Chapter

Computing Changes in Belief

Neil Tennant

in Changes of Mind

Published in print June 2012 | ISBN: 9780199655755
Published online September 2012 | e-ISBN: 9780191742125 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199655755.003.0002
Computing Changes in Belief

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This chapter introduces the basic ideas involved in our formal modeling of belief schemes as finite dependency networks. The chapter emphasizes the epistemological motivation for using each formal constituent. Beliefs are represented by (structure-less) nodes, arranged in steps that transmit justificatory support. Axioms of Configuration govern structural features of a finite dependency network. Nodes that represent current beliefs are black, while all others are white. The inference strokes of steps are usefully colored too: a thick black inference stroke shows that the step in question is transmitting justificatory support; while a pair of thin parallel strokes with white space between them shows that the step is not doing so. (Its premises have been ‘uncoupled' from its conclusion.) Axioms of Coloration ensure a correct epistemological interpretation of an equilibrium state of a network. The coloration convention helps to make vivid the necessary and permissible Action Types when propagating changes in belief. The changes are always made locally, with the continual aim of correcting violations of the Axioms of Coloration as these arise during the process of change. The changes can be initiated either by adopting a new belief (expanding), or by surrendering an old one (contracting). With expansion, the Black Lock constraint is in place; with contraction, it is White Lock. These Locks dictate what corrections are called for in response to each kind of violation of an Axiom of Coloration. The chapter works through many small examples to impart a thorough and vivid understanding of the dynamics of belief change, using these conventions.

Keywords: dependency network; nodes; steps; Axioms of Configuration; Axioms of Coloration; action types; Black Lock; White Lock

Chapter.  13096 words. 

Subjects: Philosophy of Mathematics and Logic

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