Servizio Comunitario di Informazione in materia di Ricerca e Sviluppo - CORDIS

Reversibility of belief revision

Intelligent agent's beliefs are represented by epistemic states, which encode a set of beliefs about the real world based on aviable information. They often are represented by total pre-orders. We propose an encoding of total pre-orders based on polynomials, which enable revision rules to be reversible.

Epistemic states are semantically represented by total pre-orders on interpretations. Total pre-orders are encoded by polynomials equipped with lexivographic order, which allow to easily formalising the change of total pre-orders according to the incoming observation. Each interpretation is assigned a weight, which is a polynomial. Polynomials allow to keep track of the sequence of observations and to come back to previous pre-orders, which is not possible with other representations.

An alternative but equivalent syntactic representation of epistemic states is provided by means of weighted (or stratified) belief bases,i. e. set of weighted formulas. Each formula is assigned a weight which a polynomial. A function is defined to recover a total pre-order on interpretation from: a weighted belief base.

These encodings are successfully applied to different revision rules like Papini's revision based on history, Boutilier's natural revision, Dubois and Prade's possilistic revision. These encodings add the property of reversibility to these revision operations at the semantic level as well as at the syntactic level.

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SIS lab
Universite du Sud Toulon-Var, BP 132
83957 La Garde