kb/data/en.wikipedia.org/wiki/Belief_revision-6.md

title	chunk	source	category	tags	date_saved	instance
Belief revision	7/7	https://en.wikipedia.org/wiki/Belief_revision	reference	science, encyclopedia	2026-05-05T14:44:59.576343+00:00	kb-cron

== Social choice theory == Many revision proposals involve orderings over models representing the relative plausibility of the possible alternatives. The problem of merging amounts to combine a set of orderings into a single one expressing the combined plausibility of the alternatives. This is similar with what is done in social choice theory, which is the study of how the preferences of a group of agents can be combined in a rational way. Belief revision and social choice theory are similar in that they combine a set of orderings into one. They differ on how these orderings are interpreted: preferences in social choice theory; plausibility in belief revision. Another difference is that the alternatives are explicitly enumerated in social choice theory, while they are the propositional models over a given alphabet in belief revision.

== Complexity == From the point of view of computational complexity, the most studied problem about belief revision is that of query answering in the propositional case. This is the problem of establishing whether a formula follows from the result of a revision, that is,

    K
    ∗
    P
    ⊨
    Q
  

{\displaystyle K*P\models Q}

, where

    K
  

{\displaystyle K}

,

    P
  

{\displaystyle P}

, and

    Q
  

{\displaystyle Q}

are propositional formulae. More generally, query answering is the problem of telling whether a formula is entailed by the result of a belief revision, which could be update, merging, revision, iterated revision, etc. Another problem that has received some attention is that of model checking, that is, checking whether a model satisfies the result of a belief revision. A related question is whether such result can be represented in space polynomial in that of its arguments. Since a deductively closed knowledge base is infinite, complexity studies on belief revision operators working on deductively closed knowledge bases are done in the assumption that such deductively closed knowledge base are given in the form of an equivalent finite knowledge base. A distinction is made among belief revision operators and belief revision schemes. While the former are simple mathematical operators mapping a pair of formulae into another formula, the latter depend on further information such as a preference relation. For example, the Dalal revision is an operator because, once two formulae

    K
  

{\displaystyle K}

and

    P
  

{\displaystyle P}

are given, no other information is needed to compute

    K
    ∗
    P
  

{\displaystyle K*P}

. On the other hand, revision based on a preference relation is a revision scheme, because

    K
  

{\displaystyle K}

and

    P
  

{\displaystyle P}

do not allow determining the result of revision if the family of preference orderings between models is not given. The complexity for revision schemes is determined in the assumption that the extra information needed to compute revision is given in some compact form. For example, a preference relation can be represented by a sequence of formulae whose models are increasingly preferred. Explicitly storing the relation as a set of pairs of models is instead not a compact representation of preference because the space required is exponential in the number of propositional letters. The complexity of query answering and model checking in the propositional case is in the second level of the polynomial hierarchy for most belief revision operators and schemas. Most revision operators suffer from the problem of representational blow up: the result of revising two formulae is not necessarily representable in space polynomial in that of the two original formulae. In other words, revision may exponentially increase the size of the knowledge base.

== Relevance == New breakthrough results that demonstrate how relevance can be employed in belief revision have been achieved. Williams, Peppas, Foo and Chopra reported the results in the Artificial Intelligence journal. Belief revision has also been used to demonstrate the acknowledgement of intrinsic social capital in closed networks.

== Implementations == Systems specifically implementing belief revision are:

SATEN – an object-oriented web-based revision and extraction engine (Williams, Sims) ADS – SAT solver–based belief revision (Benferhat, Kaci, Le Berre, Williams) BReLS Immortal Two systems including a belief revision feature are SNePS and Cyc.

== See also ==

== Notes ==

== References ==

== External links == Belief revision at PhilPapers Logic of Belief Revision at the Indiana Philosophy Ontology Project Zalta, Edward N. (ed.). "Logic of Belief Revision". Stanford Encyclopedia of Philosophy. ISSN 1095-5054. OCLC 429049174. Defeasible Reasoning: 4.3 Belief Revision Theory at Stanford Encyclopedia of Philosophy