Abstract Multiplication and Comultiplication of Beliefs

Multiplication and comultiplication of beliefs represent a generalisation of multiplication and comultiplication of probabilities as well as of binary logic AND and OR. Our approach follows that of subjective logic, where belief functions are expressed as opinions that are interpreted as being equivalent to beta probability distributions. We compare different types of opinion product and coproduct, and show that they represent very good approximations of the the analytical product and coproduct of beta probability distributions. We also define division and codivision of opinions, and compare our framework with other logic frameworks for combining uncertain propositions