### Abstract

a new piece of information, called input, into a belief base. When both belief

bases and inputs are propositional formulas, a set of natural and rational properties, known as AGM postulates, have been proposed to define genuine revision operations. This paper addresses the following important issue : How to revise a partially pre-ordered information (representing initial beliefs) with a new partially pre-ordered information (representing inputs) while preserving AGM postulates? We first provide a particular representation of partial pre-orders (called units) using the concept of closed sets of units. Then we restate AGM postulates in this framework by defining counterparts of the notions of logical entailment and logical consistency. In the second part of the paper, we provide some examples of revision operations that respect our set of postulates. We also prove that our revision methods extend well-known lexicographic revision and natural revision for both cases where the input is either a single propositional formula or a total pre-order.

Original language | English |
---|---|

Title of host publication | International Conference on Scaleable Uncertainty Management (SUM'12). |

Publisher | Springer-Verlag |

Pages | 219-232 |

Number of pages | 13 |

DOIs | |

Publication status | Published - Sep 2012 |

Event | International Conference on Scalable Uncertainty Management, SUM 2012 - , Germany Duration: 19 Sep 2012 → … |

### Conference

Conference | International Conference on Scalable Uncertainty Management, SUM 2012 |
---|---|

Country | Germany |

Period | 19/09/2012 → … |

### Cite this

*International Conference on Scaleable Uncertainty Management (SUM'12).*(pp. 219-232). Springer-Verlag. https://doi.org/10.1007/978-3-642-33362-0_17

}

*International Conference on Scaleable Uncertainty Management (SUM'12). .*Springer-Verlag, pp. 219-232, International Conference on Scalable Uncertainty Management, SUM 2012, Germany, 19/09/2012. https://doi.org/10.1007/978-3-642-33362-0_17

**Revision over Partial Pre-orders: A Postulational Study.** / Ma, Jianbing; Benferhat, Salem; Liu, Weiru.

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

TY - GEN

T1 - Revision over Partial Pre-orders: A Postulational Study

AU - Ma, Jianbing

AU - Benferhat, Salem

AU - Liu, Weiru

PY - 2012/9

Y1 - 2012/9

N2 - Belief revision is the process that incorporates, in a consistent way,a new piece of information, called input, into a belief base. When both beliefbases and inputs are propositional formulas, a set of natural and rational properties, known as AGM postulates, have been proposed to define genuine revision operations. This paper addresses the following important issue : How to revise a partially pre-ordered information (representing initial beliefs) with a new partially pre-ordered information (representing inputs) while preserving AGM postulates? We first provide a particular representation of partial pre-orders (called units) using the concept of closed sets of units. Then we restate AGM postulates in this framework by defining counterparts of the notions of logical entailment and logical consistency. In the second part of the paper, we provide some examples of revision operations that respect our set of postulates. We also prove that our revision methods extend well-known lexicographic revision and natural revision for both cases where the input is either a single propositional formula or a total pre-order.

AB - Belief revision is the process that incorporates, in a consistent way,a new piece of information, called input, into a belief base. When both beliefbases and inputs are propositional formulas, a set of natural and rational properties, known as AGM postulates, have been proposed to define genuine revision operations. This paper addresses the following important issue : How to revise a partially pre-ordered information (representing initial beliefs) with a new partially pre-ordered information (representing inputs) while preserving AGM postulates? We first provide a particular representation of partial pre-orders (called units) using the concept of closed sets of units. Then we restate AGM postulates in this framework by defining counterparts of the notions of logical entailment and logical consistency. In the second part of the paper, we provide some examples of revision operations that respect our set of postulates. We also prove that our revision methods extend well-known lexicographic revision and natural revision for both cases where the input is either a single propositional formula or a total pre-order.

U2 - 10.1007/978-3-642-33362-0_17

DO - 10.1007/978-3-642-33362-0_17

M3 - Conference contribution

SP - 219

EP - 232

BT - International Conference on Scaleable Uncertainty Management (SUM'12).

PB - Springer-Verlag

ER -