L3-值命题逻辑的R-演算

doi:10.11896/jsjkx.190600171

计算机科学 ›› 2020, Vol. 47 ›› Issue (4): 164-168.doi: 10.11896/jsjkx.190600171

L₃-值命题逻辑的R-演算

曹存根¹, 胡岚曦^1,2, 眭跃飞^1,2

1 中国科学院计算技术研究所北京100190;
2 中国科学院大学计算机科学与技术学院北京101408

收稿日期:2019-06-27 出版日期:2020-04-15 发布日期:2020-04-15
通讯作者: 胡岚曦(hulanxi17b@ict.ac.cn)
基金资助:
科技部重点研发计划项目(2017YFC1700300)

R-Calculi For L₃-Valued Propositional Logic

CAO Cun-gen¹, HU Lan-xi^1,2, SUI Yue-fei^1,2

1 Institute of Computing Technology,Chinese Academy of Sciences,Beijing 100190,China;
2 School of Computer Science and Technology,University of Chinese Academy of Sciences,Beijing 101408,China

Received:2019-06-27 Online:2020-04-15 Published:2020-04-15
Contact: HU Lan-xi,born in 1980,master,engineer.Her main research interests include foundation of large-scale know-ledge process.
About author:CAO Cun-gen,born in 1964,Ph.D,professor,Ph.D supervisor,is a member of CCF.His main research interests include large-scale knowledge process.
Supported by:
This work was supported by the National Key R&D Program of China (2017YFC1700300)

摘要/Abstract

摘要： 在L₃-值命题逻辑中,对应于矢列式推导的Gentzen推理系统G是单调的,而对应于余矢列式推导的Gentzen推理系统G^－是非单调的。基于G和G^－,文中给出了一个R-演算S,使得任意的R-转换Δ|A⇒Δ,C是有效的当且仅当它在S中可证。因此, S在限制A进入Δ时是单调的,而在将A添加到Δ中时是非单调的。

关键词: Gentzen推理系统, R-演算, 非单调性, 信念修正, 余矢列式

Abstract: In L₃-valued propositional logic,the Gentzen deduction system G for sequents is monotonic, and the one G^－ for co-sequents is nonmonotonic.Based on G and G^－, an R- calculus S is given so that any reduction Δ|A⇒Δ,C is valid if and only if it is provable in S.Therefore,S is monotonic inrestraining A from entering Δ,and nonmonotonic in adding A into Δ.

Key words: Belief-revision, Co-sequent, Gentzen deduction system, Nonmonotonicity, R-calculus

中图分类号:

TP301

曹存根, 胡岚曦, 眭跃飞. L₃-值命题逻辑的R-演算[J]. 计算机科学, 2020, 47(4): 164-168. https://doi.org/10.11896/jsjkx.190600171

CAO Cun-gen, HU Lan-xi, SUI Yue-fei. R-Calculi For L₃-Valued Propositional Logic[J]. Computer Science, 2020, 47(4): 164-168. https://doi.org/10.11896/jsjkx.190600171

参考文献

[1]LI W.Mathematical logic,foundations for information science[M]//Progress in Computer Science and Applied Logic.Birkhauser,2010.
[2]TAKEUTI G.Proof theory(Second Edition)[M].Mineola,New York:Dover Publications,2013.
[3]CAO C G,SUI Y F,WANG Y.The nonmonotonic propositional logics [J].Artificial Intelligence Research,2016,5:111-120.
[4]REITER R.A logic for default reasoning [J].Artificial Intelligence,1980,13:81-132.
[5]ALCHOURRÒN C E,GARDENFORS P,MAKINSON D.On the logic of theory change:partial meet contraction and revision functions [J].The Journal of Symbolic Logic,1985,50:510-530.
[6]BOCHMAN A.A foundational theory of belief and belief change[J].Artificial Intelligence,1999,108:309-352.
[7]FERMÉ E,HANSSON S O.AGM 25 years:twenty-five years of research in belief change [J].Journal of Philosophical Logic,2011,40(2):295-331.
[8]LI W.R-calculus:An inference system for belief revision [J].The Computer Journal,2007,50:378-390.
[9]DARWICHE A,PEARL J.On the logic of iterated belief revision [J].Artificial Intelligence,1997,89:1-29.
[10]FRIEDMAN N,HALPERN J Y.Belief revision:a critique[C]//Principles of Knowledge Representation and Reasoning:proceedings of the 5th International Conference.1996:421-431.
[11]AVRON A.Natural 3-valued logics-characterization and prooftheory [J].Journal of Symbolic Logic,1991,56:276-294.
[12]GOTTWALD S.A treatise on many-valued logics [M].Research Studies Press,2001.
[13]AVRON A.On the expressive power of three-valued and four-valued languages [J].Journal of Logic and Computation,1999,9:977-994.
[14]HANSSON S O.Theory contraction and base contraction unified [J].The Journal of Symbolic Logic,1993,58:602-625.
[15]HERZIG A,RIFI O.Propositional belief base update and minimal change [J].Artificial intelligence,1999,115:107-138.
[16]PYNKO A P.Implicational classes of demorg-an lattices [J].Discrete Mathematics,1999,205:171-181.
[17]SATOH K.Nonmonotonic reasoning by minimal belief revision [C]//Proceedings of the international conference on FifthGe-neration Computer Systems.Tokyo,1988:455-462.
[18]URQUHART A.Basic many-valued logic(2^nd Edition)[M]//Handbook of Philosophical Logic.Kluwer Academic Publishers,2001:249-295.

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L₃-值命题逻辑的R-演算

R-Calculi For L₃-Valued Propositional Logic

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