so it is recognized as the most effect method of the combining logics, with great significance in the theory and application of mathematical logic.In order to solve the collapsing problem in fibring proposed by Dov.M.Gabby, Cristina Sernadas, Joao Rasga and Walter A.Carnielli proposed the Modulated Fibring in 2002.
After proposed Modulated Fibring, Carlos Caleiro and Jaime Ramos had proposed another method——Cryptofibring to solve collapsing problem.This method is simpler than Modulated Fibring at structure.It uses a generalized fibring semantic of Cryptomorphisms to solve collapsing problem.
At present, describe the dynamic features of Epistemic logic is an important issue of the contemporary logic. In the double subject Epistemic logic, the logical system about knowledge or belief is constructed.They provide a basis of analysising and reasoning about knowledge and trust in particular out world.The double subject Epistemic logic can express the static features of knowledge or trust. However, knowledge and trust are the result of observation, which lead to know or trust another act in the absence of explicit guarantees may be believed and trusted and gained target in a particular circumstances. Therefore, knowledgeor trust as a series of specific observations, development and change in time. For some reason a subject, such as recommendations from other subjects may be lost at some point in time, its knowledge, trust, or add new knowledge, trust. If the time is introduced into the logic of the double subject knowledge, we can express the dynamic characteristics of the double subject knowledge and the evolution of the double subject knowledge.
This dissertation tries to use Temporalization and Fibring to build two double subjects Epistem Logic systems of Fibring.
In summary, this work includes the following three aspects:
First, pectination the data on combined logic development of of foreign and detailed the main and the latest approach. Temporalization, Fibring, Modulated fibring and Cryptofibring are discussed in this dissertation. Temporalization and Fibring are created by v.M.Gabby,the contemporary famous international logic scholar. These two ways are used mostly. Fibring is the most important and useful mechanism of the Combining Logic.Most logic scholar researc on it. In order to overcome the problem of Fibring, Modulated fibring and Cryptofibring are created.
Secondly,use fibring to build one fibring double subject Epistem Logic system--F(Bm). We combine temporal logic system with double subject Epistem Logic to build one new logics ystem:Logic system of Fibring double subject Epistem Logic--F(Bm).These systems can character dynamic characters of double subject Epistem Logic and the evolution of knowledge.
Thirdly, using Temporalization this dissertation combines temporal logic system with Epistem Logic to build one new logics ystem--Temporalization double subject Epistem Logic system T(Bm).
If we combine them and build temporal epistem logic system, then we can deal with that formula and character that nutureof the subject cognition depenging on time.
最初,合并逻辑出现在模态逻辑的环境中。因此,许多方法被特别地创造出来一方面模型化(model)克瑞普克结构的合并,另一方面模型化公理系统的合并,尽管现在它们被应用于大量的模型论和证明论概念。
Marcelo Finger和Dov.M.Gabby 1992年发表“Adding a Temporal Dimension to a Logic System"一文,首次提出了时间化(Temporalization)方法；1996年二人又发表论文"Combining Temporal Logic Systems",论述了时间逻辑系统与时间逻辑系统的合并,即将两个一维时间逻辑系统合并从而得到一个二维的时间逻辑系统。后来,Marcelo Finger对这个问题进行了更深入地研究,于2002年发表"The Unrestricted Combining of Temporal Logic Systems"一文,把关于线性时间流逻辑系统的合并推广到任意时间流。时间化方法不是任意合并两种逻辑,而是把一逻辑系统镶嵌在时间逻辑系统之中,外在地为该逻辑系统增加时间特征,把它的不同状态与不同的时刻联系起来,从而刻画该系统中的理论和模型在时间上的发展变化。这种方法部分程度地满足两个不同逻辑系统的算子之间的交互作用。并且合并后的逻辑系统保留了原来时间逻辑的几个性质,比如可靠性、完全性、可判定性、守恒性和线性时间流上的分离性等。
1996年Dov.M.Gabby创立了纤维(Fibring)方法。使用这种方法可以将两个逻辑系统合并从而得到一个新的逻辑系统；在新逻辑系统中,不但可以将命题变项和联结词混合,而且可以将推理规则合并。由于这种方法允许不同的模态算子交互作用,克服了融合方法的局限,并且在证明——理论的层面上也极易被理解,因而,纤维被认为是合并逻辑中最有效的方法,在数理逻辑的理论和应用方面具有重要意义。
