Bootstrap Contraction

Studia Logica 101 (5):1013-1029 (2013)
Abstract
We can often specify how we would contract by a certain sentence by saying that this contraction would coincide with some other contraction that we know how to perform. We can for instance clarify that our contraction by p&q would coincide with our contraction by p, or by q, or by {p, q}. In a framework where the set of potential outcomes is known, some contractions are “self-evident” in the sense that there is only one serious candidate that can be the outcome of such a contraction. Contraction by a specific contractee (sentence or set of sentences to be contracted) is bootstrapped if it is specified by saying that it coincides with some such self-evident contraction. For a wide range of (multiple) contraction operators, contractions by any contractee can be bootstrapped. This means that the selection mechanism (selection function, incision function, etc.) can be replaced by a function called a bootstrapping selector that assigns to each contractee some “self-evident” contractee that yields the same outcome. With bootstrapping we can eliminate traditional extralogical components in contraction (e.g., selection functions) and replace them by bootstrapping selectors that reflect more closely the ways in which we actually reason and argue about belief contraction
Keywords Bootstrap contraction  Partial meet contraction  Kernel contraction  Perimaximal contraction  Blockage contraction  Multiple contraction  Shielded contraction  Outcome set  Repertoire contraction  Cognitive realism  Belief change  Preface paradox
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References found in this work BETA
André Fuhrmann & Sven Ove Hansson (1994). A Survey of Multiple Contractions. Journal of Logic, Language and Information 3 (1):39-75.

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