正规多模态逻辑的混合系统
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摘要
多模态逻辑系统是在经典模态逻辑基础上增加多个模态词而得到的系统,Walter Carnielli和Claudio Pizzi在专著Modalities and Multimodalities中提出了更为一般化的多模态逻辑系统,证明了这些系统的完全性。混合逻辑系统是在模态逻辑基础上增加名词性词(nominal)作为一类特殊的命题,并增加满足算子等联结词而得到的系统,它有着更丰富的表达力。人们对经典模态逻辑和时态逻辑的混合系统已经作了研究,在此基础上,把混合逻辑的方法推广运用到更一般的正规多模态逻辑中,同时证明它的完全性。
A multimodal logic system is a system based on classical modal logic by adding multiple modal words. Walter Carnielli and Claudio Pizzi present more general multimodal logic systems in Modalities and Multimodalities,and show the completeness of these systems. Hybrid logic is a kind of special modal logic obtained by adding nominals as a special kind of proposition and satisfaction operator @ as a connective,which has more expressive power. The hybrid systems of classical modal logic and temporal logic have been fully studied,so the work of this paper is to extend the method of hybrid logic to more general standard multimodal logic,and to prove the completeness of the standard normal multimodal hybrid system.
A multimodal logic system is a system based on classical modal logic by adding multiple modal words. Walter Carnielli and Claudio Pizzi present more general multimodal logic systems in Modalities and Multimodalities,and show the completeness of these systems. Hybrid logic is a kind of special modal logic obtained by adding nominals as a special kind of proposition and satisfaction operator @ as a connective,which has more expressive power. The hybrid systems of classical modal logic and temporal logic have been fully studied,so the work of this paper is to extend the method of hybrid logic to more general standard multimodal logic,and to prove the completeness of the standard normal multimodal hybrid system.
引文
[1]CARNIELLI W,PIZZI C.Modalities and multimodalities[M].Dordrecht:Springer,2008.
[2]霍书全.普莱尔混合时态逻辑的思想基础[J].逻辑学研究,2016(2):45-60.
[3]BRAüNER T.Hybrid logic and its proof-theory[M].New York:Springer,2011.
[4]BLACKBURN P.Nominal tense logic[J].Notre Dame Journal of Formal Logic,1993,34(1):56-83.
[5]BLACKBURN P,DE RIJKE M,VENEMA Y.Modal logic[M].Cambridge:Cambridge University Press,2001.
[2]霍书全.普莱尔混合时态逻辑的思想基础[J].逻辑学研究,2016(2):45-60.
[3]BRAüNER T.Hybrid logic and its proof-theory[M].New York:Springer,2011.
[4]BLACKBURN P.Nominal tense logic[J].Notre Dame Journal of Formal Logic,1993,34(1):56-83.
[5]BLACKBURN P,DE RIJKE M,VENEMA Y.Modal logic[M].Cambridge:Cambridge University Press,2001.