当使用纤维方法将经典命题逻辑与直觉主义命题逻辑合并时,所得到的逻辑坍塌为经典命题逻辑。为了解决这个“坍塌问题”3,Cristina Sernadas, Joao Rasga和Walter A.Carnielli三人于2002年提出了调制纤维(Modulated Fibring)方法。这种方法通过使用附加格结构之间的模型来解决坍塌问题。调制纤维逻辑保持了可靠性、完全性等性质。
在Cristina Sernadas, Joao Rasga和Walter A.Carnielli提出调制纤维方法之后,Carlos Caleiro和Jaime Ramos于2004年提出了另一种解决坍塌问题的方法——隐纤维(Cryptofibring)。这种方法比调制纤维方法的结构更简单。它采用一个普遍化的隐态射的纤维语义来解决语义坍塌问题。
当前,刻画认知逻辑的动态特征也是现代逻辑研究中的重要问题。在双主体认知逻辑中,关于知道、相信的逻辑系统被构造,它们为分析和推理在特定外界和系统中的知识、信任等提供了一个基础。双主体认知逻辑能够表达知识、信任的静态特征。但是,知识、信任是观察的结果,这导致知道、相信另一种行为在没有明确保证的情况下可以被知道、相信,以致能在特殊的环境中完成目标。所以,知识、信任作为一系列明确观察的结果,是在时间上发展变化的。一个主体由于某些原因,比如来自其它主体的建议,可能在时间的某个时刻失去它的知识、信任或者增加新的知识、信任。如果将时间引入到双主体认知逻辑中,就能表达双主体认知的动态特征和双主体知识的演进。
本文力图在充分考察合并逻辑主要方法的基础上,尝试运用时间化和纤维方法,建立两个双主体时间认知逻辑系统,从而刻画双主体认知的动态特征并模拟双主体认知理论的发展变化。概括说来,本文的工作包括以下三个方面：
第一,对国外有关合并逻辑发展的资料进行了梳理,限于篇幅,对时间化、纤维、调制纤维和隐纤维这四种主要的方法进行介绍。时间化、纤维这两种方法应用最多。尤其是纤维方法,是合并逻辑中最重要的机制。国外很多逻辑学者对Dov.M.Gabby创立的这种方法进行了探讨,并对这种方法中存在的问题提出了一些解决办法。调制纤维和隐纤维这两种方法就是为了解决纤维方法中的问题而创立的。
第二,采用纤维方法,将时间逻辑系统与极小双主体认知逻辑系统Bm合并,构造一个新的逻辑系统——纤维的双主体时间认知逻辑系统F(Bm),从而表达双主体认知的动态特征及其知识的演进。它允许我们说明认知的动态并且及时地修正基于认知变化的一给定系统的认知理论。
第三,采用时间化方法,将时间逻辑系统与极小双主体认知逻辑系统Bm合并,构造一新的逻辑系统——时间化的双主体时间认知逻辑系统T(Bm),从而能以一种自然的方式表达有关主体认知的依赖于时间的性质。
Among the contemporary research on theory and application of logic, the topic of the combining logics or Combination of Logics, is one of the most interesting. The editor of Handbook of Philosophical Logic, Dov.M. Gabby, and other researchers study it and obtain important results. It has important theoretical and applicable value in Philosophy, Logic, artificial intelligence and computer, linguistics etc; and makes logic a powerful tool.
At first,the combining of Logics arise the backgroud of Modal logic.Therefore, many ways that was created specially on the one hand modelled the Combination of Kripke structure,on the other hand,modelled the Fibring axiomatic system,although nowadays they are largely applied to Model theory and the concept of proof theory.
Dov.M.Gabby and Marcelo Finger in 1992 published "Adding a Temporal Dimension to a Logic System"and put forward Temporalization methods.They published "Combining Temporal Logic Systems" 1996 and discussed the combination between temporal logic system and temporal logic system,that is combining two one-Dimension temporal logic system to obtain a two-Dimension temporal logic system. Marcelo Finger later studied it deeply and published "The Unrestricted Combining of Temporal Logic Systems",generalisationthe combination of the linear time flow to any time flow.The way is not combing arbitraryly two logics,but embeding one logic in temporal logic system and extentlly add the time to it and describe the evolution in time of a theory in L and its models. This mothed can satisfy partly the mutual action between different system operators. And the combined logic system preserves some nature of original temporal logic system, such soundness, completeness and decidability.
1996 Dov.M.Gabby established "Fibring". Using the motheds can combin two logic systems and build one new logic. In the new logic not only constructors are mixed, but proof Methods are combined. For it allows the mutual action between different system operators and overcome the defail of fuison and is well understand in the proof and theory, so it is recognized as the most effect method of the combining logics, with great significance in the theory and application of mathematical logic.In order to solve the collapsing problem in fibring proposed by Dov.M.Gabby, Cristina Sernadas, Joao Rasga and Walter A.Carnielli proposed the Modulated Fibring in 2002.
After proposed Modulated Fibring, Carlos Caleiro and Jaime Ramos had proposed another method——Cryptofibring to solve collapsing problem.This method is simpler than Modulated Fibring at structure.It uses a generalized fibring semantic of Cryptomorphisms to solve collapsing problem.
