查看“︁概率逻辑”︁的源代码

{{NoteTA |G1=Math|G2=Economics}}
'''概率逻辑'''（或'''或然性逻辑'''）的目标是组合[[概率论]]的处理不确定性的能力和[[演绎逻辑]]开发结构的能力。结果是更加丰富和更有表达力的形式化，并有广阔的可能应用领域。概率逻辑的困难是增加了它们的概率论和逻辑构件的计算复杂性。

==提议==

有很多概率逻辑的提议：
* 术语“概率逻辑”首先用于[N86]，这里的句子的真值是[[概率]]。提议的语义推广导致了概率性逻辑[[蕴涵]]，在所有句子的概率都是要么 0 要么 1 的时候，它简化为平常的逻辑[[蕴涵]]。这种推广应用于可以建立句子的有限集合的一致性的很多逻辑系统。
* 在[[概率论证]][KM95,H05]理论中，概率不直接附加到逻辑句子上。转而它假定在句子中涉及到的变量 <math>V</math> 的特定子集 <math>W</math> 定义了在对应的子-[[σ-代数]]上的一个[[概率空间]]。这引出了有关 <math>V</math> 的两个不同的概率测度，分别叫做“支持度”和“可能度”。支持度可以被当作非加性(non-additive)“可证明性的概率”，它普遍化了普通逻辑的[[蕴涵]](<math>V=\{\}</math>)和经典[[后验概率]](<math>V=W</math>)的概念。在数学上，这个观点兼容于[[Dempster-Shafer理论]]。
* [[证据推理]][RLS90]理论也定义了非加性“可证明性的概率”(或“认识概率”)作为逻辑[[蕴涵]](可证明性)和[[概率]]二者的一般概念。这个想法通过考虑一个认识算子 '''K''' 扩大了标准[[命题逻辑]]，它表示一个理性代理关于世界的知识陈述。概率接着定义在结果的所有命题句子 ''p'' 的“认识全集” '''K'''''p'' 上，并争论说这是对于分析者最好的信息。从这个角度看，[[Dempster-Shafer理论]]好像是概率推理的普遍形式。
* [[主观逻辑]][J01]理论的中心概念是关于在给定逻辑句子中涉及的某些命题变量的“评判”。一个评判(opinion)是对表达各种无知程度的单一概率值的二维扩展。对于有关某个询问变量的整体评判的计算，这个理论分别提议了对各种逻辑连结词的算子。其中多数都完全兼容于 [[Dempster组合规则]]。

==可能的应用领域==

*{{link-en|Argumentation theory}}
*[[人工智能]]
*[[生物信息学]]
*{{link-en|Formal epistemology}}
*[[博弈论]]
*[[科学哲学]]
*[[心理学]]
*[[统计]]

==引用==

* [A98] E. W. Adams. ''A Primer of Probability Logic''. CSLI Publications, Stanford, 1998.
* [C37] R. Carnap. Logical Foundations of Probability. University of Chicago Press, Chicago, USA, 1937.
* [C91] R. Chuaqui.'' Truth, Possibility and Probability: New Logical Foundations of Probability and Statistical Inference''. Number 166 in Mathematics Studies. North-Holland, 1991.
* [G94] G. Gerla. Inferences in Probability Logic. Artificial Intelligence, 70(1–2):33–52, 1994.
* [H05] R. Haenni. ''Towards a Unifying Theory of Logical and Probabilistic Reasoning''. ISIPTA'05, 4th International Symposium on Imprecise Probabilities and Their Applications, pages 193–202, Pittsburgh, USA, 2005. [https://web.archive.org/web/20060618205254/http://www.iam.unibe.ch/~run/papers/haenni05d.pdf]
* [J01] A. J?sang. ''A logic for uncertain probabilities''. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9(3):279–311, 2001.
* [KM95] J. Kohlas and P.A. Monney. A Mathematical Theory of Hints. An Approach to the Dempster-Shafer Theory of Evidence. Lecture Notes in Economics and Mathematical Systems , vol. 425. Springer. 1995.
* [K70] H. E. Kyburg. Probability and Inductive Logic. Macmillan, New York, 1970.
* [K74] H. E. Kyburg. ''The Logical Foundations of Statistical Inference''. Reidel, Dordrecht, Netherlands, 1974.
* [N86] N. J. Nilsson. ''Probabilistic logic''. Artificial Intelligence, 28(1):71–87, 1986.
* [R05] J. W. Romeijn. ''Bayesian Inductive Logic''. PhD thesis, Faculty of Philosophy, University of Groningen, Netherlands, 2005. [https://web.archive.org/web/20060823042737/http://home.medewerker.uva.nl/j.w.romeijn/bestanden/omslag%20proefschrift%20e-versie.pdf]
* [RLS92] E. H. Ruspini, J. Lowrance, and T. Strat. ''Understanding evidential reasoning''. International Journal of Approximate Reasoning, 6(3):401–424, 1992.
* [W02] J. Williamson. ''Probability Logic''. In D. Gabbay, R. Johnson, H. J. Ohlbach, and J. Woods, editors, Handbook of the Logic of Argument and Inference: the Turn Toward the Practical, pages 397-424. Elsevier, Amsterdam, 2002.

==参见==

* [[贝叶斯推理]], [[贝叶斯网络]], [[贝叶斯概率]]
* [[Dempster-Shafer theory]]
* [[Imprecise probabilities]]
* [[逻辑]], [[演绎逻辑]]
* [[概率]], [[概率论]]
* [[Probabilistic argumentation]]
* [[推理]]
* [[不确定性]]
* [[Upper and lower probabilities]]

==外部链接==

* [https://web.archive.org/web/20070504103759/http://centria.di.fct.unl.pt/~greg/progicnet/index.html] ''Probabiliy and Logic'': Web Portal
* [https://web.archive.org/web/20070930031527/http://www.kent.ac.uk/secl/philosophy/jw/2006/progicnet.htm] ''Progicnet'': Probabilistic Logic And Probabilistic Networks
* [http://www.sipta.org/] {{Wayback|url=http://www.sipta.org/ |date=20020621154429 }} ''The Society for Imprecise Probability''

[[Category:概率论]]
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