On A Linear Representation For Quantitative Belief Revision

Abstract

SummaryIn this paper, we present a method to deal with the quantitative belief change based on linear algebra. Since the epistemic state of an agent is represented by a set of the subjective probability which she conceived for each possible world, we can regard this epistemic state as a point of vector space spanned by the basis of possible worlds. The knowledge which causes the belief change is treated as a matrix on this vector space. The observation of the new fact about the current world is characterized as a projection matrix. On the other hand, the knowledge about the world change is represented by a stochastic matrix. In this framework, we present a unified method of belief change both for propositional and probabilistic knowledge so that the logical or probabilistic reasoning in the process of the belief revision and update is reduced to the matrix calculation.

Imaginary Kinematics

“…Imaging was introduced by [16] as a non-trivial alternative to conditioning on inconsistent events. Roughly, it represents the "thought experiment by a minimal action" [10] that makes a formula consistent. Going back to the propositional language, if some world ω is inconsistent with formula φ, according to a knowledge base, imaging shifts beliefs towards those that are closest to φ, called φ-worlds.…”