Residual Contraction

Marco Garapa,Maurício D L Reis

doi:10.1007/s10849-019-09296-1

Marco Garapa, Maurício D L Reis

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https://doi.org/10.1007/s10849-019-09296-1

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Abstract

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Residual Contraction

Highlights

The research area that studies the dynamics of knowledge is known as belief change
Having the above observation in mind it is natural to expect that residual contractions that are based on selection functions that select only maximal residuums are partial meet contractions
We have proposed a new operator of belief base change which generalizes the partial meet contractions

Summary

Introduction

The research area that studies the dynamics of knowledge is known as belief change ( called belief revision or belief dynamics). There are in the belief change literature several constructive methods for defining operators which satisfy all or at least some of the AGM postulates for contraction Some of those models are the (transitively relational) partial meet contractions (Alchourrón et al 1985), safe contraction (Alchourrón and Makinson 1985; Rott and Hansson 2014), system of spheres-based contraction (Grove 1988) and epistemic entrenchmentbased contraction (Gärdenfors 1988; Gärdenfors and Makinson 1988). In this paper we propose and axiomatically characterize a new class of belief base contraction operators, called residual contractions, which is a more general class than that of the partial meet contractions. In the Appendix we provide proofs for all the original results presented

Formal Preliminaries

AGM Contractions

Postulates for Base Contraction

Partial Meet Contraction

Kernel Contraction

Basic AGM-Generated Base Contraction

Residual Contractions

From Residual to Partial Meet Contractions

Maps Between Classes of Base Contraction Functions

Conclusion and Discussion