吉林大学学报(工学版) ›› 2016, Vol. 46 ›› Issue (6): 2021-2026.doi: 10.13229/j.cnki.jdxbgxb201606035

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Expressive power of decidable subclasses of open proxcheme

ZHANG Wei1, LIU Yu-hui2   

  1. 1.College of Computer Science and Engineering, Northeastern University, Shenyang 110819, China;
    2.Research Academy, Northeastern University, Shenyang 110819, China
  • Received:2015-07-02 Online:2016-11-20 Published:2016-11-20

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Abstract: An algorithm for OPEN proxcheme is proposed that functions in the two maximal decidable classes of first-order logic. The algorithm iteratively revises the formal theories according to new information and completes the evolution of the formal theories. The expressive power of the OPEN proxcheme is discussed. It is demonstrated that the OPEN proxcheme and R-calculus preserve the decidability of formulas in the two maximal decidable classes. Since the decision problem for modal logic and FO2 can be transferred to that of the two maximal decidable classes, it can be concluded that the OPEN proxcheme and R-calculus are more expressive than the modal logic and FO2. Practical examples, such as hardware description and verification, are provided.

Key words: artificial intelligence, belief revision, OPEN proxcheme, decidable logic formula classes, expressive power, mechanical theorem proving

CLC Number: 

  • TP181
[1] Alchourron C E, Gardenfors R, Makinson D. On the logic of theory change: partial meet contraction and revision functions[J]. Journal of Symbolic Logic,1985,50(2):510-530.
[2] Li W. An open logic system[J]. Science China Series A,1992,35(10):1103-1113.
[3] Li W. Mathematical Logic—Foundations for Information Science[M]. Basel: Birkhauser Verlag, 2010:45-185.
[4] Benthem J. Reasoning and programming: analogies between logic and computation[C]∥Proceedings of the 1991 International Symposium on Logic Programming,San Diego, USA,1991:717-718.
[5] Benthem J. Dynamic logic for belief revision[J]. Journal of Applied Non-Classical Logics,2007,17(2):129-155.
[6] Darwiche A, Pearl J. On the logic of iterated belief revision[J]. Artificial Intelligence,1997,89(1/2):1-29.
[7] Nayak A, Goebel R, Orgun M. Iterated belief contraction from first principles[C]∥Proceedings of 20th International Joint Conference on Artificial Intelligence, Hyderabad, India, 2007:2568-2573.
[8] 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.
[9] Li W. R-calculus: an inference system for belief revision[J]. Computer Journal,2007,50(4):378-390.
[10] Li W, Sui Y F, A sound and complete R-calculi with respect to contraction and minimal change[J]. Frontiers of Computer Science,2014,8(2):184-191.
[11] Zhang W. On the decidability of open logic[J]. Science China: Information Science, 2009,52(8):1283-1291.
[12] Li H, Luo J, Li W. A formal semantics for debugging synchronous message passing-based concurrent programs[J]. Science China: Information Science,2014,57:128101.
[13] Luan S M, Dai G Z, Li W. A programmable approach to revising knowledge base[J]. Science China:Information Science,2005,48(6):681-692.
[14] Luo J, Li W. An algorithm to compute maximal contractions for Horn clauses[J]. Science China: Information Science,2011,54(2):244-257.
[15] Zhang W. Decidable subsets of open logic and an algorithm for R-calculus[J]. Science China: Information Science,2015,58(1):012103.
[16] 刘磊,张银平. 一种基于描述逻辑的构件检索匹配算法[J]. 吉林大学学报:工学版,2008,38(3):671-675.
Liu Lei, Zhang Yin-ping. Component retrieval and matching algorithm based on description logics[J]. Journal of Jilin University(Engineering and Technology Edition),2008,38(3):671-675.
[17] 黄宏涛,王静,叶海智,等. 基于惰性切片的线性时态逻辑性质验证[J]. 吉林大学学报:工学版,2015,45(1):245-251.
Huang Hong-tao, Wang Jing, Ye Hai-zhi, et al. Lazy slicing based method for verifying linear temporal logic property[J]. Journal of Jilin University(Engineering and Technology Edition), 2015,45(1):245-251.
[18] 王生生,刘大有,吴瑕,等. 模糊空间描述逻辑及应用[J]. 吉林大学学报:工学版,2010,40(6):1634-1638.
Wang Sheng-sheng, Liu Da-you, Wu Xia, et al. Fuzzy spatial description logic and application[J]. Journal of Jilin University(Engineering and Technology Edition),2010,40(6): 1634-1638.
[19] Bärger E, Grädel E, Gurevich Y. The Classical Decision Problem[M]. Berlin: Springer, 2001:17-285.
[20] Gradel E, Kolaitis P, Vardi M. On the decision problem for two-variable first-order logic[J]. The Bulletin of Symbolic Logic,1997,3(1):53-69.
[21] Gradel E, Walukiewicz I. Guarded fixed point logic[C]∥Proceedings of 14th Symposium on Logic in Computer Science (LICS),Trento, Italy,1999:45-54.
[22] Gabbay D M. Expressive functional completeness intense logic[DB/OL]. [2015-06-23]. https://www.researchgate.net/publication/268658624_Expressive_Functional_Completeness_in_Tense_Logic_Preliminary_report.
[23] Scott D. A decision method for validity of sentences in two variables[J]. Journal of Symbolic Logic,1962,27(4):477-478.
[24] 张兴亮,郭立红,张传胜,等. CO 2 激光器高压脉冲触发系统的设计[J].中国光学,2012,5(4):416-422.
Zhang Xing-liang,Guo Li-hong, Zhang Chuan-sheng, et al. Design of high-voltage pulse trigger system for CO 2 laser[J]. Chinese Optics,2012,5(4):416-422.
[25] Etessami K, Vardi M Y, Wilke T. First-order logic with two variables and unary temporal logic[J]. Information and Computation,2002,179(2):279-295.
[26] 张旭霞,李斌,张黎明,等. 有机-无机复合纳米材料的传感应用及机理[J]. 中国光学,2015,8(4):651-666.
Zhang Xu-xia, Li Bin, Zhang Li-ming, et al. Sensing application and mechanism of organic-inorganic nanocomposites[J]. Chinese Optics,2015,8(4):651-666.
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