Towards belief contraction without compactness

Jandson S. Ribeiro, Abhaya Nayak, Renata Wassermann

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

3 Citations (Scopus)

Abstract

In the AGM paradigm of belief change the background logic is taken to be a supra-classical logic satisfying compactness among other properties. Compactness requires that any conclusion drawn from a set of propositions X is implied by a finite subset of X.There are a number of interesting logics such as Computational Tree Logic (CTL, a temporal logic) which do not possess the compactness property, but are important from the belief change point of view. In this paper we explore AGM style belief contraction in non-compact logics as a starting point, with the expectation that the resulting account will facilitate development of corresponding accounts of belief revision. We show that, when the background logic does not satisfy compactness, as long as the language in question is closed under classical negation and disjunction, AGM style belief contraction functions (with appropriate adjustments) can be constructed. We provide such a constructive account of belief contraction that is characterised exactly by the eight AGM postulates of belief contraction. The primary difference between the classical AGM construction of belief contraction functions and the one presented here is that while the former employs remainders of the belief being removed, we use its complements.
Original languageEnglish
Title of host publicationProceedings of the Sixteenth International Conference on Principles of Knowledge Representation and Reasoning (KR 2018)
Place of PublicationCalifornia
PublisherAssociation for the Advancement of Artificial Intelligence
Pages287-296
Number of pages10
Publication statusPublished - 2018
Event16th International Conference on Principles of Knowledge Representation and Reasoning - Tempe Mission Palms Hotel and Conference Center, Tempe, United States
Duration: 30 Oct 20182 Nov 2018
Conference number: 16
http://reasoning.eas.asu.edu/kr2018/

Conference

Conference16th International Conference on Principles of Knowledge Representation and Reasoning
Abbreviated titleKR-2018
CountryUnited States
CityTempe
Period30/10/182/11/18
Internet address

Keywords

  • AGM theory
  • belief contraction
  • compactness

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