A belief revision framework for revising epistemic states with partial epistemic states

Jianbing Ma, W. Liu, S. Benferhat

Research output: Contribution to journalArticle

8 Citations (Scopus)
12 Downloads (Pure)

Abstract

Belief revision performs belief change on an agent's beliefs when new evidence (either of the form of a propositional formula or of the form of a total pre-order on a set of interpretations) is received. Jeffrey's rule is commonly used for revising probabilistic epistemic states when new information is probabilistically uncertain. In this paper, we propose a general epistemic revision framework where new evidence is of the form of a partial epistemic state. Our framework extends Jeffrey's rule with uncertain inputs and covers well-known existing frameworks such as ordinal conditional function (OCF) or possibility theory. We then define a set of postulates that such revision operators shall satisfy and establish representation theorems to characterize those postulates. We show that these postulates reveal common characteristics of various existing revision strategies and are satisfied by OCF conditionalization, Jeffrey's rule of conditioning and possibility conditionalization. Furthermore, when reducing to the belief revision situation, our postulates can induce Darwiche and Pearl's postulates C1 and C2.
Original languageEnglish
Pages (from-to)20-40
JournalInternational Journal of Approximate Reasoning
Volume59
Early online date22 Jan 2015
DOIs
Publication statusPublished - Apr 2015
Externally publishedYes

Fingerprint

Belief Revision
Postulate
Partial
Order on a set
Belief Change
Possibility Theory
Preorder
Representation Theorem
Conditioning
Framework
Cover
Operator
Form

Keywords

  • Epistemic state
  • Epistemic revision
  • Belief revision
  • Probability updating
  • Iterated revision
  • Jeffrey's rule

Cite this

A belief revision framework for revising epistemic states with partial epistemic states. / Ma, Jianbing; Liu, W.; Benferhat, S.

In: International Journal of Approximate Reasoning, Vol. 59, 04.2015, p. 20-40.

Research output: Contribution to journalArticle

@article{8c54d5a0a7214c22bf375d399fb1441a,
title = "A belief revision framework for revising epistemic states with partial epistemic states",
abstract = "Belief revision performs belief change on an agent's beliefs when new evidence (either of the form of a propositional formula or of the form of a total pre-order on a set of interpretations) is received. Jeffrey's rule is commonly used for revising probabilistic epistemic states when new information is probabilistically uncertain. In this paper, we propose a general epistemic revision framework where new evidence is of the form of a partial epistemic state. Our framework extends Jeffrey's rule with uncertain inputs and covers well-known existing frameworks such as ordinal conditional function (OCF) or possibility theory. We then define a set of postulates that such revision operators shall satisfy and establish representation theorems to characterize those postulates. We show that these postulates reveal common characteristics of various existing revision strategies and are satisfied by OCF conditionalization, Jeffrey's rule of conditioning and possibility conditionalization. Furthermore, when reducing to the belief revision situation, our postulates can induce Darwiche and Pearl's postulates C1 and C2.",
keywords = "Epistemic state, Epistemic revision, Belief revision, Probability updating, Iterated revision, Jeffrey's rule",
author = "Jianbing Ma and W. Liu and S. Benferhat",
year = "2015",
month = "4",
doi = "10.1016/j.ijar.2015.01.003",
language = "English",
volume = "59",
pages = "20--40",
journal = "International Journal of Approximate Reasoning",
issn = "0888-613X",
publisher = "Elsevier",

}

TY - JOUR

T1 - A belief revision framework for revising epistemic states with partial epistemic states

AU - Ma, Jianbing

AU - Liu, W.

AU - Benferhat, S.

PY - 2015/4

Y1 - 2015/4

N2 - Belief revision performs belief change on an agent's beliefs when new evidence (either of the form of a propositional formula or of the form of a total pre-order on a set of interpretations) is received. Jeffrey's rule is commonly used for revising probabilistic epistemic states when new information is probabilistically uncertain. In this paper, we propose a general epistemic revision framework where new evidence is of the form of a partial epistemic state. Our framework extends Jeffrey's rule with uncertain inputs and covers well-known existing frameworks such as ordinal conditional function (OCF) or possibility theory. We then define a set of postulates that such revision operators shall satisfy and establish representation theorems to characterize those postulates. We show that these postulates reveal common characteristics of various existing revision strategies and are satisfied by OCF conditionalization, Jeffrey's rule of conditioning and possibility conditionalization. Furthermore, when reducing to the belief revision situation, our postulates can induce Darwiche and Pearl's postulates C1 and C2.

AB - Belief revision performs belief change on an agent's beliefs when new evidence (either of the form of a propositional formula or of the form of a total pre-order on a set of interpretations) is received. Jeffrey's rule is commonly used for revising probabilistic epistemic states when new information is probabilistically uncertain. In this paper, we propose a general epistemic revision framework where new evidence is of the form of a partial epistemic state. Our framework extends Jeffrey's rule with uncertain inputs and covers well-known existing frameworks such as ordinal conditional function (OCF) or possibility theory. We then define a set of postulates that such revision operators shall satisfy and establish representation theorems to characterize those postulates. We show that these postulates reveal common characteristics of various existing revision strategies and are satisfied by OCF conditionalization, Jeffrey's rule of conditioning and possibility conditionalization. Furthermore, when reducing to the belief revision situation, our postulates can induce Darwiche and Pearl's postulates C1 and C2.

KW - Epistemic state

KW - Epistemic revision

KW - Belief revision

KW - Probability updating

KW - Iterated revision

KW - Jeffrey's rule

U2 - 10.1016/j.ijar.2015.01.003

DO - 10.1016/j.ijar.2015.01.003

M3 - Article

VL - 59

SP - 20

EP - 40

JO - International Journal of Approximate Reasoning

JF - International Journal of Approximate Reasoning

SN - 0888-613X

ER -