Probabilistic belief contraction

Considerations on epistemic entrenchment, probability mixtures and KL divergence

Kinzang Chhogyal*, Abhaya Nayak, Abdul Sattar

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

1 Citation (Scopus)

Abstract

Probabilistic belief contraction is an operation that takes a probability distribution P representing a belief state along with an input sentence a representing some information to be removed from this belief state, and outputs a new probability distribution Pa . The contracted belief state Pa can be represented as a mixture of two states: the original belief state P, and the resultant state P¬a of revising P by ¬a. Crucial to this mixture is the mixing factor ε which determines the proportion of P and P¬a that are used in this process in a uniform manner. Ideas from information theory such as the principle of minimum cross-entropy have previously been used to motivate the choice of the probabilistic contraction operation. Central to this principle is the Kullback-Leibler (KL) divergence. In an earlier work we had shown that the KL divergence of Pa from P is fully determined by a function whose only argument is the mixing factor ε. In this paper we provide a way of interpreting ε in terms of a belief ranking mechanism such as epistemic entrenchment that is in consonance with this result. We also provide a much needed justification for why the mixing factor ε must be used in a uniform fashion by showing that the minimal divergence of Pa from P is achieved only when uniformity is respected.

Original languageEnglish
Title of host publicationAI 2015: Advances in Artificial Intelligence
Subtitle of host publication28th Australasian Joint Conference, Proceedings
EditorsBernhard Pfahringer, Jochen Renz
Place of PublicationBerlin; New York
PublisherSpringer, Springer Nature
Pages109-122
Number of pages14
ISBN (Electronic)9783319263502
ISBN (Print)9783319263496
DOIs
Publication statusPublished - Dec 2015
Event28th Australasian Joint Conference on Artificial Intelligence, AI - 2015 - Canberra, Australia
Duration: 30 Nov 20154 Dec 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9457
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other28th Australasian Joint Conference on Artificial Intelligence, AI - 2015
CountryAustralia
CityCanberra
Period30/11/154/12/15

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Chhogyal, K., Nayak, A., & Sattar, A. (2015). Probabilistic belief contraction: Considerations on epistemic entrenchment, probability mixtures and KL divergence. In B. Pfahringer, & J. Renz (Eds.), AI 2015: Advances in Artificial Intelligence: 28th Australasian Joint Conference, Proceedings (pp. 109-122). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9457). Berlin; New York: Springer, Springer Nature. https://doi.org/10.1007/978-3-319-26350-2_10