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Document Details :
Title: Splitting and Relevance
Subtitle: Broadening the Scope of Parikh's Concepts
Author(s): VAN DE PUTTE, Frederik
Journal: Logique et Analyse
Volume: 234 Date: 2016
When our current beliefs face a certain problem – e.g. when we receive new information contradicting them –, then we should not remove beliefs that are not related to this problem. This principle is known as 'minimal mutilation' or 'conservativity'. To make it formally precise, Rohit Parikh defined a Relevance axiom for (classical) theory revision, which is based on the notion of a language splitting. I show that both concepts can and should be applied in a much broader context than mere revision of theories in the traditional sense. First, I generalize their application to belief change in general, and strengthen the axiom of relevance in order to make it fully syntax-independent. This is done by making use of the least letter-set representation of a set of formulas. Second, I show that the logic underlying both concepts need not be classical logic and establish weak sufficient conditions for both the finest splitting theorem from and the least letter-set theorem from. Both generalizations are illustrated by means of the paraconsistent logic CLuNs and compared to ideas from.