Conditional Reasoning with Subjective Logic

Conditional inference plays a central role in logical and Bayesian reasoning, and is used in a wide range of applications. It basically consists of expressing conditional relationship between parent and child propositions, and then to combine those conditionals with evidence about the parent propositions in order to infer conclusions about the child propositions. While conditional reasoning is a well established part of classical binary logic and probability calculus, its extension to belief theory has only recently been proposed. Subjective opinions represent a special type of general belief functions. This article focuses on conditional reasoning in subjective logic where beliefs are represented in the form of binomial or multinomial subjective opinions. Binomial conditional reasoning operators for subjective logic have been defined in previous contributions. We extend this approach to multinomial opinions, thereby making it possible to represent conditional and evidence opinions on frames of arbitrary size. This makes subjective logic a powerful tool for conditional reasoning in situations involving ignorance and partial information, and makes it possible to analyse Bayesian network models with uncertain probabilities.