An algebraic approach to belief contraction and nonmonotonic entailment

Lee Flax*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

Abstract

The approach of Alchourrón, Gärdenfors and Makinson to belief contraction is treated algebraically. This is then used to give an algebraic treatment of nonmonotonic entailment in the context of a belief set. The algebra used is a preboolean algebra whose elements are sets of sentences and whose order relation is restricted entailment. Under plausible assumptions restricted entailment is computable; so I have proposed elsewhere [4] that restricted entailment be taken as the deductive process of an agent. It can also be shown (not here) that ordinary entailment can be retrieved from the family of entailments with finite restrictions. Nonmonotonic closure satisfies inclusion, supraclassicality and distribution, but satisfaction of idempotency and cumulativity depend on certain conditions being fulfilled. Casting the notions of belief contraction and nonmonotonic entailment in algebraic formalism facilitates the understanding and analysis of these ideas.

Original languageEnglish
Title of host publicationLogics in Artificial Intelligence - 9th European Conference, JELIA 2004
EditorsJosé Júlio Alfered, João Leite
Place of PublicationBerlin
PublisherSpringer, Springer Nature
Pages439-451
Number of pages13
Volume3229
ISBN (Print)3540232427, 9783540232421
DOIs
Publication statusPublished - 2004
Event9th European Conference on Logics in Artificial Intelligence, JELIA 2004 - Lisbon, Portugal
Duration: 27 Sep 200430 Sep 2004

Other

Other9th European Conference on Logics in Artificial Intelligence, JELIA 2004
CountryPortugal
CityLisbon
Period27/09/0430/09/04

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