信念变化的多—核收缩算子研究
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摘要
信念修正理论是目前人工智能的一个重要的研究方向，很多专家学者对此进行了广泛而深入的研究，并且根据不同的应用领域的不同需要，提出了许多信念修正的方法，其中最具有代表性的就是AGM理论。本文在AGM理论和单核收缩的基础上，讨论了被收缩的对象是一般语句集合的信念收缩理论。具体而言，主要完成以下工作：
(1)给出包-核收缩算子的构造及其公理假设系统并证明了相应的表示定理。
(2)建立了饱和的包-核收缩算子和平滑的包-核收缩算子的表示定理并证明了两者的等价性，然后讨论了后者和基于部分交收缩的包收缩算子之间的关系。
(3)给出选择-核收缩算子的构造并且给出相应的公理假设系统及表示定理，然后讨论了子核收缩算子以及相应的表示定理。
The theory of belief revision is an important branch in the research of artificial intelligence. Many researchers have discussed about it, and put forward lots of methods according to different requirements in different applicable areas, the most representative of which is the AGM theory. On the basis of the AGM theory and kernel contraction, this thesis mainly discusses the theory of belief contraction in which new information is a general set of sentences. The main work can be divided into the following parts:
(1) The thesis gives the construction of package-kernel contraction and its postulates and proof of corresponding representation theorem.
(2) It gives representation theorems of saturated package-kernel contraction and smooth package-kernel contraction, and proves that the two contraction operations coincide with each other. It discusses the relation between smooth package-kernel contraction and package contraction basing on partial meet contraction.
(3) It constructs the choice-kernel contraction and gives corresponding postulates and representation theorem, and discusses sub kernel contraction and its representation theorem.
(1)给出包-核收缩算子的构造及其公理假设系统并证明了相应的表示定理。
(2)建立了饱和的包-核收缩算子和平滑的包-核收缩算子的表示定理并证明了两者的等价性，然后讨论了后者和基于部分交收缩的包收缩算子之间的关系。
(3)给出选择-核收缩算子的构造并且给出相应的公理假设系统及表示定理，然后讨论了子核收缩算子以及相应的表示定理。
The theory of belief revision is an important branch in the research of artificial intelligence. Many researchers have discussed about it, and put forward lots of methods according to different requirements in different applicable areas, the most representative of which is the AGM theory. On the basis of the AGM theory and kernel contraction, this thesis mainly discusses the theory of belief contraction in which new information is a general set of sentences. The main work can be divided into the following parts:
(1) The thesis gives the construction of package-kernel contraction and its postulates and proof of corresponding representation theorem.
(2) It gives representation theorems of saturated package-kernel contraction and smooth package-kernel contraction, and proves that the two contraction operations coincide with each other. It discusses the relation between smooth package-kernel contraction and package contraction basing on partial meet contraction.
(3) It constructs the choice-kernel contraction and gives corresponding postulates and representation theorem, and discusses sub kernel contraction and its representation theorem.