At present, describe the dynamic features of Epistemic logic is an important issue of the contemporary logic. In the double subject Epistemic logic, the logical system about knowledge or belief is constructed.They provide a basis of analysising and reasoning about knowledge and trust in particular out world.The double subject Epistemic logic can express the static features of knowledge or trust. However, knowledge and trust are the result of observation, which lead to know or trust another act in the absence of explicit guarantees may be believed and trusted and gained target in a particular circumstances. Therefore, knowledgeor trust as a series of specific observations, development and change in time. For some reason a subject, such as recommendations from other subjects may be lost at some point in time, its knowledge, trust, or add new knowledge, trust. If the time is introduced into the logic of the double subject knowledge, we can express the dynamic characteristics of the double subject knowledge and the evolution of the double subject knowledge.
This dissertation tries to use Temporalization and Fibring to build two double subjects Epistem Logic systems of Fibring.
In summary, this work includes the following three aspects:
First, pectination the data on combined logic development of of foreign and detailed the main and the latest approach. Temporalization, Fibring, Modulated fibring and Cryptofibring are discussed in this dissertation. Temporalization and Fibring are created by v.M.Gabby,the contemporary famous international logic scholar. These two ways are used mostly. Fibring is the most important and useful mechanism of the Combining Logic.Most logic scholar researc on it. In order to overcome the problem of Fibring, Modulated fibring and Cryptofibring are created.
Secondly,use fibring to build one fibring double subject Epistem Logic system--F(Bm). We combine temporal logic system with double subject Epistem Logic to build one new logics ystem:Logic system of Fibring double subject Epistem Logic--F(Bm).These systems can character dynamic characters of double subject Epistem Logic and the evolution of knowledge.
Thirdly, using Temporalization this dissertation combines temporal logic system with Epistem Logic to build one new logics ystem--Temporalization double subject Epistem Logic system T(Bm).
If we combine them and build temporal epistem logic system, then we can deal with that formula and character that nutureof the subject cognition depenging on time.
引文
[1]许涤非：《双主体认知逻辑研究》,中国社会出版社,2006年版。
[2]张家龙：《模态逻辑与哲学》,中国社会出版社,2002年版。
[3]弓肇祥：《认知逻辑新发展》,北京大学出版社,2004年版。
[4]弓肇祥：《可能世界理论》,北京大学出版社,2003年版。
[5]唐晓嘉：《认知的逻辑分析》,西南师范大学出版社,2003年版。
[6]周昌乐：《认知逻辑导论》,清华大学出版社,2001年版。
[7]张清宇、郭世铭、李小五：《哲学逻辑研究》,中国社会科学文献出版社,1997年版。
[8]李娜：《一种弱的命题时态逻辑》, “双B”代数和计算机逻辑论文集,上海交通大学出版社,1991年5月,p209—211
[9]黎仁蔚,《N系统：一个自然时序演绎系统》,科学通报,1988年06期
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[24]Gabbay, D,1996, "An overview of fibred semantics and the combination of logics", in F. Baader and K.U. Schulz, editors, Frontiers of Combining Systems:Proceedings of the 1st International Workshop FroCos'96, Munich (Germany), volume 3 of Applied Logic, pages 1-55. Kluwer Academic Publishers.
[25]Ronald Fagin,Joseph.Y.Halpern, Y.Moses, Reasoning About Knowledge, the MIT Press,1995.
[26]John-Jules Ch. Meyer and Wiebe Van Der Hoek. Epistemic Logic for AI and Computer Science. Cambridge University Press,1995.
[27]Gabbay, D. M., Hodkinson, I., and Reynolds, M.,1994, Temporal Logic:Mathematical Foundations and Computational Aspects, Volume 1,. Oxford:Clarendon Press.
[28]Gabbay, D. M. Hodkinson, I., and Reynolds, M.,1994, Temporal Logic:Mathematical Foundations and Computational Aspects, Volume2,. Oxford:Clarendon Press.
[29](?)hrstr(?)m, P. and Hasle, P., Temporal Logic:From Ancient Ideas to Artificial Intelligence, Dordrecht, Boston and London:Kluwer Academic Publishers,1995.
[30]A tableaux method for interval temporal logic with projection. Howard Bowman and Simon J.Thompson. In TABLEAUX'98, International Conference on Analytic Tableaux and Related Methods, volume 1397 of Lecture Notes in AI, pages 108-123. Springer-Verlag, May 1998.
[31]Leslie Lamport TLA in Pictures IEEE Transactions on Software Engineering 21,9, (September 1995) 768-775.
[32]Leslie Lamport, The Temporal Logic of Actions, ACM Toplas 16,3 (May 1994) 872-923.
[33]Leslie Lamport, Introduction to TLA,16 December 1994, Pdf version of the ITL home page.
[34]Wooldridge,Dixon, Fisher,A tableau-based proof method for temporal logics of knowledge and belief,Journal of Applied Non-Classical logics,8(3):225-258,1998.
