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From Bayesian Inference to Logical Bayesian Inference

A New Mathematical Frame for Semantic Communication and Machine Learning

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Intelligence Science II (ICIS 2018)

Part of the book series: IFIP Advances in Information and Communication Technology ((IFIPAICT,volume 539))

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Abstract

Bayesian Inference (BI) uses the Bayes’ posterior whereas Logical Bayesian Inference (LBI) uses the truth function or membership function as the inference tool. LBI is proposed because BI is not compatible with the classical Bayes’ prediction and does not use logical probability and hence cannot express semantic meaning. In LBI, statistical probability and logical probability are strictly distinguished, used at the same time, and linked by the third kind of Bayes’ Theorem. The Shannon channel consists of a set of transition probability functions whereas the semantic channel consists of a set of truth functions. When a sample is large enough, we can directly derive the semantic channel from Shannon’s channel. Otherwise, we can use parameters to construct truth functions and use the Maximum Semantic Information (MSI) criterion to optimize the truth functions. The MSI criterion is equivalent to the Maximum Likelihood (ML) criterion, and compatible with the Regularized Least Square (RLS) criterion. By matching the two channels one with another, we can obtain the Channels’ Matching (CM) algorithm. This algorithm can improve multi-label classifications, maximum likelihood estimations (including unseen instance classifications), and mixture models. In comparison with BI, LBI (1) uses the prior P(X) of X instead of that of Y or θ and fits cases where the source P(X) changes, (2) can be used to solve the denotations of labels, and (3) is more compatible with the classical Bayes’ prediction and likelihood method. LBI also provides a confirmation measure between −1 and 1 for induction.

The original version of this chapter was revised: An error in Equation (31) has been corrected. The correction to this chapter is available at https://doi.org/10.1007/978-3-030-01313-4_51

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Change history

  • 14 December 2018

    The original version of this chapter contained a mistake. There was an error in Equation (31). The original chapter has been corrected.

Notes

  1. 1.

    For the strict convergence proof, see http://survivor99.com/lcg/CM/CM4MM.html.

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Authors and Affiliations

  1. College of Intelligence Engineering and Mathematics, Liaoning Engineering and Technology University, Fuxin, 123000, Liaoning, China

    Chenguang Lu

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  1. Chenguang Lu
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Correspondence to Chenguang Lu .

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Editors and Affiliations

  1. Chinese Academy of Sciences, Beijing, China

    Zhongzhi Shi

  2. University of Amsterdam, Amsterdam, The Netherlands

    Cyriel Pennartz

  3. Peking University, Beijing, China

    Tiejun Huang

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Lu, C. (2018). From Bayesian Inference to Logical Bayesian Inference. In: Shi, Z., Pennartz, C., Huang, T. (eds) Intelligence Science II. ICIS 2018. IFIP Advances in Information and Communication Technology, vol 539. Springer, Cham. https://doi.org/10.1007/978-3-030-01313-4_2

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  • DOI: https://doi.org/10.1007/978-3-030-01313-4_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-01312-7

  • Online ISBN: 978-3-030-01313-4

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