引文
1. J.Doyle. A truth maintenance system. Artificial Intelligence. 1979,12(3):231～272
2. C.E.Alchourron, P.Gardenfors and D.Makinson. On the logic of theory change: partial meet contraction and revision function. Journal of Symbolic Logic. 1985,50(2):510～530
3. R.Niederee. Multiple contraction: a further case against Gardenfors' principle of recovery. In A.Fuhrmann, Morreaueds Med. The Logic of Theory Change, Springer-Verlag. 1991:322～334
4. A.Fuhrmann, S.O.Hansson. A survey of multiple contractions. Journal of Logic, Language and Information.. 1994,3:39～76
5. A.Fuhrmann. An essay on contraction. Studies in Logic, Language and Information. TheUniversity of Chicago Press. 1996,4
6. A.Fuhrmann, S.O.Hansson. A survey of multiple contractions. Journal of Logic, Language and Information. 1994, 3:39-76
7. Zhang Dong-mo. Belief revision by sets of sentences. Journal of Computer Science and Technology. 1996,11(2):1-19
8. Li Wei, Shen Ning-chuan and Wang Ju. R-Calculus: a logical approach for knowledge base maintenance. International Journal of Artificial Intelligence Tools. 1995,4(1&2): 177～200
9. Li Wei, Shen Ning-chuan and Wang Ju. R-Calculus: a logical approach for knowledge base maintenance. International Journal of Artificial Intelligence Tools. 1995.4(1&2): 177～200
10. Li Wei. An open logic system. Science in China (Series A). 1992,22(10) :1103～1113(in Chinese)
11. Li Wei. A logical framework for knowledge base maintenance Journal of Computer Science and Technology. 1995,10(3)
12. Li Wei, Luan Shang-min. A Complete and Operational Approach to Belief Revision. Journal of Software. 2002,13(01)
13. A.Darwiche, J.Pearl. On the logic of iterated belief revision. Artificial Intellegence.1997,89(1-2):1～29
14. C.E.Alchourron, D.Makinson. On the logic of theory change: safe contraction. Studia Logica. 1985
15. C.E.Alchourron, D.Makinson. Maps between some different kinds of contraction function.The finite case. Studia Logica. 1986,45:187-198
16. P.Gardenfors and D.Makinson. Revision of knowledge systems using epistemie entrenchment, in:M.Vardi,ed.Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge, Morgan Kaufmann Publ. Los Altos, CA, 1988:83-95
17. P.Gardenfors, D.Makinson. Nonmonotonic inference based on expectations. Artificial Intelligence. 1994(65): 197-245
18. D.Makinson, P.Gardenfors. Relations between the logic of theory change and nonmonotonic logic. The Logic of Theory Change (A.Fuhrmann, M.Morreau.)Lecture Notes in AI.Springer Verlag. 1991:185-205
19. A.Bochman. Belief contraction as nonmonotonic inference. The Journal of Symboloc Logic.2000,65:605-626
20. S.Kraus, D.Lehmann and M.Magidor. Nonmonotonic reasoning, preferential models and cumulative logics. 1990,44:103-119
21. S.O.Hansson. A dyadic representation of belief, in: P.Gardenfors ed. Belief Revision (Cambridge University Press). 1992:89-121
22. S.O.Hansson. Kernel Contraction. Journal of Symbolic Logic. 1994,59:845-859
23. S.O.Hansson. Belief contraction without recovery. Studia Logica. 1992,50:251-260
24. S.O.Hansson. Reversing the Levi Identity. Journal of Philosophical Logic. 1993,22:637-669
25. S.O.Hansson. New operators for theory change. Theoria. 1989,55:114-132
26. A.Fuhrmann. Reflective modalities and theory change. Synthese. 1989,81:115-134
27. A.Fuhrmann.Theory contraction through base contraction. Journal of Philosophical Logic. 1991,20:175-203
28. S.O.Hansson. Hidden structures of belief.Logic,action and information. 1996:79-100
29. S.O.Hansson. Theory contraction and base contraction unified. Journal of Symbolic Logic. 1993,58:602-625
30. Zhu Zhao-hui, Li Bin, Xiao Xi-an and Chert Shi-fu. A representation theorem for recovering contraction relations satisfying WCI. Theoretical Computer Science. 2003,290(1):545-564
31. Andreas Herzig, Renata Wassermann. Belief change from AGM to realistic model, course at ESSLLI'01. 2001.8