[35]Stefan Wolfl, Combinations of Tense and Modality for Predicate logic, Journal of Philosophical Logic,28:371-398,1999
[36]Ohrstrom, P., Hasle, P.1993,'A.N. Prior's Rediscovery of Tense Logic. Erkenntnis, vol.39, pp.23-50.
[37]E. Allen Emerson. Temporal and modal logic. In Jan van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A, chapter 16, pages 995-1072. Elsevier,1990, Segerberg.
[38]D.Gabby and F.Guenthner:Handbook of Philosophical Logic, Volume2, Kluwer Academic Publishers,1984.
[1]张振华：《逻辑学在人工智能中的应用及其前景研究综述》,哲学动态,2002年第1期。
[2]蔡曙山：《认知科学背景下的逻辑学——认知逻辑的对象、方法、体系和意义》,江海学刊,2004年06期。
[3]许涤非：《单主体认知逻辑的研究——全知性和真知性》,湘潭师范学院学报社会科学版,2003年第02期。
[4]《纤维逻辑》邱莉榕,杨柳,史忠植,计算机科学,2006,第33卷,第1期。
[5]Caleiro, C. and Ramos, J,2007, From fibring to cryptofibring:A solution to the collapsing problem. Logica Universalis, 1(1):71-92.
[6]Alessio Lomuscio,Boz Wozna, A Temporal Epistemic Logic with a Reset Operation,AAMAS07 MAY14-18,2007,USA
[7]Wikipedia contributors. Temporal Logic. In Wikipedia, the Free Encyclopedia. May 2006. http://en.wikipedia.org/wiki/Temporal logic
[8]Fran,cois Laroussinie and Nicolas Markey.Expressiveness of Temporal Logics.The 18th European Summer School in Logic, Language and Information31 July-11 August,2006_Malaga, Spain http://www.lsv.ens-cachan.fr/_markey/ESSLLI06
[9]Caleiro, C., Carnielli, W., Rasga, J., and Sernadas, C.,2005, "Fibring of logics as a universal construction", Volume 13 of Handbook of Philosophical Logic,2nd Edition, pages 123-187, Springer.
[10]C. Caleiro, A. Sernadas and C. Sernadas, Fibring logics:past, present and future.L. C. Lamb, and J. Woods, editors, Essays in Honour of Dov Gabbay, Volume One, pages 363-388. King's College Publications,2005.
[11]C.Liu, Mozols,M.A.Orgun,A Fibred belief logic for Multi-agent AI2005,LNAI3809, pp29-38,2005.
[12]Alexandre Costa-Leite, Towards a General Theory of the Combination of Logics,Aspects of Universal logic,196-204.
[13]Caleiro and J. Ramos. Cryptofibring. Proceedings of CombLog'04Workshop on Combination of Logics:Theory and Applications, pp.87-92,2004.
[14]Kracht, M.,2004, Review of Fibring Logics, by Dov Gabbay, Oxford Logic Guides, vol.38, Oxford University Press, The Bulletin of Symbolic Logic 10(2):209-211
[15]C. Liu, M. Ozols, and M. A. Orgun. A temporalised belief logic for specifying the dynamics of trust for multi-agent systems. In Proc. of the Ninth Asian Computer Science Conference 2004, LNCS, Vol.3321, pages 142-156. Springer, Dec.2004.
[16]A.Sernadas and C.Semadas. Combining logic systems:Why, how, what for CIM Bulletin, 15:9-14, December 2003.
[17]C. Caleiro, W. A. Carnielli, M. E. Coniglio, A. Sernadas, and C. Sernadas. Fibringnon-truth-functional logics:Completeness preservation. Journal of Logic, Languageand Information,12(2),2003, pp.183-211.
[18]Antony Galton. Temporal Logic. In Edward N. Zalta (ed.), The Stanford Encyclopediaof Philosophy, December 2003. http://plato.stanford.edu/archives/win2003/entries/logic-temporal/.
[19]Sernadas, C., Rasga, J., and Carnielli, W.,2002b, "Modulated fibring and the collapsing problem", Journal of Symbolic Logic,67(4):1541-1569.
[20]Marcelo Finger, The Unrestricted Combining of Temporal Logic Systems, J.of IJPL,Vol.10.2, pp.165-189,2002.
[21]J. Rasga, A. Sernadas, C. Sernadas, and L. Viganμo. Fibring labelled deduction sys-tems. Journal of Logic and Computation,12(3),2002, pp.443{473.
[22]A Zanardo, A. Sernadas, and C. Sernadas,Fibring:Completeness preservation. Journal of Symbol Logic,66(1):414-439,2001.
[23]Val Goranko,Temporal logics of computations http://general.rau.ac.za/maths/goranko/,2000.
[24]C. Caleiro. Combining Logics. PhD thesis,IST, TU Lisbon, Portugal,2000.
