Ranked Programming

While probabilistic programming is a powerful tool, uncertainty is not always of a probabilistic kind. Some types of uncertainty are better captured using ranking theory, which is an alternative to probability theory where uncertainty is measured using degrees of surprise on the integer scale from 0 to ∞. In this paper we combine probabilistic programming methodology with ranking theory and develop a ranked programming language. We use the Scheme programming language a basis and extend it with the ability to express both normal and exceptional behaviour of a model, and perform inference on such models. Like probabilistic programming, our approach provides a simple and flexible way to represent and reason with models involving uncertainty, but using a coarser grained and computationally simpler kind of uncertainty.