Abstract
In this paper, we present a method to deal with the quantitative belief change based on the linear algebra. Since an epistemic state of 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 which 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 new fact about the current world is characterized as a projection matrix. On the other hand, the knowledge that some action changes the world is represented as a basis transformation 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 is reduced to the matrix calculation.
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Fusaoka, A. (2002). On a Linear Representation Theory for Quantitative Belief Change. In: McKay, B., Slaney, J. (eds) AI 2002: Advances in Artificial Intelligence. AI 2002. Lecture Notes in Computer Science(), vol 2557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36187-1_5
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DOI: https://doi.org/10.1007/3-540-36187-1_5
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