[25]C.Caleiro, C.Sernadas, and A.Sernadas, Mechanisms for combining logics, Research report, Section of Computer Science, Department of Mathematics, Instituto Superior Tecnico, 1049-001 Lisboa, Portugal,1999.
[26]P. Blackburn and M. Tzakova. Hybrid languages and temporal logic. LogicJournal of the IGPL,7:27-54,1999.
[27]A. Sernadas, C. Sernadas, and C. Caleiro. Fibring of logics as a categorial construc-tion. Journal of Logic and Computation,9(2),1999, pp.149-179.
[28]Dixon Fisher, Wooldridge,Resolution for temporal logics of knowledge, Journal of logic and computation,8(3):345-372,1998
[29]P. Blackburn and M. de Rijke. Why combine logics? Studia Logica,59(1):5-27,1997.
[30]Marcelo Finger, Dov M.Gabby,Combining Temporal Logic Systems,Notre Dame Journal of Formal Logic,Volume37,Number2,1996.
[31]Joeri Engelfriet,Minimal Temporal Epistemic Logic,Technical Report IR-388, Faculty of Mathematics and Computer Science, Vrije Universiteit Amsterdam,1996.
[32]Gabbay, D.1996, "Fibred semantics and the weaving of logics:Part 1", Journal of Symbolic Logic,61 (4):1057-1120.
[33]Mossakowski. T.,1996, "Using limits of parchments to systematically construct institutions of partial algebras", in Haveraaen, M., Owe, O,and Dahl, O.-J., editors, Recent Trends in Data Type Specifications, volume 1130 of Lecture Notes in Computer Science, pages 379-393, Springer.
[34]van Benthem, J.,1995, "Temporal Logic", in D. M. Gabbay, C. J. Hogger, and J. A. Robinson, Handbook of Logic in Artificial Intelligence and Logic Programming, Volume 4, Oxford:Clarendon Press, pages 241-350.
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4 Dov.M.Gabby,1999, Fibring Logics, page,l,volume 38 of Oxford Logic Guides, Oxford University Press.
5 Caleiro, C., Carnielli, W., Rasga, J., and Sernadas, G.,2005, "Fibring of logics as a universal construction", Volume 13 of Handbook of Philosophical Logic,2nd Edition, pages 123-187, Springer.
6 R.H.Thomason,Combinations of tense and modality. Handbook of Philosophical Logic, Volume2, Kluwer Academic Publishers, pages 135-166,1984.
7 Schurz, G.,1997, The Is-Ought Problem:An Investigation in Philosophical Logic, Kluwer, Dordrecht.
8 W.A.Carnielli, and M.E.Coniglio. A categorial approach to the combination oflogics. Manuscrito 22(2):69-94,
9 Marcelo Finger, Dov M.Gabby, Adding a Temporal Dimension to a Logic System, Journal of Logic,Language,andInformation,1,203-233,1992.
Marcelo Finger, Dov M.Gabby, Combining Temporal Logic Systems,Notre Dame Journal of Formal Logic, Volume37,Number2,1996.
11 Marcelo Finger, The Unrestricted Combining of Temporal Logic Systems, J.of IJPL,Vol.10.2, pp.165-189,2002.
12 Carnielli, W., Coniglio, M., Gabbay, D., Gouveia, P., and Sernadas, C., Analysis and Synthesis of Logics12,Applied Logic Series volume 35. Springer,2008.
13 Ming,xu, On some U,S-Tense Logics, Journal of Philosophical Logic,1988,17,181-202.
14 Johnp. Burgess, Axioms for Tense Logic I:"Since" and "Until", Notre Dame, Journal of Formal Logic,1982, 23, p367-374。
15 Gabbay, D. M,1996,"Fibred semantics and the weaving of logics:Part 1", Journal of Symbolic Logic, 61(4):1057-1120.
16 Gabbay, D. M,1996, "An overview of fibred semantics and the combination of logics", Frontiers of Combining Systems:Proceedings of the 1st International Workshop FroCos'96, Kluwer Academic Publishers.
17 Gabbay, D.M,1999, Fibring Logics, volume 38 of Oxford Logic Guides, Oxford University Press, New York.
19 A Zanardo, A.Sernadas, and C. Sernadas,Fibring:Completeness preservation. Journal of Symbol Logic,66(1):414-439,2001.
20 Sernadas, C., Rasga, J., and Carnielli, W.,2002b, "Modulated fibring and the collapsing problem", Journal of Symbolic Logic,67(4):1541-1569.
21 Caleiro, C., Carnielli, W., Rasga, J., and Sernadas, C.,2005, "Fibring of logics as a universal construction" Volume 13 of Handbook of Philosophical Logic,2nd Edition, pages 123-187, Springer.
