Revising Incompletely Specified Convex Probabilistic Belief Bases
This work addresses belief revision for agents with restricted probabilistic representations, but it is incremental as it builds on existing methods like Lewis Imaging and optimum entropy.
The paper tackles the problem of revising incomplete probabilistic belief bases when new propositional information is observed, proposing a method that uses boundary probability distributions and Lewis Imaging, with correctness proved and applications noted.
We propose a method for an agent to revise its incomplete probabilistic beliefs when a new piece of propositional information is observed. In this work, an agent's beliefs are represented by a set of probabilistic formulae -- a belief base. The method involves determining a representative set of 'boundary' probability distributions consistent with the current belief base, revising each of these probability distributions and then translating the revised information into a new belief base. We use a version of Lewis Imaging as the revision operation. The correctness of the approach is proved. The expressivity of the belief bases under consideration are rather restricted, but has some applications. We also discuss methods of belief base revision employing the notion of optimum entropy, and point out some of the benefits and difficulties in those methods. Both the boundary distribution method and the optimum entropy method are reasonable, yet yield different results.