2. C.E.Alchourron, P.Gardenfors and D.Makinson. On the logic of theory change: partial meet contraction and revision function. Journal of Symbolic Logic. 1985,50(2):510～530
3. R.Niederee. Multiple contraction: a further case against Gardenfors' principle of recovery. In A.Fuhrmann, Morreaueds Med. The Logic of Theory Change, Springer-Verlag. 1991:322～334
4. A.Fuhrmann, S.O.Hansson. A survey of multiple contractions. Journal of Logic, Language and Information.. 1994,3:39～76
5. A.Fuhrmann. An essay on contraction. Studies in Logic, Language and Information. TheUniversity of Chicago Press. 1996,4
6. A.Fuhrmann, S.O.Hansson. A survey of multiple contractions. Journal of Logic, Language and Information. 1994, 3:39-76
7. Zhang Dong-mo. Belief revision by sets of sentences. Journal of Computer Science and Technology. 1996,11(2):1-19
8. Li Wei, Shen Ning-chuan and Wang Ju. R-Calculus: a logical approach for knowledge base maintenance. International Journal of Artificial Intelligence Tools. 1995,4(1&2): 177～200
9. Li Wei, Shen Ning-chuan and Wang Ju. R-Calculus: a logical approach for knowledge base maintenance. International Journal of Artificial Intelligence Tools. 1995.4(1&2): 177～200
10. Li Wei. An open logic system. Science in China (Series A). 1992,22(10) :1103～1113(in Chinese)
11. Li Wei. A logical framework for knowledge base maintenance Journal of Computer Science and Technology. 1995,10(3)
12. Li Wei, Luan Shang-min. A Complete and Operational Approach to Belief Revision. Journal of Software. 2002,13(01)
13. A.Darwiche, J.Pearl. On the logic of iterated belief revision. Artificial Intellegence.1997,89(1-2):1～29
14. C.E.Alchourron, D.Makinson. On the logic of theory change: safe contraction. Studia Logica. 1985
15. C.E.Alchourron, D.Makinson. Maps between some different kinds of contraction function.The finite case. Studia Logica. 1986,45:187-198
16. P.Gardenfors and D.Makinson. Revision of knowledge systems using epistemie entrenchment, in:M.Vardi,ed.Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge, Morgan Kaufmann Publ. Los Altos, CA, 1988:83-95
17. P.Gardenfors, D.Makinson. Nonmonotonic inference based on expectations. Artificial Intelligence. 1994(65): 197-245
18. D.Makinson, P.Gardenfors. Relations between the logic of theory change and nonmonotonic logic. The Logic of Theory Change (A.Fuhrmann, M.Morreau.)Lecture Notes in AI.Springer Verlag. 1991:185-205
19. A.Bochman. Belief contraction as nonmonotonic inference. The Journal of Symboloc Logic.2000,65:605-626
20. S.Kraus, D.Lehmann and M.Magidor. Nonmonotonic reasoning, preferential models and cumulative logics. 1990,44:103-119
21. S.O.Hansson. A dyadic representation of belief, in: P.Gardenfors ed. Belief Revision (Cambridge University Press). 1992:89-121
22. S.O.Hansson. Kernel Contraction. Journal of Symbolic Logic. 1994,59:845-859
23. S.O.Hansson. Belief contraction without recovery. Studia Logica. 1992,50:251-260
24. S.O.Hansson. Reversing the Levi Identity. Journal of Philosophical Logic. 1993,22:637-669
25. S.O.Hansson. New operators for theory change. Theoria. 1989,55:114-132
26. A.Fuhrmann. Reflective modalities and theory change. Synthese. 1989,81:115-134
27. A.Fuhrmann.Theory contraction through base contraction. Journal of Philosophical Logic. 1991,20:175-203
28. S.O.Hansson. Hidden structures of belief.Logic,action and information. 1996:79-100
29. S.O.Hansson. Theory contraction and base contraction unified. Journal of Symbolic Logic. 1993,58:602-625
30. Zhu Zhao-hui, Li Bin, Xiao Xi-an and Chert Shi-fu. A representation theorem for recovering contraction relations satisfying WCI. Theoretical Computer Science. 2003,290(1):545-564
31. Andreas Herzig, Renata Wassermann. Belief change from AGM to realistic model, course at ESSLLI'01. 2001.8