22 Caleiro and J. Ramos. Cryptofibring. Proceedings of CombLog'04,Workshop on Combination of Logics: Theory and Applications,2004, pp.87-92
23C. Caleiro, A. Sernadas and C. Sernadas, Fibring logics:past,present and future,L. C. Lamb, and J. Woods, editors, Essays in Honour of Dov Gabbay, Volume One, pages 363--388. King's College Publications,2005
24 Caleiro, C. and Ramos, J., From fibring to cryptofibring:A solution to the collapsing problem. Logica Universalis,1(1):71-92,2007.
25这里所介绍的极小的双主体认知逻辑系统Bm来自许涤非的《双主体认知逻辑研究》,中国社会出版社,2006年版,67-91页。
26 Joeri Engelfriet,Minimal Temporal Epistemic Logic,Technical Report IR-388, Faculty of Mathematics and Computer Science, Vrije Universiteit Amsterdam,1996.
27 C. Liu, M. Ozols, and M. A. Orgun. A temporalised belief logic for specifying the dynamics of trust for multi-agent systems. In Proc. of the Ninth Asian Computer Science Conference 2004, LNCS, Vol.3321, pages 142-156. Springer, Dec.2004.
28 C.Liu, Mozols,M.A.Orgun,A Fibred belief logic for Multi-agent AI2005,LNAI3809, pp29-38,2005.
[2]张家龙：《模态逻辑与哲学》,中国社会出版社,2002年版。
[3]弓肇祥：《认知逻辑新发展》,北京大学出版社,2004年版。
[4]弓肇祥：《可能世界理论》,北京大学出版社,2003年版。
[5]唐晓嘉：《认知的逻辑分析》,西南师范大学出版社,2003年版。
[6]周昌乐：《认知逻辑导论》,清华大学出版社,2001年版。
[7]张清宇、郭世铭、李小五：《哲学逻辑研究》,中国社会科学文献出版社,1997年版。
[8]李娜：《一种弱的命题时态逻辑》, “双B”代数和计算机逻辑论文集,上海交通大学出版社,1991年5月,p209—211
[9]黎仁蔚,《N系统：一个自然时序演绎系统》,科学通报,1988年06期
[1]Carnielli, W., Coniglio. M., Gabbay, D., Gouveia, P., and Sernadas, C., Analysis and Synthesis of Logics. Applied Logic Series volume 35. Springer,2008.
[2]Carlos Areces and Robert Goldblatt, editors, Advances in Modal Logic, Volume 7, King's College Publications,2008.
[3]Johan van Benthem, Frank Wolter, Handbook of Modal Logic,Elsevier Science,2007.
[4]Guido Governatori,Ian Hodkinson and Yde Venema, editors,Advances in Modal Logic, Volume 6, King's College Publications,2006.
[5]Duan Zhenhua,Temporal Logic and Temporal Logic Programing,Science Press,2005.
[6]Renate Schmidt, Ian Pratt-Hartmann, Mark Reynolds and Heinrich Wansing, editors, Advances in Modal Logic, Volume 5, King's College Publications,2005.
[7]Fibring logics:past, present and future, C. Caleiro, A. Sernadas and C. Sernadas, L. C. Lamb, and J. Woods, editors, Essays in Honour of Dov Gabbay, Volume One, pages 363-388. King's College Publications,2005.
[8]Epistemic logic:a survey of the logic of knowledge/Nicholas Rescher, Pittsburgh, Pa. University of Pittsburgh Press,2005.
[9]Ben Moszkowski. A hierarchical analysis of propositional temporal logic based on intervals. In Sergei Artemov, Howard Barringer, Artur S. d'Avila Garcez, Luis C. Lamb, and John Woods, editors, We Will Show Them:Essays in Honour of Dov Gabbay, volume 2, pages 371-440. College Publications (formerly KCL Publications), King's College, London,2005.
[10]D.Gabby and F.Guenthner:Handbook of Philosophical Logic, Volume13, Kluwer Academic Publishers,2005.
[11]C. Liu, M. Ozols, and M. A. Orgun. A temporalised belief logic for specifying the dynamics of trust for multi-agent systems. In Proc. of the Ninth Asian Computer Science Conference 2004, LNCS, Vol.3321, pages 142-156. Springer, Dec.2004.
[12]Kracht, M.,2004, Review of Fibring Logics, by Dov Gabbay, Oxford Logic Guides, vol.38, Oxford University Press, The Bulletin of Symbolic Logic 10(2):209-211.
[13]Dov Gabbay and Agi Kurucz and Frank Wolter, Many-dimensional modal logics:theory and applications, Elsevier Science,2003.
[14]B. Moszkowski. A hierarchical completeness proof for interval temporal logic with finite time (preliminary version). In Proc. of the Workshop on Interval Temporal Logics and Duration Calculi (part of 15th European Summer School in Logic Language and Information (ESSLLI-2003)), pages 41-65, Vienna, August 2003.
