A survey of multiple contractions

Fuhrmann, André; Hansson, Sven Ove

doi:10.1007/bf01066356

Cited by 98 publications

(88 citation statements)

References 12 publications

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“…As far as expansion is concerned, there is no special difficulty in defining the corresponding operation in agreement with (C) and (MC): 18 16 Package change, along with other kinds of multiple change, has been studied, in particular, by Fuhrmann and Hansson (1994); see also Hansson (1999, pp. 134-139 and 258-261).…”

Section: The Belief Base (Bb-)version Of the Agm Approachmentioning

confidence: 98%

Verisimilitude and Belief Change for Conjunctive Theories

Cevolani

Crupi²,

Festa

2011

Erkenn

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Two of the best known formal approaches are the post-Popperian theories of verisimilitude (for short: PPV) and the AGM theory of belief dynamics (for short: AGM).2 Our main purpose in this paper is the analysis of some conceptual (dis)similarities and relations between PPV and AGM. In the first two sections the emergence of the logic of scientific change in contemporary philosophy of science is shortly described and the basic features of the instrumental view of theory change are illustrated. While all the versions of PPV share the thesis according to which verisimilitude, or truth approximation, is the basic aim of science, this cognitive goal does not play any explicit role within the current versions of AGM. In spite of this, we will ask whether the methods for belief change proposed within AGM are an effective tool for truth approximation. After a brief presentation of the basic elements of PPV and AGM, it will be argued that a positive answer to the above question can be given

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Section: The Belief Base (Bb-)version Of the Agm Approachmentioning

confidence: 98%

Verisimilitude and Belief Change for Conjunctive Theories

Cevolani

Crupi²,

Festa

2011

Erkenn

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“…This has been called multiple contraction (Fuhrmann and Hansson 1994). It is most naturally expressed as contraction by a set of sentences, K ÷ {a 1 , a 2 , a 3 .…”

Section: Introductionmentioning

confidence: 99%

Multiple and iterated contraction reduced to single-step single-sentence contraction

Hansson

2009

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Multiple contraction (simultaneous contraction by several sentences) and iterated contraction are investigated in the framework of specified meet contraction (s.m.c.) that is extended for this purpose. Multiple contraction is axiomatized, and so is finitely multiple contraction (contraction by a finite set of sentences). Two ways to reduce finitely multiple contraction to contraction by single sentences are introduced. The reduced operations are axiomatically characterized and their properties are investigated. Furthermore, it is shown how iterated contraction can be reduced to single-step, single-sentence contraction. However, in this framework the outcome of iterated contraction depends unavoidably on the order in which the inputs are received. This order-dependence makes it impossible to treat two inputs on an equal footing. Therefore it is often preferable to perform changes involving several pieces of information as multiple rather than iterated change.

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“…So I contract by <p and by 1Jr. This may be understood as what Fuhrmann and Hansson (1994) call package contraction by [<p, w], in which case I still retain <p v1Jr (according to Fuhrmann and Hansson (1994), and according to my rankingtheoretic reconstruction of multiple and in particular package contraction in Spohn (2010~for details see there). The result is also represented by K3 in Fig.…”

Section: The Intersection Postulate For Agm-contractionmentioning

confidence: 99%

AGM, Ranking Theory, and the Many Ways to Cope with Examples

Spohn

2013

David Makinson on Classical Methods for Non-Classical Problems

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The paper first explains how the ranking-theoretic belief change or conditionalization rules entail all of the standard AGM belief revision and contraction axioms. Those axioms have met a lot of objections and counter-examples, which thus extend to ranking theory as well. The paper argues for a paradigmatic set of cases that the counter-examples can be well accounted for with various pragmatic strategies while maintaining the axioms. So, one point of the paper is to save AGM belief revision theory as well as ranking theory. The other point, however, is to display how complex the pragmatic interaction of belief change and utterance meaning may be; it should be systematically and not only paradigmatically explored.

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A survey of multiple contractions

Cited by 98 publications

References 12 publications

Verisimilitude and Belief Change for Conjunctive Theories

Verisimilitude and Belief Change for Conjunctive Theories

Multiple and iterated contraction reduced to single-step single-sentence contraction

AGM, Ranking Theory, and the Many Ways to Cope with Examples

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