A new project I'm working on aims to establish a formalism to convert between and combine (update) beliefs measured in just about any way available. Probabilistic, Boolean-based beliefs with Bayesian updating is so much the dominant approach that anything else seems like a niche belief representation. Alternatives such as fuzzy truth and Dempster-Shafer beliefs (incorporating uncertainty) have their subdomain applications for specialized information-system components, but then these components cannot work with other components representing beliefs in a different way. Furthermore, several of these alternative representations do not yet have consistent updating rules, or clear guidelines for how to apply and interpret combined probabilities. So I want to do this.

My approach to develop a meta-structure into which each type of belief may be translated. I imagine this meta-structure will be a matrix with entries corresponding to primary beliefs, confidence in those beliefs (secondary beliefs), and credence values (weights) for the aspects of the belief which can incorporate (at least) probabilities, fuzziness, and uncertainty. All updating/combining happens with these meta-structures, and what needs to be developed is the formally and conceptually proper method for operating on these matrices. The updated belief values can then be translated into any of the included belief measures…with the proper caveats for information loss and augmentation. For example, if one converts a Dempster-Shafer value into a probability, then it must also be augmented by an uncertainty level to maintain that information.

The point is to make a formalism that works in the sense of being able to translate and combine the disparate types in a way that is consistent and conceptually coherent. These two aspects feed off each other. There are many ways the math can be done, so the epistemology comes in to narrow the scope. And the epistemology does not designate a single formal approach, but the conversions and combinations have to be commutative, associative, etc. thus our understanding of these distinct belief concepts is improved through the mathematical effort.

Applications for such a capability are easy to come by: data fusion, situational awareness, information networks, and semantic webs to name the most obvious ones. I'm going to begin with just Boolean-style truth; i.e. whether (and how much) something is true, or is an X, or has property Y, etc. It may be directly extendable to categorical data in which a discreet distributions of truth values across categories is more appropriate. This includes multi-valued logics, multi-item identification, … more than a binary evaluation. Then on to continuous multi to complete the generalization.

If you, or somebody you know, is already working on such a thing, or have advice to give on dangerous territory, or you want to jump on board with this project, feel free to contact me.