[15]Philippe Balbiani, Nobu-Yuki Suzuki, Frank Wolter, and Michael Zakharyaschev, editors, Advances in Modal Logic, Volume4, King's College Publications,2003.
[16]D.Gabby and F.Guenthner. Handbook of Philosophical Logic, Volume7, Kluwer Academic Publishers,2002.
[17]Frank Wolter, Heinrich Wansing, Maarten de Rijke, and Michael Zakharyaschev, editors,World Scientific, Advances in Modal Logic, Volume 3, King's College Publications, 2002.
[18]Goble, Lou (ed.), The Blackwell Guide to Philosophical Logic, Massachusetts:Blackwell Publishers Inc,2001.
[19]Wiebe van der Hoek. Logical Foundations of Agent-Based Computing. In Mutli-agents Systems and Applications, pages 50-73. Springer-Verlag New York, Inc.,2001.
[20]Michael Zakharyaschev, Krister Segerberg, Maarten de Rijke, andHeinrich Wansing, editors, Advances in Modal Logic, Volume 2, CSLI Publications,2000.
[21]Gabbay, D.M,1999, Fibring Logics,volume 38 of Oxford Logic Guides, Oxford University Press, New York.
[22]Joseph Y. Halpern and Richard A. Shore. Reasoning about Common Knowledge with Infinitely Many Agents. In Logic in Computer Science, pages 384-393.1999.
[23]Marcus Kracht, Maarten de Rijke, Heinrich Wansing, and Michael Zakhary aschev, editors, Advances in Modal Logic, Volume 1, CSLI Publications,1998.
[24]Gabbay, D,1996, "An overview of fibred semantics and the combination of logics", in F. Baader and K.U. Schulz, editors, Frontiers of Combining Systems:Proceedings of the 1st International Workshop FroCos'96, Munich (Germany), volume 3 of Applied Logic, pages 1-55. Kluwer Academic Publishers.
[25]Ronald Fagin,Joseph.Y.Halpern, Y.Moses, Reasoning About Knowledge, the MIT Press,1995.
[26]John-Jules Ch. Meyer and Wiebe Van Der Hoek. Epistemic Logic for AI and Computer Science. Cambridge University Press,1995.
[27]Gabbay, D. M., Hodkinson, I., and Reynolds, M.,1994, Temporal Logic:Mathematical Foundations and Computational Aspects, Volume 1,. Oxford:Clarendon Press.
[28]Gabbay, D. M. Hodkinson, I., and Reynolds, M.,1994, Temporal Logic:Mathematical Foundations and Computational Aspects, Volume2,. Oxford:Clarendon Press.
[29](?)hrstr(?)m, P. and Hasle, P., Temporal Logic:From Ancient Ideas to Artificial Intelligence, Dordrecht, Boston and London:Kluwer Academic Publishers,1995.
[30]A tableaux method for interval temporal logic with projection. Howard Bowman and Simon J.Thompson. In TABLEAUX'98, International Conference on Analytic Tableaux and Related Methods, volume 1397 of Lecture Notes in AI, pages 108-123. Springer-Verlag, May 1998.
[31]Leslie Lamport TLA in Pictures IEEE Transactions on Software Engineering 21,9, (September 1995) 768-775.
[32]Leslie Lamport, The Temporal Logic of Actions, ACM Toplas 16,3 (May 1994) 872-923.
[33]Leslie Lamport, Introduction to TLA,16 December 1994, Pdf version of the ITL home page.
[34]Wooldridge,Dixon, Fisher,A tableau-based proof method for temporal logics of knowledge and belief,Journal of Applied Non-Classical logics,8(3):225-258,1998.
[35]Stefan Wolfl, Combinations of Tense and Modality for Predicate logic, Journal of Philosophical Logic,28:371-398,1999
[36]Ohrstrom, P., Hasle, P.1993,'A.N. Prior's Rediscovery of Tense Logic. Erkenntnis, vol.39, pp.23-50.
[37]E. Allen Emerson. Temporal and modal logic. In Jan van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A, chapter 16, pages 995-1072. Elsevier,1990, Segerberg.
[38]D.Gabby and F.Guenthner:Handbook of Philosophical Logic, Volume2, Kluwer Academic Publishers,1984.
[1]张振华：《逻辑学在人工智能中的应用及其前景研究综述》,哲学动态,2002年第1期。
[2]蔡曙山：《认知科学背景下的逻辑学——认知逻辑的对象、方法、体系和意义》,江海学刊,2004年06期。
[3]许涤非：《单主体认知逻辑的研究——全知性和真知性》,湘潭师范学院学报社会科学版,2003年第02期。
[4]《纤维逻辑》邱莉榕,杨柳,史忠植,计算机科学,2006,第33卷,第1期。
[5]Caleiro, C. and Ramos, J,2007, From fibring to cryptofibring:A solution to the collapsing problem. Logica Universalis, 1(1):71-92.
