On the logic of theory change: safe contraction
type: Item
instance of: scholarly article
title: On the logic of theory change: safe contraction
zbMATH Open document ID: 0605.03002
DOI: 10.1007/BF00370430
author: Carlos E. Alchourrón
author: David Makinson
published in: Studia Logica
publication date: 1985-01-01T00:00:00Z
review text: This paper is concerned with formal aspects of the logic of theory change, and in particular with the process of shrinking or contracting a theory to eliminate a proposition. It continues work in the area by the authors and Peter Gärdenfors. The paper defines a notion of ''safe contraction'' of a set of propositions, shows that it satisfies the Gärdenfors postulates for contraction and thus can be represented as a partial meet contraction, and studies its properties both in general and under various natural constraints. The leading idea is simple. Let A be a set of propositions, \(<\) a non- circular relation over A, and x a proposition that we wish to eliminate from A. The authors call an element a of A ''safe'' with respect to x (modulo \(<\), and given some background consequence operation Cn) iff it is not a minimal element (under \(<)\) of any minimal subset (under inclusion) B of A such that \(x\in Cn(B)\); and putting A/x to be the set of safe elements of A, they define the function of safe contraction by setting \(A\dot- x=A\cap Cn(A/x)\).
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03B05
zbMATH DE Number: 3976989
zbMATH Keywords: logic of theory change
zbMATH Keywords: shrinking
zbMATH Keywords: partial meet contraction
zbMATH Keywords: consequence operation
MaRDI profile type: Publication
cites work: Q3039305
cites work: On the logic of theory change: Partial meet contraction and revision functions
cites work: Q3758800
full work available at URL: https://doi.org/10.1007/bf00370430
OpenAlex ID: W2060533443
description: scientific article; zbMATH DE number 3976989