[6]Alessio Lomuscio,Boz Wozna, A Temporal Epistemic Logic with a Reset Operation,AAMAS07 MAY14-18,2007,USA
[7]Wikipedia contributors. Temporal Logic. In Wikipedia, the Free Encyclopedia. May 2006. http://en.wikipedia.org/wiki/Temporal logic
[8]Fran,cois Laroussinie and Nicolas Markey.Expressiveness of Temporal Logics.The 18th European Summer School in Logic, Language and Information31 July-11 August,2006_Malaga, Spain http://www.lsv.ens-cachan.fr/_markey/ESSLLI06
[9]Caleiro, C., Carnielli, W., Rasga, J., and Sernadas, C.,2005, "Fibring of logics as a universal construction", Volume 13 of Handbook of Philosophical Logic,2nd Edition, pages 123-187, Springer.
[10]C. Caleiro, A. Sernadas and C. Sernadas, Fibring logics:past, present and future.L. C. Lamb, and J. Woods, editors, Essays in Honour of Dov Gabbay, Volume One, pages 363-388. King's College Publications,2005.
[11]C.Liu, Mozols,M.A.Orgun,A Fibred belief logic for Multi-agent AI2005,LNAI3809, pp29-38,2005.
[12]Alexandre Costa-Leite, Towards a General Theory of the Combination of Logics,Aspects of Universal logic,196-204.
[13]Caleiro and J. Ramos. Cryptofibring. Proceedings of CombLog'04Workshop on Combination of Logics:Theory and Applications, pp.87-92,2004.
[14]Kracht, M.,2004, Review of Fibring Logics, by Dov Gabbay, Oxford Logic Guides, vol.38, Oxford University Press, The Bulletin of Symbolic Logic 10(2):209-211
[15]C. Liu, M. Ozols, and M. A. Orgun. A temporalised belief logic for specifying the dynamics of trust for multi-agent systems. In Proc. of the Ninth Asian Computer Science Conference 2004, LNCS, Vol.3321, pages 142-156. Springer, Dec.2004.
[16]A.Sernadas and C.Semadas. Combining logic systems:Why, how, what for CIM Bulletin, 15:9-14, December 2003.
[17]C. Caleiro, W. A. Carnielli, M. E. Coniglio, A. Sernadas, and C. Sernadas. Fibringnon-truth-functional logics:Completeness preservation. Journal of Logic, Languageand Information,12(2),2003, pp.183-211.
[18]Antony Galton. Temporal Logic. In Edward N. Zalta (ed.), The Stanford Encyclopediaof Philosophy, December 2003. http://plato.stanford.edu/archives/win2003/entries/logic-temporal/.
[19]Sernadas, C., Rasga, J., and Carnielli, W.,2002b, "Modulated fibring and the collapsing problem", Journal of Symbolic Logic,67(4):1541-1569.
[20]Marcelo Finger, The Unrestricted Combining of Temporal Logic Systems, J.of IJPL,Vol.10.2, pp.165-189,2002.
[21]J. Rasga, A. Sernadas, C. Sernadas, and L. Viganμo. Fibring labelled deduction sys-tems. Journal of Logic and Computation,12(3),2002, pp.443{473.
[22]A Zanardo, A. Sernadas, and C. Sernadas,Fibring:Completeness preservation. Journal of Symbol Logic,66(1):414-439,2001.
[23]Val Goranko,Temporal logics of computations http://general.rau.ac.za/maths/goranko/,2000.
[24]C. Caleiro. Combining Logics. PhD thesis,IST, TU Lisbon, Portugal,2000.
[25]C.Caleiro, C.Sernadas, and A.Sernadas, Mechanisms for combining logics, Research report, Section of Computer Science, Department of Mathematics, Instituto Superior Tecnico, 1049-001 Lisboa, Portugal,1999.
[26]P. Blackburn and M. Tzakova. Hybrid languages and temporal logic. LogicJournal of the IGPL,7:27-54,1999.
[27]A. Sernadas, C. Sernadas, and C. Caleiro. Fibring of logics as a categorial construc-tion. Journal of Logic and Computation,9(2),1999, pp.149-179.
[28]Dixon Fisher, Wooldridge,Resolution for temporal logics of knowledge, Journal of logic and computation,8(3):345-372,1998
[29]P. Blackburn and M. de Rijke. Why combine logics? Studia Logica,59(1):5-27,1997.
[30]Marcelo Finger, Dov M.Gabby,Combining Temporal Logic Systems,Notre Dame Journal of Formal Logic,Volume37,Number2,1996.
[31]Joeri Engelfriet,Minimal Temporal Epistemic Logic,Technical Report IR-388, Faculty of Mathematics and Computer Science, Vrije Universiteit Amsterdam,1996.
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